prompt list | ground_truth string |
|---|---|
[
{
"content": "For which positive integer values of $n$ does the Diophantine equation \\((3n-3)(x^2+y^2+z^2)=(9n+1)(xy+yz+zx)\\) have no nontrivial solutions?",
"role": "user"
}
] | n \geq 3 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $0.1737 |
[
{
"content": "Given that \\(\\arg(z^{1/3}) = \\frac{1}{2} \\arg(z^2 + \\bar{z}z^{1/3})\\), find the value of \\(|z|\\), where \\(z\\) is a complex number.",
"role": "user"
}
] | 1 |
[
{
"content": "Let $f(x)$ be a quadratic function such that $f(0) = 1$. Given that \\( \\int \\frac{f(x)}{x^2(x+1)^3} \\, dx \\) is a rational function, determine the value of $f'(0)$. \\( \\boxed{} \\)",
"role": "user"
}
] | 3 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 8.29 |
[
{
"content": "Given a Poisson process $N_t$ with a rate parameter $\\lambda = 2$, compute the expected value $E(N_1N_2)$. Note that the variables $N_1$ and $N_2$ are not independent.",
"role": "user"
}
] | 10 |
[
{
"content": "Evaluate the limit of the sequence \\(s_n\\) as \\(n\\) approaches infinity, where \\(s_n\\) is defined as:\n\\[s_n = \\frac{1}{\\sqrt{n}}\\left(1 + \\frac{1}{\\sqrt{2}} + \\frac{1}{\\sqrt{3}} + \\ldots + \\frac{1}{\\sqrt{n}}\\right)\\]",
"role": "user"
}
] | 2 |
[
{
"content": "Calculate the principal value of the complex expression:\n\n\\[ PV\\left(\\left(\\frac{1+\\sqrt{3}i}{2}\\right)^{-3}\\right)^{1-i} \\]",
"role": "user"
}
] | -e^{\pi} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.35s |
[
{
"content": "Find the distributional derivative of the indicator function $\\Bbb1(Y \\ge a)$. Provide your answer in terms of distributions.",
"role": "user"
}
] | \delta(Y - a) |
[
{
"content": "Evaluate the sum: $$\\sum_{i=0}^{n}(-1)^i \\binom{n}{i} \\binom{n+i}{i}$$",
"role": "user"
}
] | (-1)^n |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 8800 |
[
{
"content": "Let $G$ be a group and $H$ a subgroup. Assume that $G$ acts on $X$ and that $H$ acts transitively on $X$. Determine whether the statement $G=G_\\omega H$ for all $\\omega\\in X$, where $G_\\omega$ denotes the stabilizer of $\\omega$ in $G$, is true or false.",
"role": "user"
}
] | True |
[
{
"content": "Determine the fundamental period of the function \\( f(x) \\) that satisfies the functional equation \\( f(x-1) + f(x+1) = f(x) \\).",
"role": "user"
}
] | 6 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3.3e-4 M |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.002469 |
[
{
"content": "Let $f(x)$ be a polynomial with complex coefficients of degree $k$ and leading coefficient $a_k$. If $f(n)$ is an integer for every integer $n$, is it true that $|a_k| \\ge \\frac{1}{k!}$?",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -4686 |
[
{
"content": "In a topological space with finitely many connected components, is the interior of a closed and connected set always connected?",
"role": "user"
}
] | No |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 28.725 m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | differentiation |
[
{
"content": "Find the maximum value of the expression \\[ \\frac{1}{a^3+2b^3+6} + \\frac{1}{b^3+2c^3+6} + \\frac{1}{c^3+2a^3+6} \\] given that \\( a, b, c > 0 \\) and \\( abc = 1 \\).",
"role": "user"
}
] | \dfrac{1}{3} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3.854e+19 |
[
{
"content": "Consider a sequence of i.i.d. random variables $(X_i)_{i \\geq 1}$ with mean 0 and variance 1. It is known from Donsker's theorem that $$\\left(\\frac{1}{\\sqrt{n}}\\sum\\limits_{i=1}^{nt}{X_i}\\right)_t \\rightarrow (W_t)_t$$ where $(W_t)_t$ is a standard Brownian motion. Determine whether the fo... | True |
[
{
"content": "Consider a bounded Lipschitz domain \\(\\Omega \\subset \\mathbb{R}^N\\) and let \\(p \\in [1, \\infty)\\). Suppose \\(u \\in W_0^{1,p}(\\Omega) \\cap L^\\infty(\\Omega)\\). Is it possible to approximate \\(u\\) by a sequence of functions \\(u_k \\in C_0^\\infty(\\Omega)\\) such that \\(\\|u_k\\|_... | Yes |
[
{
"content": "When $0.\\overline{36}$ is expressed as a common fraction in lowest terms, what is the sum of the numerator and denominator?",
"role": "user"
}
] | 15 |
[
{
"content": "Find the minimum value of the functional \\( J(y) = \\int_a^b \\sqrt{1+y'(x)^2} \\, dx \\) for functions \\( y \\) that are continuously differentiable on the interval \\([a, b]\\).",
"role": "user"
}
] | b - a |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $9,364.58 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 38cm |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $4,050 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $37,595 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 262.5 kg* m/s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 167.2ms^-1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 120.7 J/K |
[
{
"content": "Consider the sequence \\(x_n\\) defined for \\(n \\geq 0\\) with \\(0 < x_0 < 1\\) and the recurrence relation:\n\\[ x_{n+1} = x_n - x_n^2 + x_n^3 - x_n^4 + x_n^5 - x_n^6. \\]\nCalculate the limit:\n\\[ \\lim_{n \\to \\infty} n x_n. \\]",
"role": "user"
}
] | 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.9e-7 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | A SCANNING ELECTRON MICROSCOPE |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 5 m/s |
[
{
"content": "What is the product of the squares of the solutions of $2x^2 + 13x + 6 = 0$?",
"role": "user"
}
] | 9 |
[
{
"content": "Consider a non-abelian group \\(G\\) of order \\(p^3\\), where \\(p\\) is a prime number. It is known that \\(G\\) has \\(p^2 + p + 1\\) subgroups of order \\(p\\). Prove or disprove the conjecture that \\(G\\) has \\(p + 1\\) subgroups of order \\(p^2\\).",
"role": "user"
}
] | p + 1 |
[
{
"content": "Given two independent random variables $X$ and $Y$ uniformly distributed over $[0, 1]$, find the probability density function (PDF) of the product $Z = XY$. Provide the expression for the PDF of $Z$.",
"role": "user"
}
] | -\ln z |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 7.725 V |
[
{
"content": "Suppose $A \\subset \\mathbb{R}$ has a positive Lebesgue measure $\\mu(A) = a > 0$. For any $b \\in (0, a)$, does there exist a subset $B \\subset A$ such that $\\mu(B) = b$?",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | (-3.4, 2.9) ms^-1 |
[
{
"content": "Consider a continuous function $f : [0,1] \\to \\mathbb{R}$ that has no zeros on the interval $[0,1]$. Does there exist a sequence of polynomials $(p_n)$ such that none of the polynomials have zeros on $[0,1]$ and the sequence uniformly converges to $f$ on $[0,1]$?",
"role": "user"
}
] | Yes |
[
{
"content": "Given the measure space $(\\mathbb{N}, P(\\mathbb{N}))$ with two measures $\\mu$ and $\\nu$, where $\\mu$ is the counting measure and $\\nu(E) = \\sum_{n \\in E}(n+1)$ for any subset $E$ of $\\mathbb{N}$, compute the Radon-Nikodym derivative $\\frac{d\\nu}{d\\mu}$ if it exists.",
"role": "user... | n + 1 |
[
{
"content": "The solutions to $4x^2 + 3 = 3x - 9$ can be written in the form $x = a \\pm b i,$ where $a$ and $b$ are real numbers. What is $a + b^2$? Express your answer as a fraction.",
"role": "user"
}
] | \dfrac{207}{64} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $16.42 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 6.02e17 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 539.21 |
[
{
"content": "Determine whether the following statement is true: For any two equivalent norms \\(\\|\\cdot\\|_a\\) and \\(\\|\\cdot\\|_b\\), does the inequality \\(\\|u\\|_a < \\|v\\|_a\\) always imply \\(\\|u\\|_b < \\|v\\|_b\\)?",
"role": "user"
}
] | False |
[
{
"content": "In the figure, lines \\(AB\\) and \\(AC\\) are tangents to circle \\(\\odot O\\) at points \\(B\\) and \\(C\\), respectively. Point \\(P\\) is a moving point on arc \\(\\overparen{BC}\\). Line \\(PD\\) is perpendicular to \\(AB\\) at point \\(D\\), and line \\(PE\\) is perpendicular to \\(AC\\) at... | \dfrac{48}{25} |
[
{
"content": "Square $ABCD$ has side length $13$, and points $E$ and $F$ are exterior to the square such that $BE=DF=5$ and $AE=CF=12$. Find $EF^{2}$.[asy]unitsize(0.2 cm); pair A, B, C, D, E, F; A = (0,13); B = (13,13); C = (13,0); D = (0,0); E = A + (12*12/13,5*12/13); F = D + (5*5/13,-5*12/13); draw(A--B-... | 578 |
[
{
"content": "Evaluate the loop integral of the vector field \\( G(x,y,z) = g(|r|)(M(x),N(y),O(z)) \\) on any simple closed curve \\( \\gamma \\) on the sphere \\( S_{R}^{2} \\), where \\( M(x) \\), \\( N(y) \\), and \\( O(z) \\) are polynomials, \\( |r| = \\sqrt{x^2 + y^2 + z^2} \\), and \\( g: \\mathbb{R}_{+}... | 0 |
[
{
"content": "The sum of an infinite geometric series is a positive number $S$, and the second term in the series is $1$. What is the smallest possible value of $S?$",
"role": "user"
}
] | 4 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 990 |
[
{
"content": "Two interior angles of a convex pentagon are right angles and the other three interior angles are congruent. In degrees, what is the measure of one of the three congruent interior angles?",
"role": "user"
}
] | 120^\circ |
[
{
"content": "Evaluate the integral \\(\\int_{-\\infty}^\\infty \\frac{\\sin x}{1+2x^2+x^4}dx\\) using contour integration.",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 6.9 yrs |
[
{
"content": "Show that \\( \\lim_{n \\to \\infty} \\int_0^1 f_1(x)f_2(x)\\cos(2\\pi nx) \\, dx = 0 \\) for functions \\( f_1 \\in L^{3/2}([0,1]) \\) and \\( f_2 \\in L^3([0,1]) \\).",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 18.58 m/s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 8.70% |
[
{
"content": "Evaluate the integral \\( \\int\\int_D \\sqrt{x^2+y^2} \\, dx \\, dy \\) over the region \\( D \\) bounded by the curves \\( x^2+y^2=x \\) and \\( x^2+y^2=2x \\) using a change of variables to polar coordinates and reversing the order of integration.",
"role": "user"
}
] | \dfrac{28}{9} |
[
{
"content": "Determine the function to which the series \\( f(x) = \\sum_{n=1}^\\infty \\frac{(-1)^n x^{2n-1}}{2n-1} \\) converges.",
"role": "user"
}
] | -\arctan(x) |
[
{
"content": "Calculate the dot product of the bivectors \\(\\gamma_{23}\\) and \\(\\gamma_{01}\\) using the metric \\(\\eta=(1, -1, -1, -1)\\) and the formula for the dot product of two k-blades.",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | AccountCurrent YearPercentagePrevious YearPercentage
Sales100%100%
Cost of goods sold68%63%
Gross Margin32%37%
Selling Expenses13%15%
Administrative Expense14%13%
Operating Income5%9%
Income Taxes2%4%
Net Income3%5% |
[
{
"content": "Find the residue of the function \\( f(z) = \\frac{1}{z^2 \\sin z} \\) at the point \\( z_0 = 0 \\).",
"role": "user"
}
] | \dfrac{1}{6} |
[
{
"content": "Determine whether any field automorphism of the $p$-adic numbers $\\mathbb{Q}_p$ is continuous.",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | normal aging |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 47.6 lb |
[
{
"content": "Calculate \\( h'(2) \\) given that \\( h(x) = g(f(x, x)) \\), where \\( g(x) = f(x, f(x, x)) \\). The function \\( f(x, y) \\) is differentiable, and the following values are provided: \\( f(2, 2) = 4 \\), \\( f_x(2, 2) = 3 \\), and \\( f_y(2, 2) = 7 \\).",
"role": "user"
}
] | 730 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.63e11 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2823.5 J/K |
[
{
"content": "Consider a continuous map $f: \\Bbb RP^n \\to S^{n-1} \\times S^1$, where $n \\geq 2$. For odd $n$, the induced map on homology $f_*: H_n(\\Bbb RP^n) \\to H_n(S^{n-1} \\times S^1)$ is $\\Bbb Z \\to \\Bbb Z$. Determine whether the degree of $f$, denoted as $f_*(1)$, can be any integer, or if there ... | 0 |
[
{
"content": "Determine if there exists a number \\(a\\) such that all derivatives of \\(x^x\\) are positive on the interval \\((a, \\infty)\\). If such a number exists, find the smallest possible value of \\(a\\).",
"role": "user"
}
] | 1 |
[
{
"content": "Find the pair of positive integers \\((a, b)\\) such that \\(3^a + 7^b\\) is a perfect square.",
"role": "user"
}
] | (2, 1) |
[
{
"content": "In a one-dimensional random walk with 10 steps, each of size 1, the process $S_n$ is defined as the sum of the first $n$ steps, where $S_n = \\sum_{i=1}^{n} X_i$ and $X_i$ can be +1 or -1. The condition $S_i \\geq 0$ must hold for all $i$ from 1 to 10. Given that $S_{10} = 4$, determine the number... | 75 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 5.7e-21 J |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | The subject was dropped, but it was clear that it would be brought up again. |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.56e+13 |
[
{
"content": "Find the limit of the function \\( f(x,y) = (x^2 + y^2)^{|x|} \\) as \\((x, y)\\) approaches \\((0, 0)\\).",
"role": "user"
}
] | 1 |
[
{
"content": "Let \\( f(x) \\) be a monotonic function defined on \\( (0, +\\infty) \\), such that for any \\( x > 0 \\), we have \\( f(x) > -\\frac{4}{x} \\) and \\( f\\left(f(x) + \\frac{4}{x}\\right) = 3 \\). Find \\( f(8) \\).",
"role": "user"
}
] | \dfrac{7}{2} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 7200 |
[
{
"content": "Determine whether every prime number, except 2 and 5, divides a number of the form $10^k - 1$ for some integer $k$.",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -12.82 cm |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 101.5 kg |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3.363e+3 M |
[
{
"content": "Find a function \\( g(\\theta) \\) such that the quantity \\( Q(\\theta, W) = g(\\theta) W \\) follows a chi-squared distribution with \\( k \\) degrees of freedom, where \\( W(X_1, \\dots, X_n) = \\sum_{i=1}^n \\ln\\left(\\frac{X_i}{8}\\right) \\) and \\( X_1, \\dots, X_n \\) are i.i.d. with prob... | 2\theta |
[
{
"content": "Consider two lines: line $l$ parameterized as\n\\begin{align*} \nx &= 1 + 4t,\\\\\ny &= 4 + 3t\n\\end{align*}and the line $m$ parameterized as\n\\begin{align*} \nx &=-5 + 4s\\\\\ny &= 6 + 3s.\n\\end{align*}Let $A$ be a point on line $l$, $B$ be a point on line $m$, and let $P$ be the foot of th... | \begin{pmatrix} -4\\-3 \end{pmatrix} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.34 m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $19,875.16 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 600 L |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.63 kg |
[
{
"content": "Given a positive integer $d$ which is square-free, and a fundamental solution $(x_{0}, y_{0})$ to the equation $x^{2} - d y^{2} = 1$, find all positive integer solutions $(x, y)$ such that all prime factors of $x$ divide $x_{0}$.",
"role": "user"
}
] | (x_0, y_0) |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 6.22% |
[
{
"content": "Calculate the line integral \\( \\int_{\\rm C}(e^{x^2}- y{x}^{2}){\\rm d}x+ \\cos({y}^{2}){\\rm d}y \\), where \\( {\\rm C} \\) is the unit circle traversed counterclockwise. Use Green's theorem to evaluate the integral.",
"role": "user"
}
] | \dfrac{\pi}{4} |
[
{
"content": "Evaluate the volume integral \\( \\iiint_K (x^2 + y^2) \\, dx \\, dy \\, dz \\) using a different coordinate system, where the region \\( K \\) is defined by the inequalities \\( 0 \\leq x^2 + y^2 \\leq z^2 \\) and \\( 0 \\leq z \\leq 1 \\).",
"role": "user"
}
] | \dfrac{\pi}{10} |
[
{
"content": "Let\n\\[x^8 - 98x^4 + 1 = p(x) q(x),\\]where $p(x)$ and $q(x)$ are monic, non-constant polynomials with integer coefficients. Find $p(1) + q(1).$",
"role": "user"
}
] | 4 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Rolaids: 0.01478 mol H+/g; Kroger: 0.01498 mol H+/g |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Manufacturing Overhead Budget
Direct Labor Hours
6,400
8,200
10,000
11,800
Variable Overhead Costs
Indirect Labor ($1.40 x DL hours)
$8,960
$11,480
$14,000
$16,520
Indirect Materials ($0.70 x DL hours)
4,480
5,740
7,000
8,260
Utilities ($0.40 x DL hours)
2,560
3,280
4,000
4,720
Total Variable Manufacturing Overhead
$16... |
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