prompt list | ground_truth string |
|---|---|
[
{
"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... | 12238 kg/m^3 |
[
{
"content": "A polynomial $f(x)$ of degree at most $n$ satisfies $f(k) = 2^k$ for $k = 0, 1, \\ldots, n$. Determine the value of $f(n+1)$. \\( \\text{(Express your answer in terms of } n \\text{ if necessary.)} \\)",
"role": "user"
}
] | 2^{n+1} - 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... | Bid: 121.95 Yen, Ask: 111.11 Yen |
[
{
"content": "Determine whether the statement is true or false: For any $2\\pi$-periodic continuous function $f(x)$, the magnitude of the $N$th partial sum of its Fourier series, $|S_N(f,0)|$, does not diverge to infinity as $N$ approaches infinity. Here, $S_N(f,x) = \\frac{1}{2\\pi}\\int_{-\\pi}^{\\pi} \\frac{... | False |
[
{
"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... | 142 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... | 723g |
[
{
"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... | Net Income: $342,300 |
[
{
"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... | Jan. 1, 2008
Building
4,500,000
Cash
4,500,000
Dec. 31, 2008
Cash
275,000
Rent revenue
275,000
Dec. 31, 2008
Depreciation expense
90,000
Accumulated depreciation-Buildings
90,000
Dec. 31, 2008
Property tax expense
85,000
Insurance expense
10,000
Cash
95,000 |
[
{
"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... | P(N2O4) = 0.117 atm, P(NO2) = 0.705 atm |
[
{
"content": "Factorize the expression \\( \\Sigma a^{2}(b^{4}-c^{4}) \\). Choose the correct factorization from the options below:\n\n(a) \\((a-b)^{2}(b-c)^{2}(c-a)^{2}\\)\n\n(b) \\((a-b)(a+b)(b-c)(b+c)(c-a)(c+a)\\)\n\n(c) \\((a+b)^{2}(b+c)^{2}(c+a)^{2}\\)\n\n(d) None of these",
"role": "user"
}
] | B |
[
{
"content": "Determine the maximum value of the function $y = x^y$ over the interval where it converges to real numbers.",
"role": "user"
}
] | e |
[
{
"content": "Consider a point \\(x\\) in the interval \\([0,1]\\). Construct a sequence \\((y_n)\\) where each term \\(y_n\\) is the supremum of the nth terms of all sequences that converge to \\(x\\) and are contained within \\([0,1]\\). Does the sequence \\((y_n)\\) converge to \\(x\\) or to 1?",
"role":... | 1 |
[
{
"content": "On December $17,$ $1903,$ at Kitty Hawk, N.C., the $1903$ Wright Flyer became the first powered, heavier-than-air machine to achieve controlled, sustained flight with a pilot aboard.\n\n\\begin{tabular}[t]{|l|c|c|c|}\n\\multicolumn{4}{c}{\\textbf{December 17, 1903 Flights}}\\\\\\hline\n&\\textbf{P... | 3.7 |
[
{
"content": "Determine whether a non-zero proper ideal of a commutative integral domain can be its own square.",
"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... | 209 mL |
[
{
"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... | 7.24e+3 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... | 5.48% |
[
{
"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... | 2.7 |
[
{
"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... | -1.16e4 N |
[
{
"content": "Suppose that $ABC_4+200_{10}=ABC_9$, where $A$, $B$, and $C$ are valid digits in base 4 and 9. What is the sum when you add all possible values of $A$, all possible values of $B$, and all possible values of $C$?",
"role": "user"
}
] | 10 |
[
{
"content": "Compute the Galois group $\\text{Gal}(\\mathbb{Q}[\\beta]/\\mathbb{Q})$, where $\\beta$ is a root of the polynomial $x^3 - 2$. Provide your answer in terms of the structure of the group.",
"role": "user"
}
] | \{e\} |
[
{
"content": "If $X$ is a random variable with a chi-squared distribution with $k$ degrees of freedom, and $Y=\\sqrt{X}$, determine the distribution of $Y$. \\( \\text{Express your answer in terms of known distributions.} \\)",
"role": "user"
}
] | \chi(k) |
[
{
"content": "Consider a function $f: \\mathbb{R}^n \\to \\mathbb{R}$ that is integrable and weakly differentiable with respect to the $n$-th variable only. Determine whether the following statement is true or false: If \\( \\int \\cdots \\int \\left| \\frac{\\partial}{\\partial x_n} f(x_1, \\ldots, x_n) \\righ... | True |
[
{
"content": "Compute the limit \\(\\lim_{n \\to \\infty} (n!)^{\\frac{1}{n}}\\) using Stirling's approximation.",
"role": "user"
}
] | \infty |
[
{
"content": "Determine whether the limit \\( \\lim_{{n \\to \\infty}} \\sum_{{k=1}}^{\\infty} \\frac{1}{(2k-1)^{2n}} \\) converges to 1.",
"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... | 0.00482 moles |
[
{
"content": "Find all pairs \\((p, q)\\) of prime numbers satisfying the equation:\n\\[ p^3 + 7q = q^9 + 5p^2 + 18p. \\]",
"role": "user"
}
] | (29, 3) |
[
{
"content": "In the diagram, $\\triangle XYZ$ is right-angled at $X,$ with $YX=60$ and $XZ=80.$ The point $W$ is on $YZ$ so that $WX$ is perpendicular to $YZ.$ Determine the length of $WZ.$ [asy]\npair X, Y, Z, W;\nY=(0,0);\nX=(36,48);\nZ=(100,0);\nW=(36,0);\ndraw(X--Y--Z--X--W);\nlabel(\"Y\", Y, SW);\nlabel(\... | 64 |
[
{
"content": "Given two natural numbers \\( K \\) and \\( L \\), where \\( K \\) has \\( L \\) divisors and \\( L \\) has \\( \\frac{K}{2} \\) divisors, find the number of divisors of the number \\( K + 2L \\).",
"role": "user"
}
] | 4 |
[
{
"content": "Does there exist a continuous real-valued function \\( g(x) \\) such that \\( g(g(x)) = x \\) for all real numbers \\( x \\)?",
"role": "user"
}
] | Yes |
[
{
"content": "Find the maximum value of the quadratic function \\( f(x) = ax^2 + bx + c \\) on the interval \\([0,1]\\), given that \\(|f(-1)| \\leq 1\\), \\(|f(0)| \\leq 1\\), and \\(|f(1)| \\leq 1\\).",
"role": "user"
}
] | \dfrac{5}{4} |
[
{
"content": "Given a measurable set $A \\subset \\mathbb{R}$ with $\\lambda(A) > 0$, is it always possible to find two measurable sets $K_1$ and $K$ such that $K_1 \\subset A$, $K \\subset \\mathbb{R}$, $K_1 \\subset K$, $K$ is compact, and $\\lambda(K_1) = \\lambda(K)$ with $\\lambda(K_1) > 0$? Justify your a... | 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... | 3.8 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... | 0.0121 L |
[
{
"content": "Evaluate the limit \\( \\lim_{k \\to \\infty} \\int_0^k x^n \\left(1 - \\frac{x}{k} \\right)^k \\mathrm{d} x \\) for a fixed integer \\( n \\geq 0 \\).",
"role": "user"
}
] | n! |
[
{
"content": "Determine whether both solutions for the maximum likelihood estimator (MLE) of \\(\\theta\\) in the beta distribution \\(B(\\theta, 2)\\) are valid, or if one should be discarded. The solutions are:\n\\[\\theta_1 = \\frac{-a_n - 2 - \\sqrt{a_n^2 + 4}}{2a_n}\\]\n\\[\\theta_2 = \\frac{-a_n - 2 + \\s... | \theta_1 |
[
{
"content": "Evaluate the limit \\(\\lim_{z \\to 0} \\left(\\frac{\\sin z}{z}\\right)^{\\frac{1}{z^2}}\\).",
"role": "user"
}
] | e^{-\frac{1}{6}} |
[
{
"content": "Simplify the trigonometric expression for $t \\in (0, 1]$:\n\\[ \\arcsin(2t-1) + 2\\arctan\\left(\\sqrt{\\frac{1-t}{t}}\\right) \\]",
"role": "user"
}
] | \dfrac{\pi}{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... | $2,959.22 |
[
{
"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... | 2.01 |
[
{
"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 ft/sec |
[
{
"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 km/s |
[
{
"content": "Find the set of cluster points for the sequence \\(\\left\\{\\frac{m}{10^n} : m \\in \\mathbb{Z}, n \\in \\mathbb{N}\\right\\}\\).",
"role": "user"
}
] | \mathbb{R} |
[
{
"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... | $19,429.83 |
[
{
"content": "Let $A$ be an $n \\times n$ complex matrix, expressed as $A = X + iY$, where $X$ and $Y$ are real $n \\times n$ matrices. Suppose that for every square submatrix $S$ of $A$, the modulus of the determinant satisfies $|\\mathrm{det}(S)| \\leq 1$. Is it true that $|\\mathrm{det}(X)| \\leq 1$?",
"... | 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... | 42 m/s |
[
{
"content": "Find the area of the closed loop in the region $x \\ge 0$ for the Lemniscate of Gerono, described by the equation $x^4 = x^2 - y^2$. Use the parametrization $x(t) = \\sin t$, $y(t) = \\sin t \\cos t$, for $0 \\le t \\le 2\\pi$, and apply Green's theorem with $P(x,y) = 0$ and $Q(x,y) = x$.",
"r... | \dfrac{2}{3} |
[
{
"content": "Determine whether there are only a finite number of connected, locally compact Hausdorff topological spaces $X$, up to homeomorphism, such that $X$ has an open set $U$ homeomorphic to $\\mathbb{R}$ and $X - U$ is also homeomorphic to $\\mathbb{R}$. Assume connectedness to exclude the single discon... | 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... | 0.434g |
[
{
"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... | 1.53 Hz |
[
{
"content": "Is 510511 the smallest Euclid number \\( E_n \\) that is divisible by the next prime \\( p_{n+1} \\)? Specifically, verify if \\( 2 \\times 3 \\times 5 \\times 7 \\times 11 \\times 13 \\times 17 + 1 = 19 \\times 97 \\times 277 \\).",
"role": "user"
}
] | 510511 |
[
{
"content": "Determine the initial conditions for the differential equation \\( y' = y(y-4)(y+4)(y-6) \\) such that \\( \\lim_{t \\rightarrow \\infty} y(t) = 4 \\).",
"role": "user"
}
] | (0, 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... | -70 cm^3/min |
[
{
"content": "Let $f$ be a positive nonvanishing function such that \\( \\frac{1}{f(t)} \\ge y-x \\) almost everywhere for \\( y \\ge x \\) with \\( x, y, \\) and \\( t \\) in \\([0,2]\\). Determine if it is true that \\( \\frac{1}{f(t)} \\ge 2 \\) almost everywhere in \\([0,2]\\).",
"role": "user"
}
] | True |
[
{
"content": "Given a strictly increasing function \\(f: \\mathbb{N} \\rightarrow \\mathbb{N}\\) that satisfies the functional equation \\(f(f(n)) = 3n\\) for all positive integers \\(n\\), find \\(f(2017)\\).",
"role": "user"
}
] | 3864 |
[
{
"content": "Determine the convergence radius of the power series \\( \\sum_{n=1}^{\\infty}\\frac{\\sin n}{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... | 9.80 m/s^2 downward |
[
{
"content": "The income of people in two cities is represented by two Pareto-type probability density functions: \\(f(x)=\\frac{2}{x^3},1<x<\\infty\\) and \\(g(y)=\\frac{3}{y^4},1<y<\\infty\\). One person is selected at random from each city. Let \\(X\\) and \\(Y\\) be their respective incomes. Compute \\(P(X<... | \dfrac{2}{5} |
[
{
"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... | 35.7 g |
[
{
"content": "Let \\( f(z) = z^{1/3} \\) be the branch of the cube root with the domain defined by \\( 0 < \\theta < 2\\pi \\), \\( z \\neq 0 \\) (i.e., the branch cut is along the ray \\( \\theta = 0 \\)). Find \\( f(-i) \\).",
"role": "user"
}
] | i |
[
{
"content": "Determine the upper bound of the magnitude of \\(|e^{\\sin(z)}|\\) over the line segment from \\(z = 0\\) to \\(z = i\\).",
"role": "user"
}
] | 1 |
[
{
"content": "Find the number of strongly monotonic increasing functions \\(f:[n]\\to \\mathcal{P}([k])\\) with respect to the subset relation, where \\(n > k+1\\). Use the pigeonhole principle to determine the value of \\(a_{n,k}\\).",
"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... | 235868.55 J |
[
{
"content": "Find the value of $b$ such that the function $g(x) = x^4 - 2x^3 + bx - 3$ is monotonically increasing in the interval $(1, \\frac{3}{2})$. \\(b\\)",
"role": "user"
}
] | 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... | 0.285 |
[
{
"content": "Find the sum of the roots of the equation \\( \\sin ^{4} x + 5(x - 2 \\pi)^{2} \\cos x + 5 x^{2} + 20 \\pi^{2} = 20 \\pi x \\) that lie within the interval \\([-\\pi, 6\\pi]\\). Round your answer to two decimal places if necessary.",
"role": "user"
}
] | 31.42 |
[
{
"content": "Determine the values of $x$ for which the series \\( \\sum_{n=1}^\\infty \\ln \\sqrt[n]{1 + \\frac{x}{n}} \\) converges.",
"role": "user"
}
] | (-1, \infty) |
[
{
"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... | 0.039 T |
[
{
"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... | 100 mL |
[
{
"content": "Let $p$ be a prime. If $G$ is a normal subgroup of $SL(2, \\mathbb{Z}/p\\mathbb{Z})$, is $G$ also normal in $GL(2, \\mathbb{Z}/p\\mathbb{Z})$? Provide a justification for your answer.",
"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... | 614.83e3 Joule |
[
{
"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... | 14H^+ (aq) + Cr_2O_7^{2-} (aq) + 6e^- -> 2Cr^{3+} (aq) + 7H_2O (l) |
[
{
"content": "Determine the value of\n\\[2002 + \\frac{1}{2} \\left( 2001 + \\frac{1}{2} \\left( 2000 + \\dots + \\frac{1}{2} \\left( 3 + \\frac{1}{2} \\cdot 2 \\right) \\right) \\dotsb \\right).\\]",
"role": "user"
}
] | 4002 |
[
{
"content": "A satellite of mass 'm' is revolving around Earth in a circular orbit of radius \\( r_0 \\) with speed \\( v_0 \\). At a certain point in its orbit, the direction of motion of the satellite is suddenly changed by an angle \\( \\theta = \\cos^{-1}\\left(\\frac{3}{5}\\right) \\), while maintaining t... | 9 |
[
{
"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... | 240420.73 |
[
{
"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... | 0.205 C |
[
{
"content": "Calculate the limit: $$\\lim_{x\\rightarrow \\infty}x \\ln x+2x\\ln \\sin \\left(\\frac{1}{\\sqrt{x}} \\right)$$",
"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... | 8e+20 |
[
{
"content": "Two differentiable functions $f(x)$ and $g(x)$ are defined on the interval $[0, 2]$. Given that $f''(x) - g''(x) = 0$, $f'(A) = 2$, $g'(A) = 4$, $f(B) = 3$, and $g(B) = 9$, find the value of $f\\left(\\frac{3}{2}\\right) - g\\left(\\frac{3}{2}\\right)$. \\( \\boxed{?} \\)",
"role": "user"
}
... | -5 |
[
{
"content": "Evaluate the improper integral \\(\\int_{0}^{\\infty} \\left(e^{-\\frac{1}{x^2}}-e^{-\\frac{4}{x^2}}\\right) dx\\).",
"role": "user"
}
] | \sqrt{\pi} |
[
{
"content": "Find the minimum value of the function $f(x, y, z) = x + 4z$ subject to the constraint $x^2 + y^2 + z^2 \\leq 2$. Use methods other than the Maximum Modulus Principle.",
"role": "user"
}
] | -\sqrt{34} |
[
{
"content": "Consider the matrix polynomial \\( P_\\Delta(\\lambda) = (A_m + \\Delta_m)\\lambda^m + \\cdots + (A_1 + \\Delta_1)\\lambda + (A_0 + \\Delta_0) \\), where \\( A_j, \\Delta_j \\in \\mathbb{C}^{n \\times n} \\) for \\( j = 0, 1, 2, \\ldots, m \\), and \\( \\lambda \\) is a complex variable. Determine... | \infty |
[
{
"content": "Evaluate the limit: $$\\lim _{x\\to \\infty }\\frac{e^{\\left(\\frac{x}{x-1}\\right)^3}}{3x^7-25x^5-\\left(111!\\right)\\cdot \\,x}.$$",
"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... | $514.53 |
[
{
"content": "Find all triplets \\((p, q, n)\\) of odd prime numbers \\(p\\) and \\(q\\), and integer \\(n > 1\\), such that:\n\\[ q^{n+2} \\equiv 3^{n+2} \\pmod{p^n} \\]\nand\n\\[ p^{n+2} \\equiv 3^{n+2} \\pmod{q^n} \\]",
"role": "user"
}
] | (3, 3, 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... | 10/1: Cash (Debit) 81,800, Common Stock (Credit) 81,800;
10/2: No journal entry;
10/4: Rent Expense (Debit) 2,500, Cash (Credit) 2,500;
10/7: Equipment (Debit) 22,300, Cash (Credit) 5,000, Accounts Payable (Credit) 17,300;
10/8: Advertising Expense (Debit) 600, Cash (Credit) 600;
10/10: Equipment Repair Expense (Debit)... |
[
{
"content": "Is the unit ball in $L_1([0,1]^2)$, when restricted to finite dimensions, compact?",
"role": "user"
}
] | Yes |
[
{
"content": "A computer component has a lifetime (in years) that follows a Gamma distribution with a mean of 6 years and a variance of 18 years squared. Calculate the probability that the component will last at least 9 years.",
"role": "user"
}
] | 4e^{-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... | 43.84 m |
[
{
"content": "Is it always possible to extract a subsequence from any sequence in a compact metric space that converges to a unique point in the space?",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the integral \\( \\int_{|z|=2}\\frac{1}{z^{100}+1}dz \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Let \\( a_2=\\frac{1}{2} \\), and for \\( n>2 \\), \\( a_n=a_{n-1}^{\\frac{1}{n}} \\). Find \\( \\lim_{n\\to\\infty}a_n \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Evaluate the contour integral \\( \\oint_C \\frac{e^z-1}{\\sin^3(z)}dz \\) where \\( C \\) is the unit circle.",
"role": "user"
}
] | \pi i |
[
{
"content": "The side lengths of a right triangle measure $x$, $x + y$ and $x - y$ units where $0 < y < x$. What is the value of $y \\div x$? Express your answer as a common fraction.",
"role": "user"
}
] | \frac{1}{4} |
[
{
"content": "Determine the maximum value of the function \\( f(x) = 2(a-x)\\left(x+\\sqrt{x^2+b^2}\\right) \\) for real numbers \\( x \\), where \\( a \\) and \\( b \\) are constants.",
"role": "user"
}
] | a^2 + b^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... | 27.12 N |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x \\to 0} \\left(x^2 \\left(1 + 2 + 3 + \\cdots + \\left\\lfloor \\frac{1}{|x|} \\right\\rfloor \\right)\\right) \\] where \\([a]\\) is the largest integer not greater than \\(a\\) and \\(|x|\\) is the absolute value of \\(x\\). Determine if the limit is undefined.",... | \dfrac{1}{2} |
[
{
"content": "Determine whether the infinite multiplication of rank-one matrices always results in a rank-one matrix. Answer with 'yes' or 'no' and justify your reasoning.",
"role": "user"
}
] | no |
[
{
"content": "Determine whether the function \\( f(\\tau, x) = \\int_{-\\infty}^{+\\infty} \\frac{dp}{\\sqrt{p^2+1}} e^{-\\sqrt{p^2+1}\\tau + ipx} \\), where \\( \\tau > 0 \\) and \\( x \\in \\mathbb{R} \\), is invariant under the group of rotations \\( SO(2) \\), i.e., whether it depends only on \\( \\tau^2 + ... | 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... | T(x) = g ( M + (l - x)/l m) |
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