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... | {
"Month": ["January", "February", "March", "April"],
"Sales": [83000, 73000, 118000, 63000],
"Cash Sales": [20750, 18250, 29500, 15750],
"Prior Month Credit Sales": [69750, 62250, 54750, 88500],
"Total Cash Receipts": [90500, 80500, 84250, 104250]
} |
[
{
"content": "Consider a real, symmetric, $n \\times n$ matrix $A$ with the following properties:\n1) All diagonal elements $a_{ii}$ are strictly positive.\n2) All off-diagonal elements $a_{ij}$ are non-positive.\n3) The sum of the elements in each row (and therefore also in each column, since $A$ is symmetric)... | No |
[
{
"content": "Calculate the limit: \\[ \\lim_{x\\to0}\\frac{e^{\\cos x}-e}{x^2} \\] without using L'Hôpital's rule.",
"role": "user"
}
] | -\dfrac{e}{2} |
[
{
"content": "Does every smooth curve have a length?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine whether a matrix with eigenvalues only 0 and 1 is necessarily a projection matrix.",
"role": "user"
}
] | No |
[
{
"content": "Determine the highest power of two that divides the expression \\(32! + 33! + 34! + \\dots + 90!\\).",
"role": "user"
}
] | 32 |
[
{
"content": "Evaluate the limit as \\( n \\) approaches infinity: \n\\[ \\lim_{n\\to+\\infty} \\frac{e^{(n+1)^2}}{(n+1)\\int_{n}^{n+1}e^{x^2}dx} \\]",
"role": "user"
}
] | 2 |
[
{
"content": "Let $f(x) = \\frac{3}{9^x + 3}.$ Find\n\\[f \\left( \\frac{1}{1001} \\right) + f \\left( \\frac{2}{1001} \\right) + f \\left( \\frac{3}{1001} \\right) + \\dots + f \\left( \\frac{1000}{1001} \\right).\\]",
"role": "user"
}
] | 500 |
[
{
"content": "Determine the Galois group of the polynomial \\( f = x^5 + x^4 + x^3 + x \\) over the field \\( \\mathbb{Z}_2 \\).",
"role": "user"
}
] | \mathbb{Z}_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... | v1 = 10.95 m/s, v2 = 7.3 m/s |
[
{
"content": "Given the equations \\((xy)^{a - 1} = z\\), \\((yz)^{b - 1} = x\\), and \\((xz)^{c - 1} = y\\), where \\(xyz \\ne -1, 0, 1\\), find the value of \\(\\frac{1}{a} + \\frac{1}{b} + \\frac{1}{c}\\).",
"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... | 1.8 kN |
[
{
"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... | $f(\lambda) = \frac{8\pi kT}{\lambda^4}$ |
[
{
"content": "Pista's friend's phone number is a six-digit number where the first digit is 7, the fifth digit is 2, and the number is odd. Additionally, the number gives the same remainder when divided by 3, 4, 7, 9, 11, and 13. What is the phone number?",
"role": "user"
}
] | 720721 |
[
{
"content": "Determine whether the function \\( u(t) \\) defined by \\( u(t) = 0 \\) for \\( t \\neq 0 \\) and \\( u(t) = \\infty \\) for \\( t = 0 \\) is integrable with respect to the Lebesgue measure.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine whether the statement is true: For all prime numbers $n$, the fraction \\( \\frac{(n-1)! + 1}{n} \\) is also a prime number.",
"role": "user"
}
] | 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... | -0.04 V |
[
{
"content": "Find the positive integer value of \\( x \\) that satisfies the equation: \\[ \\left [\\sqrt{1}\\right]+\\left [\\sqrt{2}\\right]+\\left [\\sqrt{3}\\right]+\\ldots+\\left [\\sqrt{x^2-2}\\right]+\\left [\\sqrt{x^2-1}\\right]=125, \\] where \\([a]\\) denotes the integer part of the real number \\(a\... | 6 |
[
{
"content": "Given the linear regression model with 100 observations:\n\\[ y_i = b_0 + b_1 x_i + \\epsilon_i \\]\nThe estimated coefficients are:\n\\[ \\hat{\\beta} = \\begin{pmatrix} 9 \\\\ 1 \\end{pmatrix} \\]\nAnd the variance-covariance matrix of the estimated coefficients is:\n\\[ V(\\hat{\\beta}) = \\hat... | 27195 |
[
{
"content": "Evaluate the sum: $$\\sum_{k=1}^{\\infty} \\frac{1}{(k+1)(k-1)!}\\left(1 - \\frac{2}{k}\\right)$$",
"role": "user"
}
] | 5 - 2e |
[
{
"content": "Let $a, b, c$ be positive real numbers such that $a + b + c = 1$. Determine the maximum value of the expression \\[ Q = \\frac{2}{1 + ab + bc + ca} + \\left(\\frac{abc}{(a+2)(b+2)(c+2)}\\right)^{\\frac{1}{3}}. \\]",
"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... | (4+v)/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... | 4.58 m |
[
{
"content": "If $|x| + x + y = 10$ and $x + |y| - y = 12,$ find $x + y.$",
"role": "user"
}
] | \frac{18}{5} |
[
{
"content": "Points \\( M, N, \\) and \\( K \\) are located on the lateral edges \\( A A_{1}, B B_{1}, \\) and \\( C C_{1} \\) of the triangular prism \\( A B C A_{1} B_{1} C_{1} \\) such that \\( \\frac{A M}{A A_{1}} = \\frac{5}{6}, \\frac{B N}{B B_{1}} = \\frac{6}{7}, \\) and \\( \\frac{C K}{C C_{1}} = \\fra... | 10 |
[
{
"content": "Find all pairs of positive integers \\((x, y)\\) such that \\(2^x + 3^y\\) is a perfect square.",
"role": "user"
}
] | (4, 2) |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x \\to \\infty} \\left( \\frac{7x+10}{1+7x} \\right)^{x/3} \\]",
"role": "user"
}
] | e^{\frac{3}{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... | 1.11 |
[
{
"content": "Find the limit of the sequence \\( \\left(\\frac{3n^2-n+1}{2n^2+n+1}\\right)^{\\frac{n^2}{1-n}} \\) as \\( n \\to \\infty \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Find the largest real solution to the equation \\( \\log_x(3-x) = \\log_{x^2}(8-3x-x^2) \\).",
"role": "user"
}
] | \dfrac{1}{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... | 4.3 L |
[
{
"content": "Determine the maximum number of axes of symmetry that the union of \\( k \\) line segments on a plane can have.",
"role": "user"
}
] | 2k |
[
{
"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... | 168.2 m/s^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... | /cimages/multimages/16/iutiutu6372964464063537908.png |
[
{
"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... | -1.8 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... | 4.57% |
[
{
"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... | 31.4286 m/sec and 46.4286 m/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... | -3.82 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... | 11 years |
[
{
"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... | 7.24 m/s^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... | 26.3 h |
[
{
"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... | 10.5 ft/sec |
[
{
"content": "Find the number of automorphisms of the group $\\mathbb{Z}_{60}$ that map the element 15 to the element 45.",
"role": "user"
}
] | 8 |
[
{
"content": "Let $R = k[x_1 , \\ldots , x_n]$ be a polynomial ring over a field $k$ and $M$ be a finitely generated $R$-module. Is it true that the projective dimension of $M$, denoted as $\\text{pd }M$, satisfies $\\text{pd }M \\leq n$?",
"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... | 96 inch-pounds or 8 ft-lb |
[
{
"content": "A ship $S_1$ departs from port A at 10:00, moving in a straight line with its position at time $t$ hours after 10:00 given by $r=t(10, 20)$. A speedboat $S_2$, capable of traveling at three times the speed of $S_1$, must meet $S_1$ by traveling the shortest possible distance. Determine the latest ... | \dfrac{28}{15} |
[
{
"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... | 5.34m/s |
[
{
"content": "Consider the sequence $(a_n)_{n=0}^{\\infty}$ of real numbers. If the sequence converges to a real number $L \\neq 0$, determine the convergence and the sum of the series $\\sum\\limits_{n=0}^{\\infty} (a_n - a_{n+1})$. What does the series converge to?",
"role": "user"
}
] | a_0 - 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... | 1.966 grams |
[
{
"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... | $0.74 |
[
{
"content": "Does there exist an \\(\\mathcal{O}(n^3)\\) algorithm for deciding whether there exists a permutation matrix \\(P\\), a lower unit triangular matrix \\(L\\), an upper unit triangular matrix \\(U\\), and a block-diagonal matrix \\(D\\) with \\(1\\times1\\) and \\(2\\times2\\) blocks such that for a... | Yes |
[
{
"content": "The curve given by the equation \\( y = 2^p x^2 + 5px - 2^{p^2} \\) intersects the \\( Ox \\) axis at points \\( A \\) and \\( B \\), and the \\( Oy \\) axis at point \\( C \\). Determine the sum of all values of the parameter \\( p \\) for which the center of the circle circumscribed around trian... | -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... | 8NO_3^- + 5S_2O_3^{2-} + H_2O -> 4N_2 + 10SO_4^{2-} + 2H^+ |
[
{
"content": "Determine the radius of convergence for the power series \\( \\sum_{k=0}^\\infty \\frac{\\binom{2k}{k}}{k^k}z^k \\).",
"role": "user"
}
] | \infty |
[
{
"content": "Given the function \\( f(x) \\) satisfies the conditions: \\( f(1) = \\frac{1}{4} \\), and \\( 4 f(x) f(y) = f(x+y) + f(x-y) \\) for all \\( x, y \\in \\mathbf{R} \\), determine \\( f(2019) \\). Choose the correct answer from the following options:\n\nA: \\( \\frac{1}{2} \\)\n\nB: \\(-\\frac{1}{2}... | B |
[
{
"content": "Evaluate the integral: $$\\int_{0}^{\\pi/2}{\\frac{dx}{(1+\\tan x)^6}}$$",
"role": "user"
}
] | \dfrac{11}{60} |
[
{
"content": "Find the operator norm of the operator \\(I - S - S^2\\), where \\(S\\) is the shift operator defined on \\(\\ell^2(\\mathbb{Z})\\) by \\((Sa)_n = a_{n-1}\\) for \\(a = (a_n)_{n = 1}^\\infty \\in \\ell^2(\\mathbb{Z})\\).",
"role": "user"
}
] | \sqrt{5} |
[
{
"content": "Determine whether the sequence \\( \\left(1+\\frac{(-1)^n}{n}\\right)^{n(-1)^n} \\) converges.",
"role": "user"
}
] | e |
[
{
"content": "Consider a permutation \\( \\pi \\) of the integers from 1 to 10. Define the function\n\\[ S(\\pi) = \\sum_{i=1}^{9} (\\pi(i) - \\pi(i+1))\\cdot (4 + \\pi(i) + \\pi(i+1)), \\]\nwhere \\( \\pi(i) \\) denotes the \\( i \\)th element of the permutation. Let \\( M \\) be the maximum possible value of ... | 40320 |
[
{
"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... | 1.179 bar |
[
{
"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... | 2C_3H_7OH (l) + 5O_2 -> 6CO_2(g) + 8H_2O (g) |
[
{
"content": "How many right-angled triangles with integer sides have an inradius of 2013?",
"role": "user"
}
] | 27 |
[
{
"content": "Evaluate the contour integral: $$ \\int _0^{\\infty} \\frac{\\ln x}{x^2+1} \\, dx $$",
"role": "user"
}
] | 0 |
[
{
"content": "Given \\(\\alpha, \\beta \\in (0, \\pi)\\) and \\(\\cos \\alpha + \\cos \\beta - \\cos (\\alpha + \\beta) = \\frac{3}{2}\\), find the value of \\(2\\alpha + \\beta\\).",
"role": "user"
}
] | \pi |
[
{
"content": "Find the intersection of the fields \\(\\mathbb{Q}(\\pi^2)\\) and \\(\\mathbb{Q}(\\pi^2 - \\pi)\\).",
"role": "user"
}
] | \mathbb{Q} |
[
{
"content": "Given that the dihedral angle \\( M-AB-N \\) is a right dihedral angle, and \\( P \\) is a point on the edge \\( AB \\). Lines \\( PX \\) and \\( PY \\) lie in planes \\( M \\) and \\( N \\) respectively, with \\(\\angle XPB = \\angle YPB = 45^\\circ\\). Determine the measure of \\(\\angle XPY\\).... | 60^\circ |
[
{
"content": "Find the quadratic function \\( f(x) \\) such that \\( f(\\alpha) = \\beta \\), \\( f(\\beta) = \\alpha \\), and \\( f(1) = 1 \\), where \\( \\alpha \\) and \\( \\beta \\) are the roots of the equation \\( x^2 - x + 1 = 0 \\).",
"role": "user"
}
] | x^2 - 2x + 2 |
[
{
"content": "Determine whether the following statement is true or false: Let \\( f_n(x) \\to f(x) \\) uniformly on the domain \\( D = (0,1) \\), and assume that \\( f(x) \\) is continuous and bounded. Then there exists an \\( N \\) such that for all \\( n > N \\), \\( f_n(x) \\) is a continuous function.",
... | B |
[
{
"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 supply will decrease at a rate of 17 CD players per week. |
[
{
"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... | {
"Assets": {
"Current Assets": {
"Cash and Cash Equivalents": 200,
"Accounts Receivable": 1100,
"Inventory": 600,
"Total Current Assets": 1900
},
"Non-Current Assets": {
"Property, Plant, and Equipment": 3000,
"Accumulated Depreciation": 700,
"Net Property, Plant... |
[
{
"content": "Evaluate the integral \\(\\int_{-\\infty}^{+\\infty} \\frac{b}{1+2ax+(cx)^2} \\cdot \\frac{dx}{1-2ax+(cx)^2},\\) given that \\(a^2+b^2=c^2\\).",
"role": "user"
}
] | \dfrac{\pi}{2} |
[
{
"content": "Determine the sample size $m = n$ for independent random samples $X_1, X_2, \\dots, X_m$ and $Y_1, Y_2, \\dots, Y_n$ from normal distributions with means $\\mu_1$ and $\\mu_2$ and variances $\\sigma^2_1 = 2$ and $\\sigma^2_2 = 2.5$, respectively, such that the difference between the sample means, ... | 18 |
[
{
"content": "Find the limit \\( \\lim_{x \\to 2} \\frac{\\cos \\frac{\\pi}{x}}{x-2} \\) using the substitution \\( t = \\frac{\\pi}{2} - \\frac{\\pi}{x} \\) and trigonometric identities.",
"role": "user"
}
] | \dfrac{\pi}{4} |
[
{
"content": "Evaluate the asymptotic behavior of the sum \\( \\sum_{i=0}^{n-1} \\left[i\\frac{2^i}{2^n-1}\\right] \\) as \\( n \\) becomes large. What is the result of this sum for large values of \\( n \\)?",
"role": "user"
}
] | n - 2 |
[
{
"content": "Determine the number of positive integer solutions to the equation \\(x^4 + 4y^4 + 16z^4 + 64 = 32xyz\\).",
"role": "user"
}
] | 0 |
[
{
"content": "Dr. Math's four-digit house number $ABCD$ contains no zeroes and can be split into two different two-digit primes ``$AB$'' and ``$CD$'' where the digits $A$, $B$, $C$ and $D$ are not necessarily distinct. If each of the two-digit primes is less than 40, how many such house numbers are possible?",
... | 56 |
[
{
"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... | 9.6 |
[
{
"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... | 896 m/s |
[
{
"content": "Let \\( f \\) be a continuous integrable function on \\( \\mathbb{R} \\) such that either \\( f(x) > 0 \\) or \\( f(x) + f(x + 1) > 0 \\) for all \\( x \\in \\mathbb{R} \\). Determine whether \\( \\int_{-\\infty}^\\infty f(x)\\,dx > 0 \\) is true or false.",
"role": "user"
}
] | True |
[
{
"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... | +546kJ |
[
{
"content": "Calculate the operator norm of the linear operator $B: L^2[0,1] \\to L^2[0,1]$ defined by $Bx(t) = \\sin(t)x(t)$.",
"role": "user"
}
] | \sin(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... | 1819875.5 Pa |
[
{
"content": "What is $2a+3b$, where $a=2-i$ and $b=-1+i$?",
"role": "user"
}
] | 1+i |
[
{
"content": "Find the constant term \\(c\\) in the large \\(x\\) expansion of the expression \\(\\ln \\frac{1+e^{ax}}{1+e^{-bx}}\\), where \\(a > 0\\) and \\(b > 0\\). The leading term is \\(ax\\).",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the number of functions \\( f \\) from the set \\( S = \\{ 0, 1, 2, \\ldots, 2020 \\} \\) to itself that satisfy the following conditions for all \\( a, b, c \\in S \\):\n\n1. If \\( f(a) = a \\), then \\( a = 0 \\).\n2. If \\( f(a) = f(b) \\), then \\( a = b \\).\n3. If \\( c \\equiv a ... | 1845 |
[
{
"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... | 12.71 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... | $23,913.30 |
[
{
"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... | $45.94 |
[
{
"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... | 1.64e16 |
[
{
"content": "Let $V$ be a 10-dimensional real vector space and $U_{1}, U_{2}$ be two linear subspaces such that $U_{1} \\subseteq U_{2}$, $\\dim U_{1} = 3$ and $\\dim U_{2} = 6$. Let $E$ be the set of all linear maps $T: V \\rightarrow V$ which have $U_{1}$ and $U_{2}$ as invariant subspaces (i.e., $T(U_{1}) \... | 67 |
[
{
"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... | $25,000,000 decrease in money supply |
[
{
"content": "Calculate the flow of the vector field \\( \\overrightarrow{V}=x \\overrightarrow{i}+y\\overrightarrow{j}+z\\overrightarrow{k} \\) through the lateral surface of the cylinder defined by \\( x^2+y^2=a^2 \\) and \\( 0 \\le z \\le H \\), where \\( a, H > 0 \\).",
"role": "user"
}
] | 2\pi a^2 H |
[
{
"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... | 0.01 M |
[
{
"content": "Calculate the unconditional variance of the random variable $N$, where $N|\\Lambda$ follows a binomial distribution with parameters $\\Lambda$ and $q = 0.4$, and $\\Lambda$ has a probability function defined by $p(1) = p(2) = p(3) = p(4) = 0.25$. Provide your answer as a numerical value.",
"ro... | 0.8 |
[
{
"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... | -1.15e5 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... | {
"Assets": {
"Current Assets": {
"Cash and Cash Equivalents": 57,
"Accounts Receivable": 532,
"Inventories": 859,
"Other Current Assets": 156,
"Total Current Assets": 1604
},
"Non-Current Assets":{
"Property, Plant, and Equipment": 2022,
"Intangible A... |
[
{
"content": "Suppose $A$ and $B$ are nonempty sets. If there exist sets $C$ and $D$ such that $(A\\times B)\\cup (B\\times A)=C\\times D,$ prove that $A=B=C=D.$",
"role": "user"
}
] | A = B = C = D |
[
{
"content": "Evaluate the limit \\( \\lim_{R \\to \\infty} \\int_{0}^{\\pi} e^{-R\\sin (t)} \\, dt. \\)",
"role": "user"
}
] | 0 |
[
{
"content": "Find the limit of the sequence as \\( n \\) approaches infinity:\n\\[\n\\lim_{n \\to \\infty} \\sum_{r=0}^{2n+1} \\frac{1}{n^2+r}\n\\]",
"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... | 2.62 m |
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