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... | Date General Journal Debit Credit
September 30 Wages Expense 800
FICA Tax Expense 61.20
FUTA Expense 4.80
SUTA Expense 17.40
Federal Income Tax Withheld 80
FICA Tax Payable 122.40
FUTA Tax Payable 4.80
SUTA Tax Payable 17.40
Cash 658.80 |
[
{
"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... | Transaction costs in the supply chain |
[
{
"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... | 1.13e-34 kg m/s |
[
{
"content": "Let $g:\\mathbb{R} \\to \\mathbb{R}$ be a continuous function. Determine which of the following statements implies that $g(0) = 0$:\n\n(A) $\\lim_{n \\to \\infty}\\int_{0}^{1}g(nx)^n \\, dx=0.$\n\n(B) $\\lim_{n \\to \\infty}\\int_{0}^{1}g(x)^n \\, dx=0.$\n\n(C) $\\lim_{n \\to \\infty}\\int_{0}^{1}... | C |
[
{
"content": "Does there exist a set $E \\subseteq [0,1]^2$ such that for every $(x,y) \\in [0,1]^2$, the sets $E \\cap ([0,1]\\times \\{y\\})$ and $E \\cap (\\{x\\} \\times [0,1])$ have measure zero in $\\mathbb{R}$, but $E$ is not measurable in $\\mathbb{R}^2$?",
"role": "user"
}
] | Yes |
[
{
"content": "Calculate the limit: \\( \\lim_{n \\to \\infty} \\left( 1 + \\frac{2}{n} \\right)^{n^2} e^{-2n} \\).",
"role": "user"
}
] | e^{-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... | 0.6108 |
[
{
"content": "Given the recurrence relation \\(a_n = 2a_{n-1} - a_{n-2} - 2\\) for \\(1 < n < 50\\), with initial conditions \\(a_0 = 0\\) and \\(a_{50} = a_{49} + 1\\), find the value of \\(a_{17}\\).",
"role": "user"
}
] | 1411 |
[
{
"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... | 5.71% |
[
{
"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... | $783 |
[
{
"content": "If $f$ is holomorphic on a domain $D$ and $f$ is bounded on $D$, does this imply that $f'$ is also bounded on $D$? Justify your answer.",
"role": "user"
}
] | No |
[
{
"content": "Given the integral equation \\( f(x) = x + \\int_0^1 t(x+t)f(t) \\, dt \\), find the value of \\( \\eta = \\int_0^1 f(x) \\, dx \\).",
"role": "user"
}
] | \dfrac{42}{23} |
[
{
"content": "Determine the rank of the following set of vectors in the vector space $\\Bbb Z_{2}^n$: $(1,1,0,\\dots,0)$, $(0,1,1,0,\\dots,0)$, $\\dots$, $(0,\\dots,0,1,1)$, $(1,0,\\dots,1)$. Provide your answer as a single integer.",
"role": "user"
}
] | n-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... | 2/5Ma^2 |
[
{
"content": "Find the variance of the stochastic process \\(X_{t} = \\int_{0}^{t} W^{+}_{s}dW_{s}\\), where \\(W_{t}\\) is a Wiener process and \\(a^{+} = \\max(a, 0)\\).",
"role": "user"
}
] | \dfrac{t^2}{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... | 8014.52 m^2 |
[
{
"content": "Given a graph with N vertices (3 ≤ N ≤ 1000) and M edges, determine the minimum number of additional vertices that need to be added to ensure that every vertex is either included in the new set of vertices or is adjacent to a vertex in the new set.",
"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... | 4.2e-2 T in positive z direction |
[
{
"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... | 30 m |
[
{
"content": "Determine whether the function \\( f(x) = \\begin{cases} x^2 \\cos\\left(\\frac{1}{x}\\right), & x \\neq 0 \\\\ 0, & x = 0 \\end{cases} \\) is differentiable at \\( x = 0 \\). Justify your answer.",
"role": "user"
}
] | 0 |
[
{
"content": "Consider a sequence of independent random variables $Y_n$ defined as follows: $Y_n$ takes the value $2^n$ with probability $\\frac{1}{2^{2n}}$, $-2^n$ with probability $\\frac{1}{2^{2n}}$, and $0$ otherwise. Determine whether the sequence $\\frac{1}{n}\\sum_{i=1}^n Y_i$ converges almost surely.",
... | 0 |
[
{
"content": "Is it possible to find a sequence of Littlewood polynomials \\( f_n \\in L_n \\) such that \\( M(f_n, 1) \\leq C \\sqrt{n+1} \\) for all \\( n \\geq 1 \\), where \\( C > 0 \\) is a constant depending on the sequence?",
"role": "user"
}
] | Yes |
[
{
"content": "Find all integer solutions of the equation \\( x \\ln 27 \\log_{13} e = 27 \\log_{13} y \\). Determine the sum \\( x + y \\) for the solution \\((x, y)\\) where \\( y \\) is the smallest integer greater than 70.",
"role": "user"
}
] | 117 |
[
{
"content": "Given the sequence of real numbers \\(a_{1}, a_{2}, a_{3}, \\ldots, a_{100}\\) that satisfies the inequalities \\(a_{n} - 2022 a_{n+1} + 2021 a_{n+2} \\geq 0\\) for \\(n = 1, 2, 3, \\ldots, 98\\), and \\(a_{99} - 2022 a_{100} + 2021 a_{1} \\geq 0\\), \\(a_{100} - 2022 a_{1} + 2021 a_{2} \\geq 0\\)... | 10 |
[
{
"content": "Determine the conditions on the symmetric matrix $A \\in \\mathbb{R}^{n \\times n}$ such that the set $Z = \\{x \\in \\mathbb{R}^n \\mid x'Ax = 0\\}$ has Lebesgue measure zero.",
"role": "user"
}
] | A \neq 0 |
[
{
"content": "Evaluate the limit: \\[ \\gamma = \\lim_{n \\rightarrow \\infty} \\int_0^1 \\left(\\frac{1 - x^n}{1 - x} - \\frac{n - 1}{(n - 1) x + 1}\\right) dx \\]",
"role": "user"
}
] | \gamma |
[
{
"content": "Given four different positive integers $A, B, C, D$ such that \\( \\frac{1}{A} + \\frac{1}{B} + \\frac{1}{C} + \\frac{1}{D} = 1.1 \\), find the smallest possible value of $A + B + C + D$. What is this smallest value?",
"role": "user"
}
] | 21 |
[
{
"content": "Compute the remainder when\n${2007 \\choose 0} + {2007 \\choose 3} + \\cdots + {2007 \\choose 2007}$\nis divided by 1000.",
"role": "user"
}
] | 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... | 99300 |
[
{
"content": "Find the exact area of the surface obtained by rotating the curve \\( y = \\sqrt{9x-18} \\) about the x-axis for \\( 2 \\le x \\le 6 \\). Use the formula for the surface area of revolution: \n\\[ \\int 2\\pi y \\sqrt{1+\\left(\\frac{dy}{dx}\\right)^2} \\, dx \\]",
"role": "user"
}
] | 49\pi |
[
{
"content": "Determine the conditions on the parameters \\(a\\) and \\(b\\) for which the integral \\(\\int_0^{\\infty} e^{(a+bi)x} \\, dx\\) converges.",
"role": "user"
}
] | a < 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... | 4.77 N/C in the positive x-direction |
[
{
"content": "Given the function \\( y = e^x - 2e^{-x} \\), find the value of \\( (f^{-1})'(1) \\).",
"role": "user"
}
] | \dfrac{1}{3} |
[
{
"content": "Determine the number of ways to distribute $m$ distinct objects into $n$ distinct boxes such that each box can hold at most $k$ objects, given that $kn < m$.",
"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... | 3.42e8 m |
[
{
"content": "Find the upper asymptotic bound for the recursion:\n\\[ T(k) = 2T(k-1) + \\frac{1}{k} \\]",
"role": "user"
}
] | O(2^k) |
[
{
"content": "Verify the claim that for every power \\(x \\in \\mathbb{Z}_+\\), each \\(n^{th}\\) column \\((r_n)\\) in the factorial base representation of \\(a^x\\) has a repeating pattern with length \\((n+1)!\\).",
"role": "user"
}
] | (n+1)! |
[
{
"content": "Estimate the number of floating-point operations (flops) required to solve the linear system \\(Ax = b\\) to ten-digit accuracy using the Conjugate Gradient method, where \\(A\\) is a dense symmetric positive definite \\(1000 \\times 1000\\) matrix with a condition number \\(\\kappa(A) = 100\\).",... | 240000000 |
[
{
"content": "Does there exist a sequence of real numbers \\((a_n)_{n\\in\\mathbb{N}}\\) such that for any real number \\(L\\), there is a subsequence \\(a_{k_n}\\) with \\(\\lim_{n\\to\\infty} a_{k_n} = L\\)?",
"role": "user"
}
] | Yes |
[
{
"content": "Consider two independent simple random walks on the integers, \\(X_n\\) and \\(Y_n\\), starting at positions \\(-1\\) and \\(1\\) respectively. At each time step \\(n\\), each walk moves left or right with equal probability. Determine the expected time at which the two walks collide.",
"role":... | \infty |
[
{
"content": "Let $G$ be a noncyclic p-group of order $p^n$ with $n \\ge 2$. Determine whether there exists a surjective group homomorphism from $G$ to $\\mathbb{Z}_p \\times \\mathbb{Z}_p$. 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... | f = d_i*d_o/(d_o+d_i) |
[
{
"content": "Find the function \\( f(x) \\) such that \\( f(f(x)) = 6x - f(x) \\), given that \\( f: [0,\\infty) \\rightarrow [0,\\infty) \\) and \\( f(x) > 0 \\) for all \\( x \\in (0,\\infty) \\).",
"role": "user"
}
] | 2x |
[
{
"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) Separate tax return for filing the income.
2) Karen's parent can choose to pay tax on the interest income on their tax rate.
3) The tax can be paid by her parents at their own tax rate. |
[
{
"content": "Compute \\( \\mathbb{E}\\left[\\left(X_1 + 2X_2 + 3X_3\\right)^2\\right] \\), where \\( X_t \\) is a Wiener process.",
"role": "user"
}
] | 70 |
[
{
"content": "Evaluate the series \\( \\sum_{x=1}^{\\infty} \\frac{2^{-x}}{x} \\). Use the fact that \\( \\sum_{x=1}^{\\infty} 2^{-x} = 1 \\) to assist in your evaluation.",
"role": "user"
}
] | \ln 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... | 7.43*10^-6 s |
[
{
"content": "Given the group $G$ generated by the permutations $\\sigma$ and $\\tau$, where:\n\\[\\sigma = ( 1, 2, 3, 4, 5 ) ( 6, 10 ) ( 7, 11 ) ( 8, 12 ) ( 9, 13 )\\]\n\\[\\tau = ( 2, 5 ) ( 3, 4 ) ( 6, 7, 8, 9, 10, 11, 12, 13 )\\]\nThe orders of these permutations are 10 and 8, respectively. The subgroup $H =... | 40 |
[
{
"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... | $520,000 |
[
{
"content": "Determine whether there exist arbitrarily long sequences of consecutive positive integers such that the digital sum of each integer in the sequence is a composite number.",
"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... | 1.753 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... | 3.27 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... | -24.45 N/C |
[
{
"content": "Let $A$ be any non-empty set, and let $\\mathrm{B}(A)$ denote the set of all bounded real or complex-valued functions with set $A$ as their domain. Define a metric $d$ on $\\mathrm{B}(A)$ by \\[d(x,y) = \\sup \\{ |x(t) - y(t)| : t \\in A \\} \\text{ for all } x, y \\in \\mathrm{B}(A).\\] Is the me... | Yes |
[
{
"content": "Compute the integer $k > 2$ for which\n\\[\\log_{10} (k - 2)! + \\log_{10} (k - 1)! + 2 = 2 \\log_{10} k!.\\]",
"role": "user"
}
] | 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... | 0 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... | 9.7e-7 M |
[
{
"content": "In a convex optimization problem given by:\n\\[ \\min f_0(x) \\]\nsubject to \\( f_i(x) \\le 0, \\) for \\( i = 1, \\ldots, m, \\) and \\( Ax = b, \\)\nwhich satisfies Slater's constraint qualification, suppose \\( x^* \\) is an optimal solution with \\( f_1(x^*) = -0.2. \\) Is it true that for ev... | Yes |
[
{
"content": "Let $A_1, A_2, \\dots, A_{11}$ be the vertices of a regular 11-gon inscribed in a circle of radius 2. A point $P$ is located such that its distance from the center of the circle is 3. Calculate the sum $PA_1^2 + PA_2^2 + \\dots + PA_{11}^2$. What is this sum?",
"role": "user"
}
] | 143 |
[
{
"content": "Points $A$, $B$, $Q$, $D$, and $C$ lie on the circle shown and the measures of arcs $BQ$ and $QD$ are $42^\\circ$ and $38^\\circ$, respectively. Find the sum of the measures of angles $P$ and $Q$, in degrees.\n\n[asy]\nimport graph;\n\nunitsize(2 cm);\n\npair A, B, C, D, P, Q;\n\nA = dir(160);\nB... | 40^\circ |
[
{
"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... | -578.863 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... | 4.8e+3 |
[
{
"content": "The measure of one of the smaller base angles of an isosceles trapezoid is $60^\\circ$. The shorter base is 5 inches long and the altitude is $2 \\sqrt{3}$ inches long. What is the number of inches in the perimeter of the trapezoid? [asy]\nimport markers;\nimport olympiad; size(150); import geomet... | 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... | 1540.56 kW |
[
{
"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... | 5.3e3 N |
[
{
"content": "Ilya Muromets encounters the three-headed Dragon, Gorynych. Each minute, Ilya chops off one head of the dragon. Let $x$ be the dragon's resilience ($x > 0$). The probability $p_{s}$ that $s$ new heads will grow in place of a chopped-off one ($s=0,1,2$) is given by $\\frac{x^{s}}{1+x+x^{2}}$. Durin... | 1.36 |
[
{
"content": "Determine the number of isomorphism classes of countably infinite models of the empty theory over one binary relation, also known as the number of distinct unlabeled countable graphs.",
"role": "user"
}
] | 2^{\aleph_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... | 0.585L |
[
{
"content": "Evaluate the limit \\( \\lim_{x\\rightarrow \\infty}\\frac{\\ln(1+\\alpha x)}{\\ln(\\ln(1+\\text{e}^{\\beta x}))} \\) where \\(\\alpha, \\beta \\in \\mathbb{R}^+\\).",
"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... | 11.1 m/s |
[
{
"content": "Find the number of 4-tuples \\((a, b, c, d)\\) where each element is an integer between 1 and 10, inclusive, such that the sum \\(a + b + c + d = 21\\).",
"role": "user"
}
] | 660 |
[
{
"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... | [NO_2] = 2.4e-3 M, [N_2O_4] = 9.9e-2 M |
[
{
"content": "Evaluate the integral \\( \\int_0^1\\int_0^1\\ln(|x-y|)\\;\\mathrm{d}x\\;\\mathrm{d}y \\), considering the singularity at \\( x=y \\).",
"role": "user"
}
] | -\dfrac{3}{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... | 603 nm |
[
{
"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... | 72.05 g/mol |
[
{
"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... | 4.7 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... | $410,022 |
[
{
"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... | Under equity method reporting, the carrying value of the investment is reduced when dividends are received from the investee, when the differential is amortized, when there's goodwill impairment, or when the carrying value exceeds the market value of the investment. |
[
{
"content": "In a magic square, the sum of the three entries in any row, column, or diagonal is the same value. The figure below shows four of the entries of a magic square. Find $x$.\n[asy]\nsize(2cm);\nfor (int i=0; i<=3; ++i) draw((i,0)--(i,3)^^(0,i)--(3,i));\nlabel(\"$x$\",(0.5,2.5));label(\"$19$\",(1.5,2.... | 200 |
[
{
"content": "Let $f$ and $g$ be polynomials in $\\mathbb{Q}[x]$ such that $f = gh$ for some polynomial $h$ in $\\mathbb{R}[x]$. Is $h$ necessarily in $\\mathbb{Q}[x]$? 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... | 5000000N |
[
{
"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... | 0.96 V |
[
{
"content": "Simplify the following summation:\n\n$$ \\sum_{n=3}^{\\infty} \\frac{1}{2^n} \\sum_{i=3}^{n} \\left\\lceil\\frac{i-2}{2}\\right\\rceil $$",
"role": "user"
}
] | \dfrac{2}{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... | 9.067% |
[
{
"content": "Determine whether a computer with unlimited resources can decide if a number is prime in a finite amount of time.",
"role": "user"
}
] | Yes |
[
{
"content": "Is it possible to find a 1-dimensional nonsingular foliation on an orientable surface with one boundary component such that lines of the foliation are transverse to the boundary? Answer yes or no.",
"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... | 5.16 |
[
{
"content": "Evaluate the surface integral \\( \\int_S \\mathbf{F} \\cdot d \\mathbf{S} \\) where \\( \\mathbf{F}(x, y, z) = (x, y, z) \\) and the surface \\( S \\) is parameterized by \\( g(u,v) = \\begin{pmatrix} u-v \\\\ u + v \\\\ uv \\end{pmatrix} \\) for \\( 0 \\le u \\le 1 \\) and \\( 0 \\le v \\le 2 \\... | -2 |
[
{
"content": "Let $f \\in C^{\\infty}(\\mathbb{R};\\mathbb{R})$ be a bounded and strictly monotonically increasing function, whose $n^{th}$-derivative does not vanish except possibly at a finite number of points. For every $n \\in \\mathbb{N}$, is the set of derivatives $\\{f^n\\}_{n \\in \\mathbb{N}}$ linearly... | 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... | 3.2 years |
[
{
"content": "Let $k$ be an integer with $k > 1$. Define a sequence $\\{a_n\\}$ by $a_0 = 0$, $a_1 = 1$, and $a_{n+1} = ka_n + a_{n-1}$ for $n = 1, 2, \\ldots$. Determine all integer values of $k$ for which there exist non-negative integers $l \\neq m$ and positive integers $p, q$ such that $a_l + ka_p = a_m + ... | 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... | 24.2 m/s |
[
{
"content": "Express the operation \\( C_{ij} = B_{ik} B_{jl} A_{kl} \\) in terms of standard matrix multiplication using Einstein's notation.",
"role": "user"
}
] | C = B A B^\top |
[
{
"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... | 5.06% |
[
{
"content": "Given that $a, b, c$ are the side lengths of a triangle with an area of 1, find the minimum value of the product $ab$.",
"role": "user"
}
] | 2 |
[
{
"content": "Determine the Galois group of the polynomial \\( f(x) = x^3 - 3x - 5 \\) over \\( \\mathbb{Q} \\).",
"role": "user"
}
] | S_3 |
[
{
"content": "Find the determinant of the following NxN matrix:\n\\[ \\begin{pmatrix} 3 & 2 & \\cdots & 2 \\\\ 2 & 3 & \\cdots & 2 \\\\ 2 & 2 & 3 & \\cdots \\\\ 2 & 2 & \\cdots & 3 \\end{pmatrix} \\]",
"role": "user"
}
] | 2N + 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... | 8286.96 rpm |
[
{
"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... | $5,127.43 |
[
{
"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... | 11.05 m/s |
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