prompt list | ground_truth string |
|---|---|
[
{
"content": "Determine whether the statement is true or false: A group of order 12 always has a normal 2-Sylow subgroup.",
"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... | 7.5 mm |
[
{
"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... | 25.6% |
[
{
"content": "The truncated right circular cone has a large base radius 8 cm and a small base radius of 4 cm. The height of the truncated cone is 6 cm. How many $\\text{cm}^3$ are in the volume of this solid? [asy]\n\nimport olympiad; size(150); defaultpen(linewidth(0.8)); dotfactor=4;\n\ndraw(ellipse((0,0),4,... | 224\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... | Land = $3,330,000
Building = $21,645,000
Equipment = $8,325,000 |
[
{
"content": "Find the arc length of the cycloid described by the parametric equations \\( \\gamma(t)=(\\cos(\\frac{3}{2}\\pi-t)+t,\\sin(\\frac{3}{2}\\pi-t)+1) \\) for \\( t \\in [0, 2\\pi] \\).",
"role": "user"
}
] | 8 |
[
{
"content": "Let $T$ be a continuous linear operator. Suppose $(u_n)$ is a sequence that converges weakly to $u$, denoted as $(u_n) \\rightharpoonup u$. Additionally, assume $T(u_n) \\rightharpoonup T(u)$ and there exists a subsequence $(u_{n_k})$ such that $T(u_{n_k}) \\rightarrow T(u)$. Does it follow that $... | No |
[
{
"content": "Find the remainder when \\(5,000,000^{500,000,000,000}\\) is divided by the prime number \\(10^6 + 3\\).",
"role": "user"
}
] | 225 |
[
{
"content": "Find the minimum value of the function \\( f(x, y, z) = x^2 + 4xy + 4y^2 + 2z^2 \\), given that \\( xyz = 32 \\) and \\( x, y, z > 0 \\).",
"role": "user"
}
] | 96 |
[
{
"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... | 1.38e-20 |
[
{
"content": "In triangle $ABC,$ $\\sin A = \\frac{3}{5}$ and $\\sin B = \\frac{24}{25}.$ Enter all the possible values of $\\sin C,$ separated by commas.",
"role": "user"
}
] | \frac{3}{5}, \frac{117}{125} |
[
{
"content": "Find the limit of the sequence \\( a_n = \\frac{2n^{2n}}{(2n)!} \\) as \\( n \\to \\infty \\).",
"role": "user"
}
] | \infty |
[
{
"content": "Determine whether there are any maximal ideals in the ring \\( \\mathbb{R}[x,y]/(xy-2) \\). If so, find one maximal ideal.",
"role": "user"
}
] | (x - 2, y - 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... | 7.41e-21 J |
[
{
"content": "Compute \\( \\lim\\limits_{n\\to \\infty} \\left(n^3 \\int_{n} ^{2n}\\frac{x \\, dx} {1+x^5}\\right) \\).",
"role": "user"
}
] | \dfrac{7}{24} |
[
{
"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... | 290.83 g |
[
{
"content": "Determine the sum of the series: \\[ \\sum_{n=1}^\\infty \\frac{(-1)^{n-1}}{n} \\]",
"role": "user"
}
] | \ln 2 |
[
{
"content": "Find the residue of the function \\( f(z) = \\frac{1}{1+e^z} \\). Use a method different from the standard expansion method to determine the residue.",
"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... | 872.73 km |
[
{
"content": "Evaluate the limit \\( \\lim_{n\\to\\infty}\\int_{1}^{e}(\\ln x)^n \\ dx \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the limit \\( \\lim_{\\epsilon \\to 0} \\frac{1}{\\epsilon}\\int_0^\\infty f(x) e^{-x/\\epsilon} \\, dx \\) where \\( f \\in L^1([0,\\infty)) \\cap C([0,\\infty)) \\).",
"role": "user"
}
] | f(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... | Sales Returns and Allowances 10,000
Accounts Receivable 10,000
Inventory 7,000
Cost of Goods Sold 7,000 |
[
{
"content": "Evaluate the inward flux of the vector field \\( F = \\langle y, -x, z \\rangle \\) over the surface \\( S \\) of the solid bounded by \\( z = \\sqrt{x^2+y^2} \\) and \\( z = 3 \\).",
"role": "user"
}
] | -9\pi |
[
{
"content": "Calculate the surface integral \\( \\iint_S (x^2 + y^2 + z^2) \\, dS \\) over the upper hemisphere of the sphere defined by \\( x^2 + y^2 + (z-1)^2 = 1 \\).",
"role": "user"
}
] | 6\pi |
[
{
"content": "Evaluate the integral \\( \\int_0^\\infty \\frac{ \\ln^2(1+x)}{x^{3/2}} \\, dx \\) and verify that it equals \\( 8\\pi \\ln 2 \\).",
"role": "user"
}
] | 8\pi \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... | $71,418.64 |
[
{
"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... | 5.91 |
[
{
"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... | 17.868 m/sec |
[
{
"content": "Determine the number of units in the ring \\( R = \\mathbb{Z}_8 \\times \\mathbb{Z}_9 \\times \\mathbb{Z}_5 \\). Provide a proof for your answer.",
"role": "user"
}
] | 96 |
[
{
"content": "Determine whether an infinite-dimensional separable Hilbert space over the complex numbers \\(\\Bbb C\\) can be considered a Lie group, given that it is a Banach space.",
"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... | 0.83x10^-9 T in the +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... | Materials: 6,700
Conversion: 5,600 |
[
{
"content": "Calculate the integral \\( \\int_{-a}^{a} \\left[ \\frac{f(x)}{1+e^x} + f'(x)\\log(1+e^x) \\right]dx \\), where \\( f(x) \\) is a continuously differentiable even function on \\([-a, a]\\).",
"role": "user"
}
] | a f(a) |
[
{
"content": "Let \\( f \\) be a nonnegative, continuous, and strictly increasing function on \\([0,1]\\). For \\( p > 0 \\), let \\( x_p \\) be the number in \\((0,1)\\) that satisfies \\( f^p(x_p) = \\int_0^1 f^p(x) \\, dx \\). Determine \\( \\lim_{p \\to \\infty} x_p \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Evaluate the integral \\( \\int_{-\\infty}^{\\infty}\\frac{x^4\\sin(tx)}{\\prod_{k=1}^{n}(x^2+a_k^2)}dx \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Let \\(T: \\mathbb{R}^4 \\to \\mathbb{R}^4\\) be a linear map with a null space defined by the condition \\((x, y, w, z) \\in \\mathbb{R}^4\\) such that \\(x + y + w + z = 0\\). If the rank of \\((T - 4I_4)\\) is 3, and the minimal polynomial of \\(T\\) is \\(x(x - 4)^{\\alpha}\\), find the value ... | 1 |
[
{
"content": "Given an arithmetic sequence \\(\\{a_n\\}\\), where the sum of the first \\(m\\) terms is \\(S_m = \\frac{m}{n}\\) and the sum of the first \\(n\\) terms is \\(S_n = \\frac{n}{m}\\) with \\(n \\neq m\\), determine whether \\(S_{m+n}\\) is greater than 4.",
"role": "user"
}
] | S_{m+n} > 4 |
[
{
"content": "Let $r_1, r_2, r_3, \\ldots, r_n$ be the distinct real roots of the equation \\(x^8 - 14x^4 - 8x^3 - x^2 + 1 = 0\\). Find the value of \\(r_1^2 + r_2^2 + r_3^2 + \\cdots + r_n^2\\). Choose the correct answer from the following options:\n\n\\((A)\\,3\\quad(B)\\,14\\quad(C)\\,8\\quad(D)\\,16\\)",
... | C |
[
{
"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 magnitude of the net electrostatic force acting on the charge at the center is 11.07 N and the direction is 43.8 degrees from east to north direction. |
[
{
"content": "Evaluate the integral \\( \\iiint_B (x^2+y^2+z^2)^2 \\, dV \\) over the region \\( B \\) defined by \\( x^2+y^2+z^2 \\leq 1 \\) and \\( z \\leq 0 \\) in \\( \\mathbb{R}^3 \\).",
"role": "user"
}
] | \dfrac{2\pi}{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... | 0.89 |
[
{
"content": "Find the limit of the sequence \\( U_n = \\frac{\\sum_{k=1}^n (k+1)^{k+1}}{n^{n+1}} \\) as \\( n \\to \\infty \\).",
"role": "user"
}
] | e |
[
{
"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... | Position(ConjugacyClasses(SL(2,q)),ConjugacyClass(SL(2,q),[[Z(p)^0,Z(p)^0],[0*Z(p),Z(p)^0]])) |
[
{
"content": "Let $G$ be a finite solvable group of Fitting length $n$ with the upper Fitting series:\n\\[1 = U_0G \\leq U_1G \\leq \\cdots \\leq U_nG = G.\\]\nIs every normal subgroup of Fitting length $i$ contained in $U_iG$? Justify your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the summation \\( \\sum \\limits_{i=1}^{1999} f\\left(\\frac{i}{1999}\\right) \\) for the function \\( f(x) = \\frac{4^x}{4^x + 2} \\).",
"role": "user"
}
] | \dfrac{2999}{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... | $744717 |
[
{
"content": "Calculate the probability that the order statistics of $n$ independent and identically distributed $U(0,1)$ random variables satisfy $U_{(j)} > \\frac{\\beta j}{n}$ for all $j = 1, \\ldots, n$, where $0 \\le \\beta \\le 1$. Provide your answer as a single probability value.",
"role": "user"
... | 1 - \beta |
[
{
"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... | 0.67 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... | 33.33 |
[
{
"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... | 573,000 |
[
{
"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... | 0.61 s |
[
{
"content": "Find the limit of \\((2xy)^{xy}\\) as \\((x,y) \\to (0, 2)\\).",
"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... | 2.37m/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... | $286,133 |
[
{
"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... | 59713 Pa |
[
{
"content": "The value of the expression \\[(2^{1004}+5^{1005})^2-(2^{1004}-5^{1005})^2\\]is $k\\cdot10^{1004}$ for some positive integer $k$. What is $k$?",
"role": "user"
}
] | 20 |
[
{
"content": "Let $R$ be a finite ring and $x \\in R$ be a zero divisor. Determine if it is possible for $x^n = x^m \\neq x$ to hold for $1 < m < n$. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the integral \\( \\int_0^{\\pi/2}\\ln\\left(\\cos^2 x\\right)dx \\).",
"role": "user"
}
] | -\pi \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... | 9.52 |
[
{
"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... | 2.02 hr |
[
{
"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... | 3.66 atm |
[
{
"content": "Given the recurrence relation \\(b_n=2-\\frac{1}{n}\\sum_{i=0}^{n-1}b_i\\) with \\(b_0=1\\), find an expression for \\(b_n\\) in terms of \\(n\\).",
"role": "user"
}
] | 1 |
[
{
"content": "Calculate the limit: \\[ \\lim _{x \\rightarrow \\frac{1}{2}} \\frac{\\ln (4 x-1)}{\\sqrt{1-\\cos \\pi x}-1} \\]",
"role": "user"
}
] | \dfrac{8}{\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... | 0.687 gram |
[
{
"content": "Given positive real numbers $x$, $y$, and $z$ such that $\\frac{1}{3} \\leq xy + yz + zx \\leq 3$, find the range of possible values for $x + y + z$. Express your answer as an interval.",
"role": "user"
}
] | [1, \infty) |
[
{
"content": "Find the limit of the sequence \\(x_{n}=\\frac{1}{n+2^{0}}+\\frac{1}{n+2^{1}}+\\ldots+\\frac{1}{n+2^{n}}\\) for \\(n \\in \\mathbb{N}\\) and \\(n \\geq 1\\).",
"role": "user"
}
] | 0 |
[
{
"content": "In an isosceles right triangle \\( \\triangle ABC \\), the hypotenuse \\( AB \\) is divided by points \\( K \\) and \\( L \\) such that \\( AK : KL : LB = 1 : 2 : \\sqrt{3} \\). Find the measure of \\( \\angle KCL \\).",
"role": "user"
}
] | 45^\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... | 0.616kg |
[
{
"content": "Determine the number of solutions to the equation \\( \\int\\limits_x^{x+\\frac{1}{2}} \\cos \\left( \\frac{t^2}{3} \\right) dt = 0 \\) on the interval \\([0, 3]\\).",
"role": "user"
}
] | 1 |
[
{
"content": "Compute the intersection multiplicity of the elliptic curve given by \\(x^3 + xz^2 + z^3 + y^2z + yz^2 = 0\\) and the curve \\(x = 0\\) at the point \\((0, 1, 1)\\). Note: \\(f(x, y, z) = x^3 + xz^2 + z^3 + y^2z + yz^2 \\in \\mathbb{F}_2[x, y, z]\\).",
"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... | 0.017 |
[
{
"content": "Consider a function $f\\colon\\mathbb{R}\\rightarrow\\mathbb{R}$ that is continuous everywhere and differentiable everywhere except on a subset $S$ of $\\mathbb{R}$ with measure zero. Is it necessarily true that $S$ is countable? Provide a justification for your answer.",
"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... | $496.11 |
[
{
"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... | 16.791 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... | 2.31 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... | 594.4 kJ/Kg |
[
{
"content": "Solve the differential equation \\( y''(x) + y(x) = 0 \\) with the initial conditions \\( y(0) = 0 \\) and \\( y'(0) = 1 \\) by expressing the solution as a power series. Use the method of shifting the summation index to determine the coefficients of the power series.",
"role": "user"
}
] | \sin(x) |
[
{
"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... | 5.31% |
[
{
"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... | Accrued Expenses |
[
{
"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_1^* = 57/17
P_2^* = 59/17
Q_1^* = 194/17
Q_2^* = 143/17 |
[
{
"content": "Determine the largest open ball around zero where the matrix exponential on skew-symmetric $3\\times3$ matrices onto $SO(3)$ is a local homeomorphism or diffeomorphism.",
"role": "user"
}
] | \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... | 25 cm |
[
{
"content": "Let $H$ be a Banach space and $C \\subset H$ be a convex cone. Consider $H' \\subset H$ as a subspace and a functional $\\phi: H' \\to \\mathbb{R}$ that is continuous in the norm of $H$ and nonnegative on $H' \\cap C$. Does there exist an extension $\\tilde{\\phi}: H \\to \\mathbb{R}$ that is both... | 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... | 139 kPa |
[
{
"content": "Determine the values of the real parameter $b$ for which the equation $\\cos(5x)\\cos x = b$ has exactly one solution in the interval $[0, \\pi)$.",
"role": "user"
}
] | 1 |
[
{
"content": "Consider a group of $n$ people, each randomly choosing another person from the group. If any person chooses themselves, the group must repeat the process. Define the random variable $Y$ as the number of attempts needed until no one chooses themselves. Find the expected value of $Y$, $E(Y)$. It is ... | e |
[
{
"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... | $117,300 |
[
{
"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... | /cimages/multimages/16/24-heptadiene1123852169691759173.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... | Activity Level | Variable Manufacturing Overhead | Fixed Manufacturing Overhead | Total Cost
------- | -------- | -------- | --------
8,400 | $21,000 | $6,647 | $27,647
10,300 | $25,750 | $6,647 | $32,397
12,200 | $30,500 | $6,647 | $37,147
14,100 | $35,250 | $6,647 | $41,897 |
[
{
"content": "Suppose we have two sequences \\((x_n)\\) and \\((y_n)\\). If \\((x_n)\\) is bounded and \\(|x_n - y_n| < \\frac{1}{n}\\) holds for all \\(n\\), and a subsequence \\((x_{n_i})\\) of \\((x_n)\\) converges to a limit \\(a\\), does the subsequence \\((y_{n_i})\\) also converge to \\(a\\)? Justify you... | Yes |
[
{
"content": "An inspector starts from city \\(A\\) and must check the condition of all roads between settlements, with road lengths of 13 km, 12 km, and 5 km. Determine the shortest route the inspector should take, allowing him to finish at any preselected point.",
"role": "user"
}
] | 30 |
[
{
"content": "Is it true that for functions $(f_i)$ on $L^p(\\mathbb{R}^n)$, where $p \\geq 1$, the following inequality holds: \\[ \\left\\| \\sum_{i=1}^{\\infty} |f_i| \\right\\|_p \\leq \\sum_{i=1}^{\\infty} \\|f_i\\|_p \\]?",
"role": "user"
}
] | True |
[
{
"content": "Evaluate the limit: $$\\lim_{n\\to\\infty}{n\\left(\\ln(n+2)-\\ln n\\right)}$$",
"role": "user"
}
] | 2 |
[
{
"content": "For any real numbers \\(x\\) and \\(y\\) satisfying \\(x^2y + 6y = xy^3 +5x^2 +2x\\), it is known that \\((x^2 + 2xy + 3y^2) \\, f(x,y) = (4x^2 + 5xy + 6y^2) \\, g(x,y)\\). Given that \\(g(0,0) = 6\\), find the value of \\(f(0,0)\\).",
"role": "user"
}
] | 19 |
[
{
"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... | 0.31 |
[
{
"content": "Consider the linear recurrence relation \\(x_n = \\alpha_n x_{n-1}+ \\beta_n x_{n-2} + y_n,\\) where \\((\\alpha_n)\\) and \\((\\beta_n)\\) are sequences that converge to positive constants \\(\\alpha\\) and \\(\\beta\\), respectively, and \\((y_n)\\) is a bounded sequence. Suppose the limiting au... | 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... | 9359981.28e-28 J |
[
{
"content": "Points $P$ and $Q$ are midpoints of two sides of the square. What fraction of the interior of the square is shaded? Express your answer as a common fraction.\n\n[asy]\nfilldraw((0,0)--(2,0)--(2,2)--(0,2)--(0,0)--cycle,gray,linewidth(1));\nfilldraw((0,1)--(1,2)--(2,2)--(0,1)--cycle,white,linewidth(... | \frac{7}{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... | 8.85 x 10^-3 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... | No, the tensions on either side are: T1= ( (4M2 + m) / (2M1 + 2M2 + m) ) * M1*g and T2= ( (4M1 + m) / (2M1 + 2M2 + m) ) * M2*g, where M1 and M2 are the masses of the blocks, m is the mass of the pulley, and g is acceleration due to gravity. |
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