prompt list | ground_truth string |
|---|---|
[
{
"content": "Consider the matrix product \\(\\begin{pmatrix} 1&1&1 \\\\ 1&w&w^2 \\\\ 1&w^2&w^4 \\end{pmatrix} \\begin{pmatrix} 1&0&0 \\\\ 0&-1&0 \\\\ 0&0&0 \\end{pmatrix} \\begin{pmatrix} 1&1&1 \\\\ 1&1/w&1/w^2 \\\\ 1&1/w^2&1/w^4 \\end{pmatrix}\\), where \\(w\\) is a non-real cube root of unity. Determine the ... | D |
[
{
"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. Cost of gasoline
2. Maintenance and repairs
3. Cost of train ticket
4. Reduction in resale value of car due to mileage used and wear and tear
5. Cost of parking car in Chicago |
[
{
"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... | 2,161.91 mi |
[
{
"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... | 13.6 ns |
[
{
"content": "Determine the values of $x$ for which the series \\( \\sum \\frac{x^n}{x^{2n}-1} \\) converges.",
"role": "user"
}
] | (-\infty, -1) \cup (-1, 1) \cup (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... | $t = \frac{a^2}{L} \int_{0}^{\eta} (1-e\cos\eta)^2\frac{\sqrt{1 - e^2}\left(1+\tan^2\frac\eta2\right)}{\left(1+\tan^2\frac\eta2\right) - e^2 + e^2\tan^2\frac\eta2}\,d\eta$ |
[
{
"content": "Determine whether there exists a random variable $Y$ taking values in $\\{-1, 1\\}$ for a real-valued random variable $X$ with $|X| \\leq 1$ almost surely, such that the conditional expectation $E[Y | \\sigma(X)] = X$. Consider if extending the probability space is necessary.",
"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... | $41.25 |
[
{
"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... | Vertical Analysis
2014
Amount Percentage
Net sales $751,930 100%
Cost of goods sold 477,180 63.5%
Gross profit 274,750 36.5%
Selling expenses 117,610 15.6%
Administrative expenses 74,870 10%
Total operating expenses 192,480 25.6%
Income before taxes 82,270 10.9%
Income tax expense 35,850 4.8%
Net income 46,420 6.1%
20... |
[
{
"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... | \frac{\omega}{k} |
[
{
"content": "A particle starts at position 0 on the integer number line. Every second, it moves one unit to the left or right with equal probability of \\( \\frac{1}{2} \\). What is the probability that the particle reaches position +1?",
"role": "user"
}
] | 1 |
[
{
"content": "Determine whether monoids of endomorphisms of nonisomorphic groups can be isomorphic.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine whether there exists an entire function $f$, which is not a polynomial, such that there is a disk $D_\\epsilon(0)$ for some $\\epsilon > 0$ where the restriction of $f$ to $D_\\epsilon(0)$ is injective.",
"role": "user"
}
] | Yes |
[
{
"content": "Given a discrete random variable $X$ that can take integer values from $0$ to $20$, and the mean of $X$ is $0.005$, determine the maximum possible variance of $X$. Provide your answer as a single number.",
"role": "user"
}
] | 0.099975 |
[
{
"content": "Calculate the gradient with respect to the matrix $\\pmb{A}$ of the function $\\log(\\det(\\pmb{A}\\pmb{X}))$, where both $\\pmb{X}$ and $\\pmb{A}$ are positive definite matrices.",
"role": "user"
}
] | \pmb{A}^{-1} |
[
{
"content": "Evaluate the Riemann-Stieltjes integral \\( \\int_{0}^2 x \\, d\\alpha \\), where \\( \\alpha(x) = x \\) for \\( 0 \\le x \\le 1 \\) and \\( \\alpha(x) = 2 + x \\) for \\( 1 < x \\le 2 \\).",
"role": "user"
}
] | 4 |
[
{
"content": "Let $H$ be a separable Hilbert space, and let $Q: B(H) \\rightarrow B(H)/B_0(H)$ be the natural quotient map, where $B(H)$ is the algebra of bounded operators and $B_0(H)$ is the algebra of compact operators on $H$. Consider the orthonormal basis of $H$ and let $P_n$ be the projection onto the spa... | Yes |
[
{
"content": "Evaluate the limit: $$\\lim_{(x,y) \\to (0,0)} \\frac{x^2y + x^4}{x^2 + y^2}$$",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the limit \\( \\lim_{y \\to 0} [\\log(a+iy) - \\log(a-iy)] \\) for complex numbers, where \\( a > 0 \\) and \\( y > 0 \\). Use the principal value of the complex logarithm.",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the limit \\( L = \\lim_{x \\rightarrow \\infty} \\left(\\sqrt[11]{\\prod_{n=1}^{11}\\left(2x+\\frac{n(2n+1)}{2}\\right)}-2x\\right) \\).",
"role": "user"
}
] | 49 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 18.435 degrees west of horizontal |
[
{
"content": "In a right isosceles triangle $ABC$ with hypotenuse $AB$, a semicircle $\\\\Gamma\\\\$ is drawn with diameter $AC$. The semicircle intersects $AB$ at $A$. If a point $P$ on $\\\\Gamma\\\\$ satisfies $PC = k$, where $k \\leq AC$, find the area of triangle $PBC$ using synthetic geometry.",
"role... | \dfrac{k^2}{2} |
[
{
"content": "Can the surface defined by the equation \\(xy - y\\log(z) + \\sin(xz) = 0\\) be locally represented as \\(z = f(x, y)\\) near the point \\((0, 2, 1)\\) using the implicit function theorem? Assume \\(f\\) is a smooth function. Determine if the necessary condition for this representation is satisfie... | Yes |
[
{
"content": "Calculate the surface area of the portion of the cylinder defined by \\(y^2+z^2=2z\\) that is intersected by the cone \\(x^2=y^2+z^2\\).",
"role": "user"
}
] | 16 |
[
{
"content": "Two positive numbers $p$ and $q$ have the property that their sum is equal to their product. If their difference is $7$, what is $\\frac{1}{\\frac{1}{p^2}+\\frac{1}{q^2}}$? Your answer will be of the form $\\frac{a+b\\sqrt{c}}{d}$, where $a$ and $b$ don't both share the same common factor with $d$... | 161 |
[
{
"content": "Determine all natural numbers $e$ for which there exists a natural number $f$ such that $e > f$ and a polyhedron with $e$ vertices and $f$ faces exists.",
"role": "user"
}
] | e \geq 6 |
[
{
"content": "Solve the equation \\( \\ln (x+1)=\\frac{x}{4-x} \\) for the exact value of \\( x \\).",
"role": "user"
}
] | 0 |
[
{
"content": "What is the slope of the line containing the midpoint of the segment with endpoints at $(2, 4)$ and $(0, -2)$ and the midpoint of the segment with endpoints at $(5, 1)$ and $(1, 5)?$ Express your answer in simplest form.",
"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... | $7,400 |
[
{
"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 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... | DateAccountDebitCredit
December 31Interest Expense$228,887.17
Premium on Bonds Payable$5,112.83
Cash $234,000 |
[
{
"content": "Compute the intersection multiplicity of the curves $V(f)$ and $V(g)$ at the point $p = [1:0:-1]$, where $f = x^2 + y^2 - z^2$ and $g = (x-z)^2 - y^2$.",
"role": "user"
}
] | 0 |
[
{
"content": "Calculate the limit: \\( \\displaystyle \\lim_{x\\rightarrow \\infty} \\; (\\ln x)^{3 x} \\).",
"role": "user"
}
] | \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... | Quarter 1: 160,125
Quarter 2: 190,250
Quarter 3: 200,125
Quarter 4: 179,875
Year: 730,375 |
[
{
"content": "Determine the number of real roots of the equation \\(x^2 + 10x + (\\sin(x))^2 = \\cos(x)\\).",
"role": "user"
}
] | 2 |
[
{
"content": "Determine the third homotopy group of the space $S^2 \\times S^1$, where $S^n$ denotes the $n$-dimensional sphere.",
"role": "user"
}
] | \mathbb{Z} |
[
{
"content": "Find a number that is divisible by all integers less than or equal to half of itself, but not divisible by any integer greater than half of itself.",
"role": "user"
}
] | 6 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 590 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... | 11884.07 kJ |
[
{
"content": "Determine the number of pairs \\((m, n)\\) of non-zero integers such that the equation \\(n^{2}x^{3} + 2020x^{2} + mx = 0\\) has exactly two real solutions.",
"role": "user"
}
] | 16 |
[
{
"content": "Find the two rightmost digits of \\(3^{40000005}\\) using the Euler Totient function.",
"role": "user"
}
] | 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... | 45 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... | 260.7ms^-1 |
[
{
"content": "Determine the smallest integer $d^*$ such that the inequality \\( \\frac{\\left(\\sum_{i=1}^d i^{-p}\\right)^2}{\\sum_{i=1}^d i^{-2p}} \\ge \\frac{1}{2}\\frac{\\zeta(p)^2}{\\zeta(2p)} \\) holds, where $\\zeta(s)$ is the Riemann Zeta function and $H_d^{(p)}$ are the Harmonic numbers.",
"role": ... | 2 |
[
{
"content": "Find all pairs of natural numbers \\((n, m)\\) such that \\(n^4(n+1) + 1 = 7^m\\).",
"role": "user"
}
] | (2, 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... | 11.3J |
[
{
"content": "Given two finite CW-spaces $K$ and $L$ with dimensions $n$ and $n-1$, respectively, and two maps $\\phi: K \\to X$ and $\\psi: L \\to X$, where $\\phi$ is $n$-connected and $\\psi$ is $(n-1)$-connected, determine if there exists an $(n-1)$-connected map $\\eta: L \\to K$ such that $\\phi \\circ \\... | 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... | 3.828e11 |
[
{
"content": "Let $X_1, X_2, \\ldots$ be independent identically distributed (i.i.d.) random variables with $E(X_i) = 2$ and $\\text{Var}(X_i) = 1$. Determine the almost sure limit of the sequence:\n\\[ Y_n = \\frac{\\sum_{i=1}^n X_i \\sum_{i=1}^n (X_i - 2)^2}{n^2} \\]",
"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... | 3.76 |
[
{
"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... | 3.6864e-25 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... | Ba(NO_3)_2(aq) + Na_2CO_3(aq) rarr BaCO_3(s)darr + 2Na(NO_3)(aq) |
[
{
"content": "Let $A$ be a positive-definite real matrix such that $x^T A x > 0$ for every nonzero real vector $x$. Does it follow that $\\mathrm{det}(A) > 0$?",
"role": "user"
}
] | Yes |
[
{
"content": "Verify the optimality of the solution obtained using the Lagrange multiplier method for minimizing the function \\( f(x,y,z) = x^2 + y^2 + z^2 \\) subject to the constraints \\( x^2 + y^2 + z^2 = 5 \\) and \\( x^2 + y^2 + z^2 - 2x - 3 = 0 \\). The solution provided by MATLAB is \\( x = \\lambda = ... | 5 |
[
{
"content": "Find the length of the primary component of the ideal \\((xy, y^2)\\) at the origin in the polynomial ring \\(\\mathbb{R}[x, y]\\).",
"role": "user"
}
] | 2 |
[
{
"content": "Let \\( \\phi \\) be a function on \\( \\mathbb{R}^n \\) and \\( ty=(ty_1,\\dots,ty_n)\\in \\mathbb{R}^n \\). Suppose that \\( \\nu_i(y)=y_i \\int_0^1 s^{n-1} \\phi(sy) \\, ds. \\) Find an expression for \\( \\sum_{i=1}^n \\frac{\\partial \\nu_i}{\\partial y_i} \\) in terms of \\( \\phi \\).",
... | \phi(y) |
[
{
"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... | Genetical diversity |
[
{
"content": "Determine the equation of the line with the least positive slope that passes through the point \\((1, 0)\\) and does not intersect the curve \\(4x^2 - y^2 - 8x = 12\\).",
"role": "user"
}
] | y = 2x - 2 |
[
{
"content": "Determine the cardinality of the set \\( S \\) of all closed intervals on the real number line with rational (positive) lengths.",
"role": "user"
}
] | \mathfrak{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... | 3.6 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... | 5449 years |
[
{
"content": "If $a$ and $b$ are real numbers, $a^2b^3=\\frac{32}{27}$, and $\\frac{a}{b^3}=\\frac{27}{4}$, what is $a+b$?",
"role": "user"
}
] | \frac83 |
[
{
"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... | 3.9 m |
[
{
"content": "Find the sum of the roots of the equation \\(\\cos(12x)=5\\sin(3x)+9\\tan^2(x)+\\frac{1}{\\tan^2(x)}\\) for \\(0\\le x\\le 2\\pi\\).",
"role": "user"
}
] | 3\pi |
[
{
"content": "Compute the degree of the zero cycle in the Fano variety of lines on a smooth quadric $Q \\subset \\mathbb{P}_k^3$, where $F_{osc} = \\{[l] \\in F(Q), \\exists P\\text{ plane such that } 2l \\subseteq P \\cap Q\\}$.",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the value of $p$ for which the series \\(\\sum_{n=1}^{\\infty} \\frac{1}{n^p} \\cdot \\cos\\left(\\frac{\\pi}{3}\\cdot n\\right)\\) converges absolutely using the integral test.",
"role": "user"
}
] | p > 1 |
[
{
"content": "Evaluate the limit: $$\\lim _{n \\rightarrow \\infty}\\left(n \\ln \\left(1-\\frac{1}{n}\\right) \\cos \\left(\\pi \\sqrt{4 n^2+10}\\right)\\right)$$",
"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... | East |
[
{
"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... | $1.3 |
[
{
"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... | 74 km/h |
[
{
"content": "Let \\( f(x) = \\frac{1}{2}(x + \\sqrt{x^2 + 4}) \\). Find the value of \\( f^{-1}(x) + f^{-1}\\left(\\frac{1}{x}\\right) \\) for \\( x \\neq 0 \\).",
"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... | HNO3 > HClO4 > HClO2 > HClO > HBrO |
[
{
"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... | 1.97e-35 atm |
[
{
"content": "If $X_1, X_2, \\ldots, X_n$ are independent and identically distributed standard normal random variables, does the vector $(\\bar{X}, X_1 - \\bar{X}, \\ldots, X_n - \\bar{X})$ follow a multivariate normal distribution, where $\\bar{X}$ is the sample mean of $X_1, X_2, \\ldots, X_n$?",
"role": ... | Yes |
[
{
"content": "Determine the number of roots of the polynomial \\( z^7 + 2z^3 + 1 \\) in the region \\( \\frac{1}{2} \\leq |z| < 1 \\).",
"role": "user"
}
] | 3 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 7 cars |
[
{
"content": "Determine the height above the ground from which an observer can see exactly one-fourth of the Earth's surface, assuming the Earth is a sphere with radius \\( r \\).",
"role": "user"
}
] | r |
[
{
"content": "Calculate the surface integral of the vector field \\( \\vec{G}(x,y,z) = y\\hat{i} - x\\hat{j} + (x^2 - y^2)\\hat{k} \\) over the portion of the paraboloid \\( z = 4 - x^2 - y^2 \\) that lies above the plane \\( z = 0 \\), with the surface oriented upward.",
"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 kg and 3 kg |
[
{
"content": "Use Stokes' Theorem to evaluate \\(\\displaystyle\\iint_S\\mathrm{curl}~\\mathbf{F}\\cdot d\\mathbf{S}\\) where \\(\\mathbf{F}(x,y,z) = (x+y)z~\\mathbf{i}+ (x-z)y~\\mathbf{j}+ (z-y)x~\\mathbf{k}\\) and \\(S\\) is the part of the sphere \\(x^2+y^2+z^2 = 16\\) that lies above the plane \\(z = 2\\), ... | -24\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... | 32.05 |
[
{
"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{eq}_b{/eq} = {eq}\rho{/eq}Vg |
[
{
"content": "Let $x_1,$ $x_2,$ $x_3,$ $\\dots,$ $x_{100}$ be positive real numbers such that $x_1^2 + x_2^2 + x_3^2 + \\dots + x_{100}^2 = 1.$ Find the minimum value of\n\\[\\frac{x_1}{1 - x_1^2} + \\frac{x_2}{1 - x_2^2} + \\frac{x_3}{1 - x_3^2} + \\dots + \\frac{x_{100}}{1 - x_{100}^2}.\\]",
"role": "use... | \frac{3 \sqrt{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... | Factors to consider include customer budget, competition, reputation, and risk. It's a difficult task because overpricing can lose the job, while underpricing leads to losses for the contractor. |
[
{
"content": "In how many ways can 80 gold bars be distributed among 3 peasants and 3 kings such that each king receives at least 10 bars and each peasant receives at most 10 bars?",
"role": "user"
}
] | 906411 |
[
{
"content": "Determine the maximum dimension of a subspace M of the space of 6x6 skew-symmetric matrices over the real numbers, where all non-zero elements of M have rank 2.",
"role": "user"
}
] | 5 |
[
{
"content": "Evaluate the limit of the integral: \\[ I = \\lim_{n \\to \\infty} \\int_0^1 \\frac{1 + nx^2}{(1 + x^2)^n} \\log(2 + \\cos(x/n))\\,dx. \\] Find the value of \\( I \\).",
"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... | 1100 s |
[
{
"content": "In triangle \\( \\triangle DAN \\), inscribed in circle \\( C \\), let \\( AE \\) be the angle bisector of \\( \\angle DAN \\) with \\( E \\) on \\( C \\). Given \\( DA = 2 \\), \\( AN = 1 \\), and \\( AE = 2.5 \\), if \\( AE \\) intersects \\( DN \\) at \\( I \\), find the length of \\( AI \\).",... | \dfrac{4}{5} |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\to\\infty}\\sum_{k=0}^{n} \\binom{n}{k}\\frac{1}{n^k(k+5)}. \\]",
"role": "user"
}
] | 9e - 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... | 492 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... | 17.11% |
[
{
"content": "Consider a road with \\( n \\) parking spots and \\( n \\) drivers. Each driver has a favorite parking spot. If a driver's favorite spot is occupied, they park in the nearest available spot down the road. If all spots from their favorite onward are occupied, they leave without parking. Determine t... | (n+1)^{n-1} |
[
{
"content": "How many solutions does the equation \\[\\frac{(x-1)(x-2)(x-3)\\dotsm(x-100)}{(x-1^2)(x-2^2)(x-3^2)\\dotsm(x-100^2)} = 0\\]have for $x$?",
"role": "user"
}
] | 90 |
[
{
"content": "There are four distinct positive integers $a,b,c,d$ less than $8$ which are invertible modulo $8$. Find the remainder when $(abc+abd+acd+bcd)(abcd)^{-1}$ is divided by $8$.",
"role": "user"
}
] | 0 |
[
{
"content": "Find all continuous functions \\( f: [a, b] \\to \\mathbb{R} \\) that satisfy the condition \\( \\int_{a}^{x} f(t) \\, dt = \\int_{x}^{b} f(t) \\, dt \\) for every \\( x \\in (a, b) \\).",
"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... | c) 5.56 Percent |
[
{
"content": "Let $P$ be a plane passing through the origin. When $\\begin{pmatrix} 5 \\\\ 3 \\\\ 5 \\end{pmatrix}$ is projected onto plane $P,$ the result is $\\begin{pmatrix} 3 \\\\ 5 \\\\ 1 \\end{pmatrix}.$ When $\\begin{pmatrix} 4 \\\\ 0 \\\\ 7 \\end{pmatrix}$ is projected onto plane $P,$ what is the resu... | \begin{pmatrix} 1 \\ 3 \\ 1 \end{pmatrix} |
[
{
"content": "Determine for which real values of $p$ the integral \\( \\int_0^1 e^{x}x^p\\ dx \\) converges.",
"role": "user"
}
] | p > -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... | 140 mL |
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