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... | 0.0987 atm |
[
{
"content": "If $\\mathbf{M}$ and $\\mathbf{N}$ are positive semi-definite matrices, $\\alpha \\in (0,1)$, and $\\mathbf{L}=\\alpha\\mathbf{M} + (1-\\alpha) \\mathbf{N}$ is positive definite, does it imply that both $\\mathbf{M}$ and $\\mathbf{N}$ are positive definite? Answer with 'yes' or 'no' and justify yo... | 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... | E = \frac{2GM}{d\sqrt{L+ 4d^2}} |
[
{
"content": "Find the product of the nonreal roots of $x^4-4x^3+6x^2-4x=2005.$",
"role": "user"
}
] | 1 +\sqrt{2006} |
[
{
"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... | 3297 K |
[
{
"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... | 4e+16 Hz |
[
{
"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... | 155 mmHg |
[
{
"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... | 154.16 million mi/hr |
[
{
"content": "Determine the Galois group of the polynomial \\(x^3 - x - 1\\) over \\(\\mathbb{Q}\\).",
"role": "user"
}
] | S_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... | $2,181.82 |
[
{
"content": "Determine whether the following statement is true or false: Let $f \\in C[a, b]$ be differentiable in $(a, b)$. If $f(a) = f(b) = 0$, then, for any real number $\\alpha$, there exists $x \\in (a, b)$ such that $f'(x) + \\alpha f(x) = 0$. Justify your answer.",
"role": "user"
}
] | True |
[
{
"content": "The duration $Y$ of long-distance telephone calls (in minutes) is a random variable with the following properties: $P(Y=3)=0.2$ and $P(Y=6)=0.1$. Otherwise, $Y$ has a continuous density function given by \\( f(y)= \\begin{cases} (1/4)ye^{-y/2}, & y>0 \\\\ 0, & \\text{elsewhere.} \\end{cases} \\) F... | 4 |
[
{
"content": "For any natural number $n$, does there exist a set of real numbers $\\{x_1, x_2, \\ldots, x_n\\}$ such that:\n\n- If $i > j$, then $x_i > x_j$.\n- If $i = j$, then $x_i = x_j$.\n- If $i < j$, then $x_i < x_j$.\n- The equation $\\sum_{i=1}^n a_ix_i = \\sum_{i=1}^n b_ix_i$ holds only if $a_i = b_i$ ... | Yes |
[
{
"content": "Given that the function \\( f(x) \\) and the product \\( f(x)g(x) \\) belong to the Sobolev space \\( \\mathcal{W}^{s+1} \\) with \\( s \\ge 1 \\), and \\( g \\in \\mathbb{L}^{\\infty}(\\mathbb{R_+}) \\) where \\( \\mathbb{R}_+ = [0,\\infty) \\). Additionally, for all \\( k \\ge 0 \\), \\( \\int x... | 0 |
[
{
"content": "Evaluate the integral \\(\\int_\\Gamma\\dfrac{2z+i}{z^3(z^2+1)}\\mathrm{d}z\\) where \\(\\Gamma:|z-1-i| = 2\\) is a positively oriented circle.",
"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... | 584 |
[
{
"content": "Compute the limit \\(\\lim_{x\\to 0^{+}}(\\cos x-1)e^{\\cot x}\\).",
"role": "user"
}
] | -\infty |
[
{
"content": "Let X and Y be independent random variables, each uniformly distributed on the interval [0,1]. Given that the smaller of X and Y is less than 1/4, find the conditional probability that the larger of X and Y is greater than 3/4.",
"role": "user"
}
] | \dfrac{2}{7} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.09 |
[
{
"content": "Determine the area enclosed by the curve defined by the equation \\((x^2 + y^2)^2 = 4x^2y^2\\).",
"role": "user"
}
] | 0 |
[
{
"content": "Can the symmetric group $S_6$ act transitively on a set with 4 elements? Justify your answer.",
"role": "user"
}
] | No |
[
{
"content": "What is the value of \\(1^i\\)?",
"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... | $4,478 |
[
{
"content": "Compute the limit: \\[ \\lim_{x \\to 0} \\left(\\frac{e^{x^2} -1}{x^2}\\right)^\\frac{1}{x^2} \\]",
"role": "user"
}
] | \sqrt{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... | 212425 rad |
[
{
"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... | 0.1224 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... | 169.74 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... | $4,662.5 |
[
{
"content": "Let $B_1$ and $B_2$ be two Banach spaces, and let $L(B_i,B_j)$ and $K(B_i,B_j)$ denote the spaces of bounded and compact linear operators between them, respectively, for $i,j=1,2$. Given $T \\in L(B_1,B_1)$, suppose there exists $S \\in K(B_1,B_2)$ and a constant $c>0$ such that for any $v \\in B_... | 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... | $22,800 |
[
{
"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... | Burgess Company
Statement of Cash Flow
For the fiscal year ending XX
Cash flows from operating activities
Profit 115
Adjustments for:
Depreciation Expense 124
Working capital changes:
(Increase) / Decrease in trade and other receivables -65
(Increase) / Decrease in inventories -45
Increase / (Decrease) in Accounts Payable 95
Increase / (Decrease) in Accrued Liabilities 25
Increase / (Decrease) in Income Tax Payable 6
Net cash generated (used) from operating activities 255
Cash flows from investing activities
Sale (Purchase) of Property, Plant, and Equipment -49
Net cash generated (used) from investing activities -49
Cash flows from financing activities
Proceeds (payments) from Bond Payable -170
(Dividends) Injections -66
Net cash generated (used) from financing activities -236
Net increase in cash and cash equivalents -30
Cash and cash equivalents at beginning of period 79
Cash and cash equivalents at end of period 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... | 2347.83 m |
[
{
"content": "There exist integers $a,$ $b,$ and $c$ such that\n\\[(x - a)(x - 10) + 1 = (x + b)(x + c).\\]Enter all possible values of $a,$ separated by commas.",
"role": "user"
}
] | 8,12 |
[
{
"content": "Let $G = D \\ltimes C$ be a finite non-nilpotent group, where $D = N_G(B) = (A \\ltimes B)$ is a maximal subgroup of $G$. Here, $A \\cong \\mathbb{Z}_r$, $B = B_1 \\times B_2 \\cong \\mathbb{Z}_s \\times \\mathbb{Z}_s$, and $C \\cong \\mathbb{Z}_t$, with $r, s, t$ being distinct prime numbers. Ass... | [B_1, A] = 1 |
[
{
"content": "Compute the Jacobi symbol \\(\\left(\\frac{77}{257}\\right)\\) using the properties of Jacobi symbols. Show all steps in your calculation.",
"role": "user"
}
] | -1 |
[
{
"content": "Determine the values of $p$ for which the integral \\( \\int_{0}^{1} \\frac{1}{\\sqrt{y^{-p}-1}} \\, dy \\) converges.",
"role": "user"
}
] | p > 0 |
[
{
"content": "Find all values of $x > 4$ which satisfy\n\\[\\sqrt{x - 4 \\sqrt{x - 4}} + 2 = \\sqrt{x + 4 \\sqrt{x - 4}} - 2.\\]",
"role": "user"
}
] | [8,\infty) |
[
{
"content": "Find the residue of the function \\(g(z)=\\frac{1}{(z^3-1)^2}\\) at the isolated singularity \\(z=1\\).",
"role": "user"
}
] | -\dfrac{2}{9} |
[
{
"content": "For a polynomial $p(x),$ define its munificence as the maximum value of $|p(x)|$ on the interval $-1 \\le x \\le 1.$ For example, the munificence of the polynomial $p(x) = -x^2 + 3x - 17$ is 21, since the maximum value of $|-x^2 + 3x - 17|$ for $-1 \\le x \\le 1$ is 21, occurring at $x = -1.$\n\n... | \frac{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... | 6.538% |
[
{
"content": "Let $X_1, X_2, \\ldots, X_n$ be iid continuous random variables. What is the probability that $X_n$ is greater than the maximum of $X_1, X_2, \\ldots, X_{n-1}$?",
"role": "user"
}
] | \dfrac{1}{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... | 5.396 kW |
[
{
"content": "Determine the values of $n$ for which an open connected subset of $\\mathbb{R}^n$ can have a fundamental group with torsion.",
"role": "user"
}
] | n \geq 4 |
[
{
"content": "In a flock of pigeons, each pigeon dislikes exactly $k$ other pigeons. Determine the minimum number of groups required to arrange the pigeons such that no pigeon is in a group with any pigeon it dislikes.",
"role": "user"
}
] | k + 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.407 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... | -$616,730 |
[
{
"content": "In acute triangle $\\triangle ABC$, $O$ is the circumcenter and $\\angle BAC = 60^{\\circ}$. Extend $CO$ to intersect $AB$ at point $D$, and extend $BO$ to intersect $AC$ at point $E$. Determine the value of $\\frac{BD}{CE}$.",
"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... | 464,442.28 |
[
{
"content": "Evaluate the integral \\( \\int_{-\\tfrac\\pi2}^{\\tfrac\\pi2} \\ln(\\cos \\tau) \\cos \\tau \\, d\\tau \\) using the beta function.",
"role": "user"
}
] | 2 \ln 2 - 2 |
[
{
"content": "Calculate the sum of the infinite series: \\[ \\sum_{n=0}^{\\infty} \\frac{(n+1)(2n+1)}{3^n} \\]",
"role": "user"
}
] | \dfrac{27}{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... | $6,341.99 |
[
{
"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... | -1.475e-3 m^3 |
[
{
"content": "Determine whether all fixed points of the function \\( f(z) = \\frac{z-i}{iz+3} \\) are in the region \\( \\{z \\in \\Bbb C: \\Im(z)>0\\} \\). State whether the statement is TRUE or FALSE.",
"role": "user"
}
] | FALSE |
[
{
"content": "In a Markov chain with six states, where state 6 is absorbing, each non-absorbing state has a 50% chance of moving one step up or down, except state 1, which always moves to state 2. Calculate the expected number of steps to reach the absorbing state if the starting state is chosen randomly with e... | \dfrac{95}{6} |
[
{
"content": "A ball is dropped from $405$ meters and rebounds two-thirds the distance it falls each time it bounces. How many meters will the ball have traveled when it hits the ground the fourth time?",
"role": "user"
}
] | 1545 |
[
{
"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... | 75 g |
[
{
"content": "Evaluate the iterated integral by changing to polar coordinates: \\[ \\int_0^{1/2}\\int_0^{\\sqrt{1-x^2}}xy\\sqrt{x^2+y^2}\\,dy\\,dx \\]",
"role": "user"
}
] | \dfrac{19}{480} |
[
{
"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... | $22,000 |
[
{
"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... | 47.9 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... | 1.5696 m/s^2 |
[
{
"content": "Suppose N objects are placed randomly along the circumference of a circle. Calculate the probability that all these objects lie together along an arc of length f, where f is a fraction less than 1/2 of the circle's circumference.",
"role": "user"
}
] | N f^{N-1} |
[
{
"content": "Let $\\mathbf{F}$ be a vector field defined on $\\mathbb{R}^2 \\setminus\\{(0,0)\\}$ by $$\\mathbf{F}(x,y) = \\frac{y}{x^2+y^2}i - \\frac{x}{x^2+y^2}j.$$ Let $\\gamma, \\alpha: [0,1] \\to \\mathbb{R}^2$ be defined by $$\\gamma(t) = (8\\cos 2\\pi t, 17\\sin 2\\pi t)$$ and $$\\alpha(t) = (26\\cos 2\... | 7 |
[
{
"content": "Let \\( f : [0,1] \\rightarrow [-1,1] \\) be a non-zero function such that \\( f(2x) = 3f(x) \\) for \\( x \\in \\left[0, \\frac{1}{2}\\right] \\). Evaluate \\( \\lim_{x \\to 0^+} f(x) \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\to\\infty} \\frac{\\int_{0}^{x} e^{t^2-x^2}\\, dt}{\\frac{1}{x}} \\]",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Find the area of triangle $JKL$ below.\n\n\n[asy]\nunitsize(1inch);\npair P,Q,R;\nP = (0,0);\nQ= (sqrt(3),0);\nR = (0,1);\ndraw (P--Q--R--P,linewidth(0.9));\ndraw(rightanglemark(Q,P,R,3));\nlabel(\"$J$\",P,S);\nlabel(\"$K$\",Q,S);\nlabel(\"$L$\",R,N);\nlabel(\"$20$\",(Q+R)/2,NE);\nlabel(\"$60^\\ci... | 50\sqrt{3} |
[
{
"content": "Jason is trying to remember the five digit combination to his safe. He knows that he only used digits 1 through 5 (possibly repeated), that every even digit was followed by an odd digit, and every odd digit was followed by an even digit. How many possible combinations does Jason need to try?",
... | 180 |
[
{
"content": "A square and a triangle have the same area. If the square has a side length of 6 units and the triangle has a base of 8 units, what is the length, in units, of the altitude to that base of the triangle?",
"role": "user"
}
] | 9 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 829 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... | PCl |
[
{
"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 unemployment rate increases from its natural rate of 6% to u%. |
[
{
"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... | Four factors that reduce the size of the money multiplier are: currency drain ratio, savings, taxes, and import spending. |
[
{
"content": "Does the sequence $0.000\\ldots1$, with infinitely many zeros followed by a single 1, represent a real number equal to 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... | 0.2134 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... | $13,333.33 |
[
{
"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... | 1.69 g cm^(-3) |
[
{
"content": "Consider a bin containing 1047 distinct numbers. You extract 10 elements without replacement, note them, and then reinsert them into the bin. This process is repeated 50 times. What is the expected number of different elements you will have seen after these 50 extractions?",
"role": "user"
}... | 399 |
[
{
"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... | 0.515 g |
[
{
"content": "Calculate the flux of the vector field \\( \\boldsymbol{\\mathrm{F}} = x\\boldsymbol{\\mathrm{i}} + 4y \\boldsymbol{\\mathrm{j}} \\) outwards across the triangle with vertices at \\((0,0), (2,0), (0,2)\\).",
"role": "user"
}
] | 10 |
[
{
"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... | 5.52 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... | 50% chance of BO genotype and 50% chance of AO genotype |
[
{
"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... | 2.42e+9 N |
[
{
"content": "Evaluate the double integral \\( \\iint_R \\sqrt{\\frac{x+y}{x-2y}} \\, dA \\) using a change of variables, where \\( R \\) is the region bounded by the lines \\( y - \\frac{x}{2} = 0 \\), \\( y = 0 \\), and \\( x+y = 1 \\).",
"role": "user"
}
] | \dfrac{1}{3} |
[
{
"content": "Side $AB$ of regular hexagon $ABCDEF$ is extended past $B$ to point $X$ such that $AX = 3AB$. Given that each side of the hexagon is $2$ units long, what is the length of segment $FX$? Express your answer in simplest radical form.",
"role": "user"
}
] | 2\sqrt{13} |
[
{
"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... | 1.50e-6 C |
[
{
"content": "In the triangular pyramid \\(ABCD\\), it is given that \\(DC = 9\\), \\(DB = AD\\), and the edge \\(AC\\) is perpendicular to the face \\(ABD\\). A sphere of radius 2 touches the face \\(ABC\\), the edge \\(DC\\), and also touches the face \\(DAB\\) at the intersection point of its medians. Determ... | 36 |
[
{
"content": "Simplify the expression: \\( \\sqrt[3]{18+5\\sqrt{13}}+\\sqrt[3]{18-5\\sqrt{13}} \\).",
"role": "user"
}
] | 3 |
[
{
"content": "Find the Ramsey number for the graphs $(m+1)K_4$ and $K_4$, given that $R(mK_4,K_4) + 4 \\leq R((m+1)K_4,K_4)$ for $m \\geq 2$. Provide your answer as a single number.",
"role": "user"
}
] | 4m + 18 |
[
{
"content": "Given that vectors $\\vec{a}$ and $\\vec{b}$ are both non-zero, and that $\\vec{a} + 3\\vec{b}$ is perpendicular to $7\\vec{a} - 5\\vec{b}$, and $\\vec{a} - 4\\vec{b}$ is perpendicular to $7\\vec{a} - 2\\vec{b}$, find the angle between $\\vec{a}$ and $\\vec{b}$.",
"role": "user"
}
] | \dfrac{\pi}{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... | Sales: $2,600,000
Cost of Goods Sold: $1,000,000
Gross Profit: $1,600,000
Selling and Administrative Expenses: $240,000
Operating Income: $1,360,000
Other Revenue: $80,000
Other Expenses: $50,000
Income Before Taxes and Extraordinary Items: $1,390,000
Income Tax Expense: $417,000
Income Before Extraordinary Items: $973,000
Earthquake Loss (Net of Tax): $175,000
Net Income: $798,000
Earnings Per Share: $7.98 |
[
{
"content": "What is the greatest common factor of $154$ and $252$?",
"role": "user"
}
] | 14 |
[
{
"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... | Investment Section:
Common stock of Eidman Co. $102,000
Common stock of Pickerill Inc. $252,000
Debt investment $152,000
Total investment $506,000 |
[
{
"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... | 18.43% |
[
{
"content": "Determine the values of the parameter $x$ for which the infinite series \\( \\sum_{n=1}^\\infty \\frac{x^n}{\\ln(n+1)} \\) converges.",
"role": "user"
}
] | [-1, 1) |
[
{
"content": "Determine whether the product of a transcendental number and a rational number can be a rational number.",
"role": "user"
}
] | Yes |
[
{
"content": "Find the sum of the alternating harmonic series \\( \\sum_{n=1}^{\\infty} \\frac{(-1)^{n+1}}{n} \\).",
"role": "user"
}
] | \ln 2 |
[
{
"content": "Determine the maximum power of 2 that completely divides \\(3^{1024} - 1\\).",
"role": "user"
}
] | 12 |
[
{
"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... | 7.03 m/s |
[
{
"content": "Let the complex number \\( z = \\cos \\theta + \\mathrm{i} \\sin \\theta \\) where \\( 0^{\\circ} \\leqslant \\theta \\leqslant 180^{\\circ} \\). The complex numbers \\( z \\), \\( (1+\\mathrm{i})z \\), and \\( 2\\bar{z} \\) correspond to the points \\( P \\), \\( Q \\), and \\( R \\) on the compl... | 3 |
[
{
"content": "Find the last three digits of the sum \\( S = \\sum_{i=2}^{10^7} (i^7 + i^5) \\).",
"role": "user"
}
] | 998 |
[
{
"content": "Suppose \\( k \\) is a field that is finitely generated as a \\( \\mathbb{Z} \\)-algebra. Is \\( k \\) necessarily finite?",
"role": "user"
}
] | Yes |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.