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... | 0.90 |
[
{
"content": "Determine which of the following combinations represents the general solution of a second-order non-homogeneous linear differential equation with the given solutions $y_1(x)=1+xe^{x^2}$, $y_2(x)=(1+x)e^{x^2}-1$, and $y_3(x)=1+e^{x^2}$:\n\n1. $(C_1+1)y_1+(C_2-C_1)y_2-C_2y_3$\n2. $C_1(y_1-y_2)+C_2(y... | 4 |
[
{
"content": "Find the function $f(n)$ such that \\( \\binom{\\binom{n}{2}}{2} = 3\\binom{f(n)}{4} \\).",
"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... | 19.2 m/s^2 |
[
{
"content": "Given that the domain of the function \\( f(x) \\) is \\( (0, \\infty) \\), and it satisfies the equation \\( f(x) - 2x f\\left(\\frac{1}{x}\\right) + 3x^2 = 0 \\), find the minimum value of \\( f(x) \\).",
"role": "user"
}
] | 3 |
[
{
"content": "Let $A$ be an $n \\times n$ matrix, and $B$ be an $n \\times m$ matrix with $m \\leq n$. If $\\text{rank}[A\\ B]=n$, determine if $\\text{rank}[A\\ B B^T]=n$.",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | (R-r)\dot{\theta}=R\dot{\psi}-r\dot{\phi} |
[
{
"content": "Evaluate the limit: $$\\lim_{b \\to 0}\\int _0^{\\infty}\\frac{\\left(x^2-1\\right)\\cos \\left(bx\\right)}{\\left(x^2+1\\right)^2}dx$$ using real analysis methods.",
"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... | 13.98% |
[
{
"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... | 87.6e6 J |
[
{
"content": "Determine the maximum number of distinct fourth-order partial derivatives of a function \\( f: \\mathbb{R}^7 \\to \\mathbb{R} \\) that is \\( C^4 \\) at the origin. Consider all combinations of \\( \\frac{\\partial^4 f}{\\partial x_{i_4}\\partial x_{i_3}\\partial x_{i_2}\\partial x_{i_1}}(0) \\), ... | 210 |
[
{
"content": "In a $5 \\times 5$ grid, there is one correct square in each row. You start by picking any of the five squares in the first row. From each square, you can move forward, forward and up, or forward and down to the next row. The correct path is guaranteed to be contiguous. What is the probability tha... | \dfrac{1}{259} |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\to 0} \\frac{(1+3x+2x^2)^{1/x} - (1+3x-2x^2)^{1/x}}{x} \\]",
"role": "user"
}
] | 4e^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... | 82 degrees Celcius |
[
{
"content": "Evaluate the integral \\( \\int_{-\\infty}^\\infty \\frac{\\sin x}{x-i} \\, dx \\).",
"role": "user"
}
] | \dfrac{\pi}{e} |
[
{
"content": "Find the minimum value of \\(|5^{4m+3} - n^2|\\) for positive integers \\(n\\) and \\(m\\).",
"role": "user"
}
] | 275 |
[
{
"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... | $37,500 |
[
{
"content": "Evaluate the integral \\( \\int^{+\\infty}_0 \\frac{e^{-x^2}}{(x^2+\\frac{1}{2})^2} \\, dx \\).",
"role": "user"
}
] | \sqrt{\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... | 200 rackets |
[
{
"content": "Find the residue of \\( \\left(\\frac{z+1}{3z-2}\\right)^2 \\) at the pole \\( z=\\frac{2}{3} \\).",
"role": "user"
}
] | \dfrac{10}{27} |
[
{
"content": "Evaluate \\( \\lfloor (3 + \\sqrt{5})^{34} \\rfloor \\pmod{100} \\) without using a calculator.",
"role": "user"
}
] | 47 |
[
{
"content": "Calculate the flux integral \\(\\int_S (\\nabla \\times \\vec{F}) \\cdot \\vec{n} \\, dS\\) where \\(\\vec{F} = (y,z,x^2y^2)\\) and \\(S\\) is the surface given by \\(z = x^2 + y^2\\) with \\(0 \\leq z \\leq 4\\), oriented so that \\(\\vec{n}\\) points downwards.",
"role": "user"
}
] | 4\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... | 0.5 bananas per apple |
[
{
"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... | cognitive reserve hypothesis |
[
{
"content": "Given complex numbers \\( z_{1}, z_{2}, z_{3} \\) such that \\( \\left|z_{1}\\right| \\leq 1 \\), \\( \\left|z_{2}\\right| \\leq 1 \\), and \\( \\left|2 z_{3}-\\left(z_{1}+z_{2}\\right)\\right| \\leq \\left|z_{1}-z_{2}\\right| \\), determine the maximum value of \\( \\left|z_{3}\\right| \\).",
... | \sqrt{2} |
[
{
"content": "Find the Laurent series of the function \\( f(z) = \\frac{2}{z} - \\frac{3}{z-2} + \\frac{1}{z+4} \\) in all possible regions of convergence about \\( z=0 \\). Determine the residue of \\( f(z) \\) at \\( z=0 \\).",
"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... | 24.0 |
[
{
"content": "The circle graph below represents the opinions of $100$ students about their favorite sports. Each student chose exactly one of these four options: Basketball, Hockey, Football, and Other. The following statements are true about the graph:\n\n$\\bullet$ The number of students who chose Basketball... | 30\% |
[
{
"content": "Let \\( S \\) be the surface defined by \\( \\{(x,y,z) : x^{2} + y^{2} + 2z = 2, z \\geq 0 \\} \\). Given the vector field \\( \\mathbf{F} = (y, xz, x^{2} + y^{2}) \\), find the net flux of \\( \\mathbf{F} \\) through the surface \\( S \\). Assume \\( \\mathbf{n} \\) is the outward normal vector."... | 2\pi |
[
{
"content": "Find all pairs of prime numbers \\((p, q)\\) such that \\(p^2 - 2q^2 = 17\\).",
"role": "user"
}
] | (5, 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... | $2,232,099.51 |
[
{
"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... | 25.816% |
[
{
"content": "If $z$ is a complex number such that $|z^3 + z^{-3}| \\leq 2$, determine the maximum possible value of $|z + z^{-1}|$. Choose the correct option:\n(A) $2$\n(B) $2^{1/3}$\n(C) $2\\sqrt{2}$\n(D) $1$",
"role": "user"
}
] | A |
[
{
"content": "Evaluate the limit \\(\\lim_{x\\to 0^+}\\cfrac{x^{e^{x\\log(x) - 1}}}{x}.\\)",
"role": "user"
}
] | \infty |
[
{
"content": "How many multiples of $17$ are greater than $-50$ and less than $50$?",
"role": "user"
}
] | 5 |
[
{
"content": "Given that \\( 0 < x < \\frac{\\pi}{2} \\) and \\( \\sin x - \\cos x = \\frac{\\pi}{4} \\), and \\( \\tan x + \\frac{1}{\\tan x} = \\frac{a}{b - \\pi^c} \\), where \\( a, b, \\) and \\( c \\) are positive integers, find the value of \\( a + b + c \\).",
"role": "user"
}
] | 50 |
[
{
"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... | 5.68 cm |
[
{
"content": "In trapezoid \\(ABCD\\), squares \\(ADEF\\) and \\(BCGH\\) are constructed on the bases \\(AD\\) and \\(BC\\) outside the trapezoid. The diagonals of the trapezoid intersect at point \\(O\\). Given that \\(BC = 2\\), \\(GO = 7\\), and \\(GF = 18\\), find the length of segment \\(AD\\).",
"role... | \dfrac{22}{7} |
[
{
"content": "Let $A, B \\in M_n$ and suppose $AA^* = BB^*$. Is it true that there exists a unitary matrix $U$ such that $A = BU$?",
"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... | 67,045 |
[
{
"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... | 3.29 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... | 781 atoms |
[
{
"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... | 1.61e6 N/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... | 0.20 |
[
{
"content": "Consider a sequence \\(a_{1}, a_{2}, a_{3}, a_{4}, \\cdots\\), with \\(a_{1}=\\frac{1}{2}\\), defined by the relation \\( a_{n}=2 a_{n} a_{n+1}+3 a_{n+1} \\) for all \\(n=1,2,3, \\cdots\\). Define another sequence \\(b_{n}=1+\\frac{1}{a_{n}}\\) for all \\(n=1,2,3, \\cdots\\). Determine the largest... | 35 |
[
{
"content": "Given an orthonormal basis $\\{\\varphi_n\\}$ of the space $L^2(E)$, for any function $f\\in L^2(E)$, the series representation is\n\\[ f=\\sum_{n=1}^{\\infty}\\langle f,\\varphi_n\\rangle\\varphi_n, \\]\nwhere the series converges absolutely. Consequently, as $n$ approaches infinity, the absolute... | Yes |
[
{
"content": "The area of a triangle is 600 square feet. Find the altitude, in feet, of the triangle if the length of the corresponding base is 30 feet.",
"role": "user"
}
] | 40 |
[
{
"content": "Let $f(X)$ be an irreducible polynomial over $\\mathbf{Q}$ with odd degree and one real root. If all real embeddings of $\\mathbf{Q}(x)$ into $\\mathbb{R}$ preserve the sign of the real root $x$, does the coefficient $a_0$ of $f(X)$ have the same sign as $x$? Answer with 'yes' or 'no'.",
"role... | no |
[
{
"content": "Express the sum of the series \\( \\sum_{n=1}^{\\infty} \\frac{(-1)^n}{n^2} \\) in terms of \\( s \\), where \\( s = \\sum_{n=1}^{\\infty} \\frac{1}{n^2} \\).",
"role": "user"
}
] | -\dfrac{s}{2} |
[
{
"content": "If $a$ and $b$ are integers with $a > b$, what is the smallest possible positive value of $\\frac{a+b}{a-b} + \\frac{a-b}{a+b}$?",
"role": "user"
}
] | 2 |
[
{
"content": "Find the volume of the solid generated by rotating the region bounded by \\( y = \\begin{cases}\\frac{\\sin x}{x}&\\text{ if }x>0\\\\1&\\text{ if }x=0\\end{cases} \\), \\( y = 0 \\), \\( x = 0 \\), and \\( x = \\pi \\) about the \\( y \\)-axis using the method of cylindrical shells.",
"role": ... | 4\pi |
[
{
"content": "Determine the minimum positive integer value of $n$ for which the expression \\(\\dfrac{(2i)^n}{(1+i)^{n-4}}\\) is a negative integer.",
"role": "user"
}
] | 8 |
[
{
"content": "Given a family of $R$-modules $\\{ P_{i}\\} _{i\\in I}$, if the direct sum $\\oplus_{i\\in I}P_{i}$ is a projective module, does it imply that each module $P_{i}$ is projective for all $i\\in I$? Answer 'yes' or 'no' and justify 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... | ```
Particulars | Actual | Flexible budget | variance | Flexible budget
---|---|---|---|---| Activity level | 360 | 360
Variable expense:
Indirect material | 4,182 | 4,392 | 210 F
Electricity | 2,536 | 2,556 | 20 F
Total variable expense | 6,718 | 6,948 | 230 F
Fixed cost:
Administrative | 6,540 | 6,500 | 40 U
Rent | 6,310 | 6,400 | 90 F
Total fixed expense | 12,850 | 12,900 | 50 F
``` |
[
{
"content": "Evaluate the limit: $$\\lim_{{x \\to \\infty}} \\left[(x+3)^{1 + \\frac{1}{x}} - x^{1 + \\frac{1}{x+3}}\\right]$$",
"role": "user"
}
] | 3 |
[
{
"content": "Find a natural number whose Collatz sequence length exceeds the logarithmic trend of $\\ln(x)^C$, where $C$ is a constant.",
"role": "user"
}
] | 27 |
[
{
"content": "Given that $X$ and $Y$ are continuous random variables with the joint density function: \\[ f_{X,Y}(x,y) = \\begin{cases} 24xy & \\text{if } 0 < x < 1, \\ 0 < y < 1, \\ 0 < x + y < 1 \\\\ 0 & \\text{otherwise} \\end{cases} \\] find the probability density function of $Z = X + Y$. Express your answ... | 4z^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... | 12 Hz |
[
{
"content": "Given positive numbers $a$ and $b$ such that $\\frac{2}{a} + \\frac{1}{b} = 1$, determine the minimum value of the expression $a + b + \\sqrt{a^2 + b^2}$.",
"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... | 1.2755 m |
[
{
"content": "If \\(\\lim\\limits_{n\\to \\infty}a_n=a\\), determine the value of \\(\\lim\\limits_{n\\to \\infty}\\frac{1}{\\ln(n)}\\sum_{r=1}^{n}\\frac{a_r}{r}\\). Choose the correct option:\n\n(A) 0\n(B) \\(a\\)\n(C) \\(\\frac{a}{2}\\)\n(D) None of these",
"role": "user"
}
] | B |
[
{
"content": "For a random walk in $\\mathbb{Z}^2$ with increments having finite support and an expectation vector on the horizontal axis, determine whether the probability of first intersecting a vertical line at a given height scales with $t$ or $\\sqrt{t}$ as $t$ approaches infinity.",
"role": "user"
}... | \sqrt{t} |
[
{
"content": "If a function $f$ is of bounded variation on the interval $[a,b]$, is $f$ Riemann integrable on $[a,b]$?",
"role": "user"
}
] | Yes |
[
{
"content": "Given a non-negative integer $N$, a positive constant $C$, and a real number $x$, determine whether there exists a function $f \\in C^{\\infty}_c(\\mathbb{R})$ with compact support such that $\\partial^{N+1}f(x) > C\\sum_{k=1}^{N}\\sup|\\partial^{k} f|$. Assume $x=0$ to simplify the problem.",
... | Yes |
[
{
"content": "Evaluate the limit: $$ \\lim_{x\\to0} \\frac{\\left(1+\\sin{x}+\\sin^2{x}\\right)^{\\frac{1}{x}} - \\left(1+\\sin{x}\\right)^{\\frac{1}{x}}}{x} $$",
"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... | 602 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... | 6.45e+24 kg |
[
{
"content": "How many degrees are in the sum of the measures of the six numbered angles pictured? [asy]\ndraw((3,8)--(10,4)--(1,0)--cycle,linewidth(1));\ndraw((7,8)--(9,0)--(0,4)--cycle,linewidth(1));\nlabel(\"1\",(3,8),SSE);\nlabel(\"2\",(7,8),SSW);\nlabel(\"3\",(10,4),2W);\nlabel(\"4\",(9,0),NW+NNW);\nlabel(... | 360^\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... | 764937.0537 m/s |
[
{
"content": "Let $f:[0,1]\\rightarrow\\mathbb{R}$ be a measurable function. Define $F(x,y) = f(x) - f(y)$. Is the function $F$ necessarily measurable on the product space $[0,1] \\times [0,1]$?",
"role": "user"
}
] | Yes |
[
{
"content": "Given Stirling's approximation for $n!$ as $n! \\sim c\\sqrt{n}\\left(\\frac{n}{e}\\right)^n$, find the constant $c$ such that $c = \\sqrt{2\\pi}$.",
"role": "user"
}
] | \sqrt{2\pi} |
[
{
"content": "Find the number of positive integers that are the products of exactly three distinct primes \\(p_1\\), \\(p_2\\), and \\(p_3\\) such that \\(p_1 + p_2 + p_3 = a + b + c\\), where \\(5002 = a \\cdot b \\cdot c\\) and \\(a\\), \\(b\\), and \\(c\\) are distinct primes.",
"role": "user"
}
] | 8 |
[
{
"content": "Find the minimum value of the expression \\[ P = \\frac{x^2}{\\sqrt{x^3+8}} + \\frac{y^2}{\\sqrt{y^3+8}} + \\frac{z^2}{\\sqrt{z^3+8}} \\] given that \\( x, y, z \\) are positive real numbers such that \\( xy + yz + zx = 3 \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Find the shortest distance from the origin to the surface defined by the equation $xyz^2 = 2$. Express your answer in simplest form.",
"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... | go beyond the words of a constitution or statute to consider the broader societal implications of their decisions. |
[
{
"content": "Determine the order of the image of the homomorphism \\( \\varphi: \\mathbb{Z}^2 \\to S_{15} \\) given by \\( \\varphi(1,0)=(2,7,3)(3,11,5)(12,13) \\) and \\( \\varphi(0,1)=(14,15)(1,4,6,8,9,10) \\).",
"role": "user"
}
] | 60 |
[
{
"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... | 3.224% |
[
{
"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... | $162,143.11 |
[
{
"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... | /cimages/multimages/16/untitled687712485417641437318.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... | _{6}^{13} 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... | TITOV COMPANY
Internal Income Statement for 2014
Budget Actual Variance
Sales $502,000 $493,600 $8,400 U
Variable expenses:
Product costs $(191,000) 186,400 $4,600 F
Selling expenses (46,000) 48,000 2,000 U
Other expenses (3,000) 4,600 1,600 U
Contribution margin $262,000 $254,600 $7,400 U
Fixed expenses:
Product costs $(15,700) 15,400 $300 F
Selling expenses (23,900) 23,470 430 F
Other expenses (1,700) 1,890 190 U
Operating income (loss) $220,700 $213,840 $6,860 U
Interest expense (700) 560 140 F
Net income (loss) $220,000 $213,280 $6,720 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... | 46.35 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... | 8.41 % |
[
{
"content": "Calculate the sum \\( S = f\\left(\\frac{1}{2009}\\right) + f\\left(\\frac{2}{2009}\\right) + f\\left(\\frac{3}{2009}\\right) + \\cdots + f\\left(\\frac{2008}{2009}\\right) \\) where \\( f(x) = \\frac{1}{e^{1-2x} + 1} \\).",
"role": "user"
}
] | 1004 |
[
{
"content": "Two of the roots of\n\\[ax^3 + (a + 2b) x^2 + (b - 3a) x + (8 - a) = 0\\]are $-2$ and 3. Find the third root.",
"role": "user"
}
] | \frac{4}{3} |
[
{
"content": "Let $f: [0, 1] \\rightarrow \\mathbb{R}^+$ be a continuous density function with cumulative distribution function $F$. Assume $f > 0$ over $(0, 1)$ and that the function \\( \\frac{1 - F(x)}{f(x)} \\) is decreasing. Determine if \\( \\lim_{x \\rightarrow 1} \\frac{1 - F(x)}{f(x)} = 0 \\) when $f(1... | 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... | 4.43m/s |
[
{
"content": "Given a directed multigraph $G$ of arbitrary cardinality, determine whether there exists a $G$-spacious topological space $T$ that is clean or admits an embedding of $G$. Consider known results such as: \\(\\mathbb{R}^2\\) admits clean $G$-drawings for finite and some countable graphs, and embeddi... | 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... | Evaluation of gross profit margin, operating profit margin, and net profit margin |
[
{
"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... | -247.5 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... | 21.48 degrees |
[
{
"content": "Compute the sum of the series \\( \\sum_{k=1}^{\\infty} \\frac{k^2}{k!} \\).",
"role": "user"
}
] | 2e |
[
{
"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... | 223.2 g Fe |
[
{
"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... | 61.95 ft |
[
{
"content": "Given a continuous function $f(x)$ defined for $1 \\leq x \\leq 3$, where $f(x)$ assumes only rational values, and $f(2) = 10$, find the value of $f(1.5)$. \\( \\boxed{10} \\)",
"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... | 0.038 M |
[
{
"content": "Evaluate the limit \\( \\lim_{x\\rightarrow 0}{\\frac{(2+x)^x-2^x}{x^2}} \\) using Taylor series expansions and the concept of equivalents, such as \\(\\sin x \\sim x\\), \\(\\ln(1+x) \\sim x\\), and \\(a^x - 1 \\sim x \\ln a\\).",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Is there an injective map \\( f: \\mathbb{R}^{2} \\to \\mathbb{R} \\) such that the Euclidean metric \\( d^2 \\) on \\( \\mathbb{R}^2 \\) is equal to the pullback metric \\( f^*d^1 \\) on \\( \\mathbb{R} \\)?",
"role": "user"
}
] | No |
[
{
"content": "Given that \\( x, y, z \\) are positive numbers such that \\( x^2 + y^2 + z^2 = 1 \\), find the minimum value of the expression:\n\\[ \nS = \\frac{xy}{z} + \\frac{yz}{x} + \\frac{zx}{y}.\n\\]",
"role": "user"
}
] | \sqrt{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... | 116.31 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.