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... | Common stock-$10 par value, 94,000 shares authorized, issued, and outstanding $940,000
Paid-in capital in excess of par value, common stock $326,000
Retained earnings $1,040,000
Total stockholders' equity $2,306,000 |
[
{
"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... | 6.46e+9 |
[
{
"content": "In the mad postman scenario, $n$ distinct parcels must be delivered to $n$ unique destinations. The postman assigns addresses randomly. Determine the expected number of parcels that are correctly delivered to their destinations.",
"role": "user"
}
] | 1 |
[
{
"content": "A particle is initially located at a point on a line. In the first second, it splits into two halves that move 1 unit apart in opposite directions. In each subsequent second, each resulting particle splits into two halves that move 1 unit apart from their previous positions. When two particles col... | 4 |
[
{
"content": "Find the sum of the infinite series: $$\\sum_{n=1}^{\\infty} \\frac{(-1)^n}{(n+1)(n+3)(n+5)}.$$",
"role": "user"
}
] | -\dfrac{7}{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... | 0.0149 M |
[
{
"content": "Calculate the arc length of the polar curve given by \\( r = a(1-\\cos\\theta) \\) over the interval \\( \\theta = 0 \\) to \\( \\theta = 2\\pi \\).",
"role": "user"
}
] | 8a |
[
{
"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... | 2.04 x 10^5 m/s |
[
{
"content": "Given three sets \\( A \\), \\( B \\), and \\( C \\) such that \\( n(A) + n(B) + n(C) = n(A \\cup B \\cup C) \\) and \\( |A| = |B| = 100 \\), find the minimum value of \\( |A \\cap B \\cap C| \\).",
"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... | 1 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... | 1. Information is transcribed in DNA to mRNA.
2. mRNA leaves the nucleus.
3. Ribosome attaches to the mRNA.
4. tRNA anticodon carries an amino acid that compliments the mRNA codon.
5. The chain of amino acids forms a protein. |
[
{
"content": "Compute the integral \\( \\int_C i^*\\eta \\) where \\( \\eta=(x^2+y^2)dz \\) and \\( C=\\{(x,y,-1): x^2+y^2=1\\} \\), with \\( i \\) being the inclusion map.",
"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... | 18.1% |
[
{
"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... | 3.0s |
[
{
"content": "If a function $f$ has a pole of order $k+1$ at $z_0$, find the residue of the function $\\frac{f'}{f}$ at $z_0$ in terms of $k$. Provide your answer in terms of $k$. \\( \\boxed{} \\)",
"role": "user"
}
] | - (k + 1) |
[
{
"content": "Calculate the length of the tangent vector \\( \\frac{\\partial}{\\partial \\theta} \\) at the north pole \\( N \\) of the sphere \\( \\mathbb{S}^2 \\) with radius \\( r \\), given the metric:\n\\[ g = r^2 \\, d\\varphi \\otimes d\\varphi + r^2 \\sin^2 \\varphi \\, d\\theta \\otimes d\\theta \\]\n... | 0 |
[
{
"content": "For any integer \\( n \\geq 1 \\), provide an example of a finite graph \\( G = (V, E) \\) such that its spatial dimension \\( \\text{dim}_s(G) = n \\).",
"role": "user"
}
] | K_{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... | 10.1m/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... | $2.91 |
[
{
"content": "Evaluate the limit \\(\\lim_{x\\rightarrow 0^{+}}\\left(3^{x}-2^{x}\\right)^{\\frac{1}{x}}.\\)",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the integral \\( \\iiint_{x^2+y^2+z^2 \\le z}\\sqrt{x^2+y^2+z^2}\\,dx\\,dy\\,dz \\) using spherical coordinates. Provide your answer to two decimal places.",
"role": "user"
}
] | 0.31 |
[
{
"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... | 7.80 |
[
{
"content": "Calculate the expected time until a bank balance, modeled by a Brownian motion with positive drift, first becomes negative.",
"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... | -2.0625 |
[
{
"content": "Vectors $\\mathbf{a}$ and $\\mathbf{b}$ satisfy $\\|\\mathbf{a}\\| = 3$ and $\\|\\mathbf{b}\\| = 8.$ Also, the angle between vectors $\\mathbf{a}$ and $\\mathbf{b}$ is $135^\\circ.$ Find $\\|2 \\mathbf{a} + \\mathbf{b}\\|^2.$",
"role": "user"
}
] | 100 - 48 \sqrt{2} |
[
{
"content": "Suppose \\(f(x)\\) is differentiable on \\((0,+\\infty)\\) and \\(\\lim_{x\\rightarrow +\\infty} \\frac{f(x)}{x}=0.\\) Prove that there exists a sequence \\(x_n\\rightarrow\\infty\\) such that \\(\\lim_{n\\rightarrow\\infty}f'(x_n)=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... | The ions can be separated by using sodium chloride, sodium hydroxide, and ammonium sulfide. Adding NaCl will precipitate the silver ions as AgCl. After precipitating the silver and lead ions, we make the solution basic by adding sodium hydroxide. The addition of ammonium sulfide precipitates the copper ions as CuS. |
[
{
"content": "Evaluate the surface integral \\( \\iint_\\Sigma \\mathbf{f} \\cdot d \\mathbf{a} \\) where \\( \\mathbf{f}(x,y,z)=(x^2,xy,z) \\) and \\( \\Sigma \\) is the part of the plane \\( 6x+3y+2z=6 \\) with \\( x,y,z\\geq 0 \\).",
"role": "user"
}
] | \dfrac{7}{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... | 3.99 s |
[
{
"content": "Evaluate the integral \\( I = \\int_{-\\infty}^{\\infty} \\frac{\\sin^2{x}}{x^2} \\, dx \\).",
"role": "user"
}
] | \pi |
[
{
"content": "Evaluate the contour integral \\( \\int_\\beta \\frac{e^z}{e^z-\\pi} \\mathrm{d}z \\), where \\( \\beta \\) is a loop in the annulus \\( \\{z:10<|z|<12\\} \\) that winds \\( N \\) times about the origin in the counterclockwise direction, and \\( N \\) is an integer.",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether the limit of the recursive sequence \\(a_{n+1}=\\frac{n+1}{\\frac{1}{a_{n}}-(n+1)}\\) converges to the same value regardless of the initial value \\(a_0\\). If it does, find the limit of the sequence.",
"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... | 136.82 g/mol |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 109.8 J/K |
[
{
"content": "Find the limit of the expression \\( \\frac{1}{n}\\left[1+2\\sum_{k=1}^{n-1}\\sqrt{1-\\frac{n-k}{n}}\\right] \\) as \\( n \\to \\infty \\).",
"role": "user"
}
] | \dfrac{4}{3} |
[
{
"content": "Evaluate the limit: $$ \\lim_{x\\to+\\infty}\\left(\\frac{2}{\\pi}\\text{arccot}\\;x\\right)^{x} $$",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the limit \\( \\lim_{n\\to\\infty} \\frac{a_n}{n^2} \\), where \\( a_n \\) is the sum of all roots \\( x_1, x_2, \\ldots, x_k \\) of the equation \\( f(x) = \\frac{x}{2n} \\) for \\( f(x) = \\sin(\\pi x) \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether the following statement is true or false: In any compact metric space \\( X \\), every sequence \\( \\{x_n\\} \\subset X \\) has an accumulation point in \\( X \\), but not necessarily a limit in \\( X \\).",
"role": "user"
}
] | A |
[
{
"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-5 mol NaF |
[
{
"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... | 5.6e-5 |
[
{
"content": "Express the sum \\( \\left[\\frac{n+1}{2}\\right]+\\left[\\frac{n+2}{4}\\right]+\\cdots+\\left[\\frac{n+2^{i}}{2^{i+1}}\\right]+\\cdots \\) as a simple function of the positive integer \\(n\\).",
"role": "user"
}
] | 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... | 2.1e2 atm |
[
{
"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... | 0.00995N |
[
{
"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... | 157.5 m |
[
{
"content": "Let $X$ be a set. Define mappings $F, G : \\text{Map}(X, X)\\times\\text{Map}(X, X)\\to\\text{Map}(X, X)$ such that $F(f, g) = f\\circ g$ and $G(f, g) = g\\circ f$. What is the necessary and sufficient condition on $X$ that ensures $F=G$?",
"role": "user"
}
] | |X| \leq 1 |
[
{
"content": "Let $f_1(x) = x^2 - 1$, and for each positive integer $n \\geq 2$, define $f_n(x) = f_{n-1}(f_1(x))$. Determine the number of distinct real roots of the polynomial $f_{2004}(x)$. \\( \\text{Express your answer as a single integer.} \\)",
"role": "user"
}
] | 2005 |
[
{
"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... | 1887.78 |
[
{
"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... | April: $199,500
May: $192,500
June: $221,500 |
[
{
"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... | 3.18 m/s^2 |
[
{
"content": "Determine whether the statistic \\( T(\\mathbf{X}) = (\\min(\\mathbf{X}), \\max(\\mathbf{X})) \\) is a minimal sufficient statistic for \\( \\theta \\) when \\( \\mathbf{X} \\) is a random sample from a Uniform\\((\\theta, \\theta+1)\\) distribution.",
"role": "user"
}
] | Yes |
[
{
"content": "In triangle ABC, AB = 2017 units. O is the midpoint of AB. D is an interior point of triangle ABC such that \\( \\angle DAP = \\angle DBQ \\). Find the value of \\( OP - OQ \\).",
"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... | $180 million |
[
{
"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... | 74246-26 |
[
{
"content": "Compute the expectation \\( \\sum_{n=0}^{\\infty} nP_{n} \\) given the following conditions: \\( G(n) = e^{-\\lambda} \\cdot \\frac{\\lambda^n}{n!} \\) for \\( \\lambda > 0 \\), and \\( \\sum_{j=0}^{n} G(j)P(n-j) + (n+1)[P(n+1)-P(n)] = 0 \\) for all \\( n \\in \\mathbb{N} \\), with \\( \\sum_{n=0}... | \lambda |
[
{
"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... | 8.95 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\rightarrow \\infty}\\left(\\frac{\\sin ^3n^2-5\\cdot \\sin ^2n^2+3}{\\sqrt{\\ln \\left( \\left| \\dfrac{1}{\\tan ^{19}e^ {- n }}+3\\right| \\right)+\\sin \\left( \\dfrac{1}{\\tan ^{24}e^ {- n }} \\right)}}\\right) \\]",
"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... | W = (1/2)(Q^2/C) = (1/2)QV |
[
{
"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... | 27350 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... | $110,000 |
[
{
"content": "Calculate the length of the closed curve defined by the equation \\(x^{2/3} + y^{2/3} = 4\\).",
"role": "user"
}
] | 48 |
[
{
"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... | -7,590.36 GBP |
[
{
"content": "Determine whether the following inequality holds for all points $x, y$ on the boundary of a bounded, convex domain $\\Omega \\subset \\mathbb{R}^n$ (with $0 \\in \\Omega$): $$ C_2\\left|x-y\\right|^2\\leq\\left|\\frac{x}{|x|}-\\frac{y}{|y|}\\right|^2\\leq C_1\\left|x-y\\right|^2, \\forall x,y\\in ... | Yes |
[
{
"content": "Find the values of \\( \\lambda \\) for which the system of equations \\( \\sin x \\cos y = 2\\lambda - 4 \\) and \\( \\sin y \\cos x = 1- \\lambda \\) has solutions.",
"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... | 6.03 |
[
{
"content": "Given positive integers \\( a, b, \\) and \\( c \\) such that \\( a < b < c \\), and the product of any two numbers minus 1 is divisible by the third number, find the value of \\( a^{2} + b^{2} + c^{2} \\).",
"role": "user"
}
] | 38 |
[
{
"content": "A triangular array of squares has one square in the first row, two in the second, and in general, $k$ squares in the $k$th row for $1 \\leq k \\leq 11.$ With the exception of the bottom row, each square rests on two squares in the row immediately below (illustrated in the given diagram). In each s... | 640 |
[
{
"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... | 2.00619 sec |
[
{
"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 amount of antimony in the sample is 1.99 g and the percentage in the sample is 20.7%. |
[
{
"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... | 0.109e20 m/s^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... | 4.27 years |
[
{
"content": "Determine whether the function \\( f(x) = \\sum_{n=1}^{\\infty}\\frac{(-1)^n}{n^2+1} x^n \\) is concave up at \\( x = 0 \\).",
"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... | \epsilon^2\left(y^{(4)}+y\right)-y^{(2)}=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... | 2.5 A |
[
{
"content": "Evaluate the limit \\( \\lim_{n \\to \\infty} g_n(x) \\), where \\( g_n(x) = \\frac{n^2x}{(1+x)^n} \\) for \\( x > 0 \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether a continuous function \\( f:\\mathbb{R}\\rightarrow\\mathbb{R} \\), which maps every subgroup \\( G \\) of \\( \\mathbb{R} \\) to a subgroup of \\( \\mathbb{R} \\), must be an endomorphism of \\((\\mathbb{R},+)\\) in the form \\( f(x)=ax \\) for some real number \\( a \\).",
... | f(x) = ax |
[
{
"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... | 11.29% |
[
{
"content": "Find the probability limit for the connectivity of a complete bipartite random graph $G(n,n,p)$ in the Erdős-Rényi model when $np = \\ln n + w(n)$, with $w(n) \\rightarrow -\\infty$ as $n \\rightarrow \\infty$. Specifically, calculate:\n\n\\[\n\\lim_{n\\rightarrow\\infty}\\mathbb{P}[G(n,n,p) \\tex... | 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... | $141,498.62 |
[
{
"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... | 0.5986 |
[
{
"content": "What is the smallest positive integer with exactly 10 positive integer divisors?",
"role": "user"
}
] | 48 |
[
{
"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... | 1.12 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... | 10.58 and -10.58 |
[
{
"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... | C6H12O6 + 4Cr2O7(2-) + 32H+ -> 6CO2 + 8Cr(3+) + 22H2O |
[
{
"content": "Given the polynomial $f(x) = ax^2 + bx + c$, where $f(0) = 0$ and $f(2) = 2$, find the minimum value of the integral $\\int_{0}^{2} |f'(x)| \\, dx$. Provide your answer as a single numerical value.",
"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... | 108433.87 |
[
{
"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... | -$66,460.79 |
[
{
"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... | 5.60 |
[
{
"content": "If \\(a_n \\ge b_n \\ge 0\\) and \\(\\sum a_n\\) is divergent, does this imply that \\(\\sum b_n\\) is also divergent? Answer 'yes' or 'no' and justify your answer.",
"role": "user"
}
] | no |
[
{
"content": "Calculate the expectation \\( \\text{E}[X(X - 1) \\ldots (X - k + 1)] \\) where \\( X \\) is a Poisson-distributed random variable with parameter \\( \\lambda \\), and \\( k \\in \\mathbb{N} \\) is fixed.",
"role": "user"
}
] | \lambda^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... | 9.07% |
[
{
"content": "A die is initially placed with the number 6 on top. It is then turned randomly to one of the four adjacent faces. Let $P_n$ be the probability that after $n$ such turns, the die will again show the number 6 on top. Determine the limit $\\lim_{n \\to \\infty} P_n$. \\( \\text{Express your answer as... | \dfrac{1}{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... | 23.8 degrees Celsius |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\to\\infty} \\frac{x^2\\left(2-e^{-z/x}-e^{z/x}\\right)}{z^2} \\] without using L'Hopital's rule or any trigonometric limits.",
"role": "user"
}
] | -1 |
[
{
"content": "Given an open set $O$ in a topological space and a point $x \\in O$, determine whether there always exists a non-empty connected open set $U \\subset O$ with $x \\in U$. Provide a justification for your answer.",
"role": "user"
}
] | No |
[
{
"content": "Let $0 \\le x, y, z \\le 3$. Determine the maximum value of the expression \\[ M = \\sqrt{x^2 + y^2 - 2xy} + \\sqrt{y^2 + z^2 - 2yz} + \\sqrt{z^2 + x^2 - 2xz}. \\]",
"role": "user"
}
] | 6 |
[
{
"content": "Given that the real numbers \\( a \\) and \\( b \\) satisfy that both quadratic trinomials \\( x^2 + ax + b \\) and \\( x^2 + bx + a \\) have two distinct real roots each, and the product of their roots results in exactly three distinct real roots, find all possible values of the sum of these thre... | 0 |
[
{
"content": "In an acute triangle $\\triangle ABC$, $AD$ is the altitude from $A$ to $BC$, and $CE$ is the angle bisector of $\\angle ACB$. Given that $\\angle CEA = 45^\\circ$, find the measure of $\\angle EDB$. \\(\\text{Express your answer in degrees.}\\)",
"role": "user"
}
] | 45 |
[
{
"content": "If two congruent $n \\times n$ matrices $A$ and $B$ are both diagonalized with all non-zero eigenvalues, and the eigenvalues are ordered in descending order down the diagonal, must the number of positive eigenvalues of $A$ be equal to the number of positive eigenvalues of $B$? Justify your answer ... | 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... | Net sales $270,000
Cost of goods sold 165,000
Gross Profit 105,000
Interest expense 3,000
Selling expenses 15,000
Administrative expenses 35,000
Income from continuing operations 52,000
Discontinued operations loss 20,000
Income or Loss before tax 32,000
Income tax expense 9,600
Net income 22,400 |
[
{
"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... | |U| = \frac{F_0}{\sqrt{\left[\left(M(jw)^2 + K\right)^2 + \left(\eta(jw)\right)^2\right]}} |
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