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... | 28 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... | 60000 units |
[
{
"content": "Given that $X$ and $Y$ are independent random variables with moment generating functions $M_x(t) = \\frac{(8+e^t)^2}{81}$ and $M_y(t) = \\frac{(1+3e^t)^3}{64}$, respectively, find the probability $P(X+Y = 1)$. Provide your answer as a single probability value.",
"role": "user"
}
] | \dfrac{37}{324} |
[
{
"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... | Meiosis consists of two divisions: Meiosis I and Meiosis II.
Meiosis I:
Prophase I: Chromosomes condense, nuclear membrane dissolves, homologous chromosomes form bivalents, and crossing over occurs.
Metaphase I: Spindle fibers attach to centromeres and align chromosomes at the center.
Anaphase I: Homologous chromosom... |
[
{
"content": "What is the area, in square units, of an isosceles right triangle with a hypotenuse of 20 units?",
"role": "user"
}
] | 100\text{ square units} |
[
{
"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... | $368,261.12 |
[
{
"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... | 8,100 kg 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... | Magnitude: 3.23 N
Direction: South |
[
{
"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... | 12.85 |
[
{
"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... | 5.18% |
[
{
"content": "Find the splitting field of the polynomial \\( f(x) = x^{p^8} - 1 \\) over the field \\( \\mathbb{Z}_p \\).",
"role": "user"
}
] | \mathbb{Z}_p |
[
{
"content": "Evaluate the integral \\( \\int_0^{\\pi} \\cos(x)\\, dx \\) using the Riemann sum and the formula \\( \\sum_{i=1}^n \\cos(i\\beta) = \\frac{\\sin(\\frac{(n+1)\\beta}{2})\\cos(\\frac{n\\beta}{2})}{\\sin(\\frac{\\beta}{2})} \\).",
"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... | -0.1167 m/s |
[
{
"content": "Evaluate the limit: $$ \\lim_{x\\to\\infty} (\\sqrt[100]{(x + 3)(x + 6)...(x + 300)} - x) $$",
"role": "user"
}
] | \dfrac{303}{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... | 65.21 m/s |
[
{
"content": "Find the smallest integer $n$ such that there are more groups of order $n$ than the integer $n$ itself.",
"role": "user"
}
] | 32 |
[
{
"content": "Determine the number of ways to distribute 15 distinct balls into 5 indistinguishable boxes.",
"role": "user"
}
] | 255514355 |
[
{
"content": "Two subgroups H and K of a group G have orders 12 and 30, respectively. Determine which of the following could NOT be the order of the subgroup of G generated by H and K:\n\nA. 30\nB. 60\nC. 120\nD. 360\nE. Countable infinity",
"role": "user"
}
] | A |
[
{
"content": "In triangle $\\triangle{ABC}$, $\\angle{ABC}=90^{\\circ}$, $AB=BC$, and $AC=\\sqrt{3}-1$. Determine the minimum value of $AP+BP+CP$ for any point $P$ in the plane of $\\triangle{ABC}$.",
"role": "user"
}
] | 1 |
[
{
"content": "Let $f(x)$ be a differentiable function, and suppose there exists some $a$ where $f'(a) \\ne 0$. Calculate the limit:\n\\[ \\lim_{h\\rightarrow0}\\frac{f(a+3h)-f(a-2h)}{f(a-5h)-f(a-h)}. \\]",
"role": "user"
}
] | -\dfrac{5}{4} |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\rightarrow 0^+} \\frac{\\log(x+\\sqrt{1+x^2})-\\sin x}{(2^{x^2}-1)(\\sin (e^{x^2}-1))} = 0. \\]",
"role": "user"
}
] | 0 |
[
{
"content": "Find the closed form expression for the sequence of numbers represented by the sum: \\[ \\sum_{k=0}^n \\binom{n}{k}^2 \\] where \\( n \\) is a non-negative integer.",
"role": "user"
}
] | \dbinom{2n}{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... | 1211.4376 kg/m^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... | 5.55 |
[
{
"content": "Calculate the limit: \\[ \\lim_{x \\rightarrow 0} \\frac{2x - \\sqrt[3]{8 - x^2}\\sin x}{1 - \\cos\\sqrt{x^3}} \\]",
"role": "user"
}
] | \dfrac{5}{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... | -0.114kJ/K |
[
{
"content": "Determine if there exists a solution in positive integers for the system of equations: \\[ \\begin{array}{l} x_{1}^{2}+x_{2}^{2}+\\cdots+x_{1985}^{2}=y^{3}, \\\\ x_{1}^{3}+x_{2}^{3}+\\cdots+x_{1985}^{3}=z^{2} \\end{array} \\] where $x_{i} \\neq x_{j}$ for $i \\neq j$. Answer with 'yes' or 'no'.",
... | yes |
[
{
"content": "Evaluate the limit \\(\\lim_{n\\rightarrow \\infty}\\left\\{\\left(2+\\sqrt{3}\\right)^{2n}\\right\\},\\) where \\(n\\in \\mathbb{N}.\\)",
"role": "user"
}
] | 1 |
[
{
"content": "Evaluate the integral \\( F(y) = \\int_{-\\infty}^{\\infty} \\frac{dx}{(1+x^2)(1+(x+y)^2)} \\).",
"role": "user"
}
] | \dfrac{2\pi}{y^2 + 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... | 5.4e-3 m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 119.93 |
[
{
"content": "Let N couples be randomly seated at a rectangular table, with men on one side and women on the other. Define the random variable X as the number of couples seated directly across from each other. Calculate the variance of X.",
"role": "user"
}
] | 1 |
[
{
"content": "Let $A$ be a real $n \\times n$ matrix and $p(x)$ be a polynomial. Determine if $p(\\lambda)$ is an eigenvalue of $p(A)$ given that $\\lambda$ is an eigenvalue of $A$. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine if the operator \\(T: C([0,1]) \\to C([0,1])\\) defined by \\[Tf(x) = x^2+ \\int_{0}^1 \\frac{1}{10+|x-t|^2}(f(t)+1)^2 \\ dt\\] is a contraction mapping on the closed ball \\(B\\) of radius \\(3\\) centered at the zero function.",
"role": "user"
}
] | Yes |
[
{
"content": "Find the number of square units bounded by the $x$-axis, the $y$-axis and the line $x+ y= 6$.",
"role": "user"
}
] | 18 |
[
{
"content": "Evaluate the limit \\(\\lim_{n \\to \\infty}\\dfrac{\\int_2^{n+1}\\frac{\\ln x}{x}\\,\\mathrm dx}{\\ln^2 n}.\\)",
"role": "user"
}
] | \dfrac{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... | Deferred tax asset: $60,000
Valuation allowance: $30,000 |
[
{
"content": "Calculate the integral \\( \\oint_{c(0,2)} \\frac{z^{3}-2}{z(z^{2}-1)}\\,\\mathrm{d}z \\) over the circle \\( c(0,2) \\) with the parametrization \\( t \\rightarrow 0 + 2\\mathrm{e}^{\\mathrm{i}t} \\). Determine the poles of the integrand that lie within the circle.",
"role": "user"
}
] | 0 |
[
{
"content": "Find all positive integer solutions to the equation \\( \\sigma(n) = \\frac{3n(n-1)}{2} \\), where \\( \\sigma(n) \\) is the sum of divisors function. Given that \\( n = 2 \\) is a solution, determine if there are any other solutions.",
"role": "user"
}
] | 2 |
[
{
"content": "Let $U = [u_1 \\ u_2 \\ \\cdots \\ u_n]$ be an orthogonal matrix, where $u_i$ is the $i$-th column of $U$. Given a unit vector $x \\in \\mathbb{R}^n$, determine if the sum $\\sum_{i=1}^n (x^T u_i)^2$ equals 1.",
"role": "user"
}
] | 1 |
[
{
"content": "Is the Lebesgue measure restricted to a set of measure 1 in \\(\\mathbb{R}^n\\) a probability measure?",
"role": "user"
}
] | Yes |
[
{
"content": "Let G be an abelian group with generators x and y, where the order of x is 16 and the order of y is 24. Given that $x^{2} = y^{3}$, determine the order of the group G.",
"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... | 300 kPa |
[
{
"content": "Let $M$ be a closed translation invariant linear subspace of $L^2(\\mathbb{R}^n)$. Is there a measurable subset $E \\subseteq \\mathbb{R}^n$ such that $M = \\{f \\in L^2(\\mathbb{R}^n) : \\hat{f}$ vanishes a.e. on $E \\}$?",
"role": "user"
}
] | Yes |
[
{
"content": "The greatest common divisor of two positive integers less than $100$ is equal to $3$. Their least common multiple is twelve times one of the integers. What is the largest possible sum of the two integers?",
"role": "user"
}
] | 129 |
[
{
"content": "Evaluate the limit: $$\\lim_{x \\to 0}\\left(\\frac{\\tan\\left(\\pi\\cos^2x\\right)}{x^2}\\right)$$ without using L'Hospital's rule.",
"role": "user"
}
] | -\pi |
[
{
"content": "Let $N = \\lceil\\delta^{-\\gamma}\\rceil$, with $0 < \\gamma < 1$. Determine whether \\( \\lim_{\\delta \\to 0} f(t,\\delta,\\lceil \\delta^{-\\gamma}\\rceil)=0 \\) for all \\( t > 0 \\), where \\( f(t,\\delta, N)= e^{-t/\\delta} \\sum_{k=0}^{N-1}\\frac{(t/\\delta)^k}{k!} \\).",
"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... | 2.52 seconds |
[
{
"content": "Two million marked points lie entirely within a circle with a diameter of 1 cm. Determine if there exists a line such that exactly one million of these points are on each side of the line.",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.775 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... | external environment -> capsule -> cell wall -> plasma membrane -> cytoplasm |
[
{
"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... | 18.8 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 9,661.49 |
[
{
"content": "Determine the smallest cardinality of a base for the topological space \\((X, \\tau)\\), where \\(X = \\mathbb{R}^2\\) and \\(\\tau = \\{\\emptyset, \\mathbb{R}^2, \\{(x, y) \\in \\mathbb{R}^2 \\mid x^2 + y^2 < r \\}, r \\in \\mathbb{R}, r > 0\\}\\).",
"role": "user"
}
] | \aleph_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... | 4.92 |
[
{
"content": "Let $p$ be a prime number of the form $12n + 11$. Consider the set $M = \\{1, 2, \\ldots, p-1\\}$. A subset $S$ of $M$ is called *essential* if the product $\\Pi_S$ of all elements in $S$ is not less than the product $\\bar{\\Pi}_S$ of all other elements in $M$. The *deviation* of the subset $S$ i... | 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... | $1,042,768.62 |
[
{
"content": "Calculate \\( [3]^{2014^{2014}} \\mod 98 \\) using Euler's Theorem and the Chinese Remainder Theorem.",
"role": "user"
}
] | 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... | 0.2642 femtometre |
[
{
"content": "Let $G$ be a group acting on an ordered set, preserving its order, i.e., if $a<b$, then $g(a)<g(b)$ for all $g\\in G$. Does this imply that there exists a left order on $G$, i.e., if $f<g$, then $fh<gh$ for all $h\\in G$?",
"role": "user"
}
] | No |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4.3e-13 M |
[
{
"content": "Assume that \\(x_1, \\dots, x_n\\) are non-negative real numbers such that \\(x_1 + \\dots + x_n \\in \\mathbb{Q}\\) and \\(x_1 + 2x_2 + \\dots + nx_n \\in \\mathbb{Q}\\). Does this imply that the numbers \\(x_1, \\dots, x_n\\) are rational?",
"role": "user"
}
] | No |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2,2-dimethylpentane |
[
{
"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... | 8.56L |
[
{
"content": "Calculate the limit: \\[ \\lim_{x\\to\\infty}\\left(\\frac{c+\\sqrt{x}}{-c+\\sqrt{x}}\\right)^x\\exp(-2c\\sqrt{x}) \\]",
"role": "user"
}
] | 1 |
[
{
"content": "Given \\( x > 0 \\), \\( y > 0 \\), and the following system of equations:\n\\[\n\\left\\{\n\\begin{array}{l}\n\\cos^2(\\pi x) + 2 \\sin(\\pi y) = 1, \\\\\n\\sin(\\pi x) + \\sin(\\pi y) = 0, \\\\\nx^2 - y^2 = 12\n\\end{array}\n\\right.\n\\]\n\nFind the ordered pair \\((x, y)\\).",
"role": "use... | (4, 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... | 0.314 kg |
[
{
"content": "Determine the number of isomorphism classes of associative rings with identity that have 35 elements.",
"role": "user"
}
] | 1 |
[
{
"content": "Determine if there exists a natural number \\( m \\) such that the equation \\( 8m+1 = (2p+1)^2-(2q)^2 \\) holds for some natural numbers \\( p \\) and \\( q \\), with \\( p \\neq m \\) and \\( q \\neq m \\).",
"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... | m(9) = 3 * (1/2)^(9/432) |
[
{
"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... | 2C_4H_{10}O(l) + 13O_2(g) -> 8CO_2(g) + 10H_2O(g) |
[
{
"content": "The quadratic equation $ax^2+8x+c=0$ has exactly one solution. If $a+c=10$, and $a<c$ find the ordered pair $(a,c)$.",
"role": "user"
}
] | (2,8) |
[
{
"content": "Find the limit of the bounded solution $u(x,t)$ of the heat equation $u_t = u_{xx}$ with the initial condition $u(x,0) = \\frac{e^{2x}-1}{e^{2x}+1}$ as $t \\to \\infty$, specifically for $x = 1$. Express your answer as a single value or expression.",
"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... | 3.32 kg and 1.68 kg or 1.68 kg and 3.32 kg |
[
{
"content": "Determine whether a surjective function can exist between a simply connected domain and a non-simply connected domain. Provide a justification for 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... | 1.05 L |
[
{
"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... | Bank Reconciliation
For Aug. 31
ParticularsAmount ($)
Cash balance according to Bank Statement27,261
Add: Deposit in transit, not recorded by Bank6,131
Less: Outstanding checks14,624
Adjusted Balance18,768
Cash balance according to Company's Books18,257
Add: Error in recording check as 580 instead of 58522
Le... |
[
{
"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_z = k[Q(0.5a)]/[(r^2 + (0.5a)^2)^(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... | 2.59 |
[
{
"content": "Given i.i.d. random variables with mean \\( \\mu \\) and variance 1, let \\( \\bar{X}_n = \\frac{1}{n}(X_1 + \\cdots + X_n) \\). Use the Central Limit Theorem to approximate the probability:\n\n\\[ P\\left(|\\bar{X}_n - \\mu| \\ge \\frac{2}{\\sqrt{n}}\\right) \\]",
"role": "user"
}
] | 0.0456 |
[
{
"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... | 486 days |
[
{
"content": "Consider the region $R$ bounded by the curve $y = \\sqrt{x+a}$, where $a > 0$, the $y$-axis, and the $x$-axis. When $R$ is rotated about the $y$-axis, a solid $S$ is generated. Let $T$ be an inscribed cone within $S$, sharing the same circular base and having a height of $\\sqrt{a}$. Compute the v... | \dfrac{8}{5} |
[
{
"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... | Al2(CrO4)3 |
[
{
"content": "Let a sequence be defined by $a_1=1$ and $a_{n+1}=(n+1)(1+a_n)$ for $n \\geq 1$. If $P_n=\\prod_{i=1}^n(1+a_i^{-1})$, find the value of $\\lim_{n\\to\\infty}P_n$. \\(\\text{Express your answer as a single number or expression.}\\)",
"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... | $12.5 |
[
{
"content": "A ball travels on a parabolic path in which the height (in feet) is given by the expression $-16t^2+64t+31$, where $t$ is the time after launch. What is the maximum height of the ball, in feet?",
"role": "user"
}
] | 95 |
[
{
"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... | 3.80 years |
[
{
"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... | 10.33 atm |
[
{
"content": "Find the maximum value of the function \\( f(x,y) = 2x^3 - 3x^2 \\) subject to the constraint \\( g(x,y) = (3-x)^3 - y^2 = 0 \\), where \\( f(x,y) \\) and \\( g(x,y) \\) are defined on \\( \\mathbb{R}^2 \\).",
"role": "user"
}
] | 27 |
[
{
"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 firm's expected cash receipts for June, July, and August are $64,250, $80,500, and $91,250 respectively. |
[
{
"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... | Yes, by making at least two known length cuts and measuring the change in frequency. Then the following equations can be used to determine L and k.
\\begin{cases}
\left( 1 + \frac{\Delta F_{2}}{F} \right)\,\left( 1 + \frac{\Delta L_{2}}{L} \right) = \left( 1 + \frac{\Delta F_{1}}{F} \right)\,\left( 1 + \frac{\Delta L_{... |
[
{
"content": "In the finite field \\(\\mathbb{F}_{101}\\), where the discrete logarithms are given as \\(L_2(3)=69\\) and \\(L_2(5)=24\\), compute the discrete logarithm \\(L_2(60)\\).",
"role": "user"
}
] | 95 |
[
{
"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... | 25.9 MJ |
[
{
"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... | 1.19 meters |
[
{
"content": "Find the value of the normalizing constant \\(a\\) for the probability density function given by \\(f(x) = ax^2 e^{-kx}\\) for \\(k > 0\\) and \\(0 \\le x \\le \\infty\\).",
"role": "user"
}
] | \dfrac{k^3}{2} |
[
{
"content": "Consider the irreducible polynomial $g = X^4 + X + 1$ over $F_2$ and let $E$ be the extension of $F_2 = \\{0, 1\\}$ with a root $\\alpha$ of $g$. Could $E$ have a subfield of order 8?",
"role": "user"
}
] | No |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Invariance is achieved for \(\sigma = \frac{1-D}{4}\) |
[
{
"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... | 1.417 ms^{-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... | 263.5 hr |
[
{
"content": "In the cuboid $ABCD-A_1B_1C_1D_1$, $AB=4$, $BC=CC_1=2\\sqrt{2}$. Let $M$ be the midpoint of $BC_1$, and $N$ be the midpoint of $MC_1$. If the angle between the skew lines $AN$ and $CM$ is $\\theta$ and the distance is $d$, find the value of $d \\sin \\theta$. \\(\\boxed{\\text{Your answer here}}\\... | \dfrac{4}{5} |
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