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... | -3.189*10^-8*GMm N |
[
{
"content": "Find the maximum value of \\(|z^2 - 2iz + 1|\\) given that \\(|z| = 3\\).",
"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... | 24.9 g |
[
{
"content": "Given an integer $N$, consider the set $S = \\{0, 1, \\ldots, 2^N - 1\\}$. Determine the number of subsets $A \\subseteq S$ such that the XOR of all elements in $A$ is zero. Note that the XOR sum of an empty set is zero, and XOR here is a bitwise operation.",
"role": "user"
}
] | 2^{2^N - 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... | -5.0 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... | $395.36 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\to \\infty}\\left(\\frac{2\\arctan(x)}{\\pi}\\right)^x. \\]",
"role": "user"
}
] | e^{-\frac{2}{\pi}} |
[
{
"content": "Solve the equation $x^2 + y^2 = pz^2$ for $x, y, z \\in \\mathbb{N}$, where $p$ is a prime such that $p \\equiv 3 \\pmod{4}$. Prove that the only solution is $x = y = z = 0$.",
"role": "user"
}
] | x = y = z = 0 |
[
{
"content": "Find a monic quartic polynomial, in $x,$ with rational coefficients such that $2+\\sqrt{2}$ and $1-\\sqrt{3}$ are roots of the polynomial.",
"role": "user"
}
] | x^4-6x^3+8x^2+4x-4 |
[
{
"content": "Find the minimum value of the expression \\( x + 2y + 3z \\) subject to the constraint \\( x^3 y^2 z = 1 \\). Then, compute \\( m^3 \\), where \\( m \\) is the minimum value found.",
"role": "user"
}
] | 72 |
[
{
"content": "For a generic choice of matrix $A$ and vector $b$ in the system of linear equations $Ax = b$, can the elements of the solution vector $x$ be distinct?",
"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 |
[
{
"content": "Let \\( \\mu \\) and \\( \\nu \\) be measures with \\( \\nu(\\Omega) = 3 \\). Suppose \\( g \\) is the Radon-Nikodym derivative of \\( \\nu \\) with respect to \\( \\mu + \\nu \\). Calculate \\( \\mu(\\{x: g(x) > 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... | 105900 |
[
{
"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... | -4.9eV |
[
{
"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... | Individual tickets: 2400
Family tickets: 600 |
[
{
"content": "Evaluate the double integral \\( \\iint_R x e^{-\\sqrt{x^2+y^2}} \\, dx \\, dy \\) using polar coordinates, where \\( R \\) is the region in the first quadrant (\\( x \\ge 0, y \\ge 0 \\)).",
"role": "user"
}
] | 2 |
[
{
"content": "Find the greatest common divisor (GCD) of the complex numbers \\(4 + 22i\\) and \\(17 + i\\) in the Gaussian integers \\(\\mathbb{Z}[i]\\).",
"role": "user"
}
] | 1 + 3i |
[
{
"content": "Evaluate the limit \\( \\lim\\limits_{x\\to 0} f(x) \\) where\n\\[\n f(x) = \\frac{e^{x^{2}} \\sin x - x \\left(1+\\frac{5 x^2}{6}\\right)}{x^{5}}\n\\]",
"role": "user"
}
] | \dfrac{41}{120} |
[
{
"content": "Let \\( \\alpha \\) be a root of \\( x^7 - 1 \\) with \\( \\alpha \\neq 1 \\). Determine the degree of the field extension \\( [\\mathbb{Q}(\\alpha + \\alpha^{-1}):\\mathbb{Q}] \\).",
"role": "user"
}
] | 3 |
[
{
"content": "Determine whether the inequality \\( 2\\varphi(n) > n \\) holds for all integers \\( n = 2^k - 1 \\) where \\( k \\) is an odd integer.",
"role": "user"
}
] | Yes |
[
{
"content": "In triangle $ABC$, an interior point $P$ is defined as \"good\" if there are exactly 27 rays emanating from $P$ that intersect the sides of the triangle, dividing it into 27 smaller triangles of equal area. Determine the number of good points for a given triangle $ABC$. Provide your answer as a si... | 325 |
[
{
"content": "Let $X \\subset \\mathbb{R}$ and let $f, g: X \\to X$ be continuous functions such that $f(X) \\cap g(X) = \\emptyset$ and $f(X) \\cup g(X) = X$. Which one of the following sets cannot be equal to $X$?\n\nA) $[0,1]$\nB) $(0,1)$\nC) $[0,1)$\nD) $\\mathbb{R}$",
"role": "user"
}
] | A |
[
{
"content": "Calculate the limit: $$\\lim_{x \\to 0}(\\cos x)^{1/x^4}$$",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the surface integral \\( \\iint_S y \\, dS \\), where \\( S \\) is the hemisphere defined by \\( z = \\sqrt{R^2 - x^2 - y^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... | $7,018.50 |
[
{
"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... | \frac{\partial V}{\partial T} = -\frac{f_T}{f_V} = - \frac{\frac{a(b-V)}{T^2(V+c)^2}-R}{p+\frac{a}{T(V+c)^2} - (V-b)\frac{2a}{T(V+c)^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... | 76.8 m |
[
{
"content": "What is the expected number of tosses needed to roll three consecutive sixes with a fair six-sided die?",
"role": "user"
}
] | 258 |
[
{
"content": "Can a metric function $d_X$ on a set $X$ have exactly three distinct values?",
"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... | 1.12 V |
[
{
"content": "A rotation centered at the origin takes $\\begin{pmatrix} 13 \\\\ 0 \\end{pmatrix}$ to $\\begin{pmatrix} 5 \\\\ -12 \\end{pmatrix}.$ Which vector does the rotation take $\\begin{pmatrix} 0 \\\\ 1 \\end{pmatrix}$ to?",
"role": "user"
}
] | \begin{pmatrix} 12/13 \\ 5/13 \end{pmatrix} |
[
{
"content": "Find the asymptotic bounds in the form of \\(\\Theta(\\cdot)\\) for the recurrence relation: \\[T(n) = T\\left(\\frac{n}{\\log n}\\right) + \\log \\log n\\]",
"role": "user"
}
] | \Theta(\log 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... | 19.76% |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.81 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... | Health Insurance Expense |
[
{
"content": "Suppose $g$ is a nonnegative radial function with compact support on $\\mathbb{R}^{3}$, and $f$ is a radial solution of $(-\\Delta + g)f = 0$ with $f(0) = 0$. Given that $\\frac{df(0)}{dr} = 0$, determine whether it follows that $\\lim_{r\\to 0}r^{2}\\frac{df}{dr} = 0$. Provide a justification for... | 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... | [HI]: 0.456 M
[I2]: 0.0608 M
[H2]: 0.0608 M |
[
{
"content": "In a regular tetrahedron \\(ABCD\\), let \\(M\\) be the midpoint of the height \\(DD_1\\). Calculate the dihedral angle \\(A-M-B-C\\) in radians.",
"role": "user"
}
] | \dfrac{\pi}{2} |
[
{
"content": "Find the 6-digit number such that when it is multiplied by 2, 3, 4, 5, and 6, the resulting numbers are permutations of the original number's digits.",
"role": "user"
}
] | 142857 |
[
{
"content": "Given a function $f:[0,1]\\to \\mathbb{R}$ that satisfies the following integrals: \\( \\int_{0}^{1}f(x)dx=1 \\), \\( \\int_{0}^{1}xf(x)dx=1 \\), and \\( \\int_{0}^{1}f(x)^2dx=4 \\), determine the value of \\( \\int_{0}^{1}f(x)^3dx \\).",
"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... | 45.1 grams |
[
{
"content": "Evaluate the line integral \\( \\int_{L} (x+2xy)dy + y^{2}dx \\) along the circle \\( L=\\{(x,y)|x^2+y^2=y\\} \\) using Green's theorem.",
"role": "user"
}
] | \dfrac{\pi}{4} |
[
{
"content": "What is the smallest positive integer $n$ such that $\\frac{1}{n}$ is a terminating decimal and $n$ contains the digit 9?",
"role": "user"
}
] | 4096 |
[
{
"content": "Determine whether a perfect square, represented as \\(a^2\\), can be expressed as the sum of three or more distinct natural numbers squared, such as \\(a^2 = b^2 + c^2 + d^2\\), where \\(b\\), \\(c\\), and \\(d\\) are distinct natural numbers.",
"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... | Dec. 3, 2015:
Notes Receivable 36,000
Accounts Receivable - Chicago Clothing & Bags Co. 36,000
(To record receipt of note)
Dec. 31, 2015:
Interest Receivable (36,000 * 6% * 28/360) 168
Interest Revenue 168
(To record accrued interest)
Dec. 31, 2015:
Interest Revenue 168
Income Summary 168
(To close interest revenue)
Mar. 2, 2016:
Cash 36,540
Notes Receivable 36,000
Interest Receivable 168
Interest Revenue 372
(To record collection of note and interest) |
[
{
"content": "Given the function \\( f(x) = x^3 - 4x^2 + 4x \\), its graph is denoted as the curve \\( C \\). For any \\( x_1 \\neq \\frac{4}{3} \\), the curve \\( C \\) and its tangent at point \\( P_1(x_1, f(x_1)) \\) intersect at another point \\( P_2(x_2, f(x_2)) \\). The curve \\( C \\) and its tangent at ... | \dfrac{1}{16} |
[
{
"content": "Let $u_1, \\cdots , u_k$ be linearly independent vectors in $\\mathbb{R}^m$. Consider the matrix $A = \\sum_{i=1}^{k} u_i u_i^T$. Determine the dimension of the null space of $A$. \\( \\text{Provide your answer as a single integer.} \\)",
"role": "user"
}
] | m - k |
[
{
"content": "If $U$ is a Lie group with a closed subgroup $K$ such that both $U$ and $U/K$ are simply-connected, is $K$ necessarily connected?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the number of binomial coefficients in the expansion of \\((1+x)^{2018}\\) that are divisible by 13.",
"role": "user"
}
] | 1395 |
[
{
"content": "Calculate the area bounded by the curve \\( y = \\frac{2}{\\pi} \\left[ \\left|\\cos^{-1}(\\sin x)\\right| - \\left|\\sin^{-1}(\\cos x)\\right| \\right] \\) and the x-axis over the interval \\( \\frac{3\\pi}{2} \\le x \\le 2\\pi \\).",
"role": "user"
}
] | \dfrac{\pi}{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... | 24234.75 cal |
[
{
"content": "Determine whether the equation \\(5x^2 + y^4 = 7\\) has any solutions in the 3-adic numbers.",
"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... | 66.324 seconds |
[
{
"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... | 3.2e-4 m |
[
{
"content": "How many ways are there to select three committees from 10 people, such that each committee serves a different purpose, someone has to be in every committee, and everyone serves in exactly one committee? Use generating functions to find the solution.",
"role": "user"
}
] | 55980 |
[
{
"content": "Determine whether the sequence \\( \\cos(\\pi \\sqrt{n^2 + n}) \\) is convergent.",
"role": "user"
}
] | 0 |
[
{
"content": "Given a function $f(x,y)$ defined on the domain $D = [0,1] \\times [0,1]$, where $f$ is continuous with respect to each variable separately, and $f$ vanishes on a dense subset of $D$, does $f$ vanish on the entire domain $D$? Answer with 'Yes' or 'No'.",
"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... | 2500 |
[
{
"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... | 8.29% |
[
{
"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... | 14.92% |
[
{
"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... | 13.1 |
[
{
"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... | 1.54 |
[
{
"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... | 1.08 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... | a_max = (T-mg)/m |
[
{
"content": "Melinda will roll two standard six-sided dice and make a two-digit number with the two numbers she rolls. For example, if she rolls a 6 and a 3, she can either form 36 or 63. What is the probability that she will be able to make an integer between 10 and 20, inclusive? Express your answer as a com... | \frac{11}{36} |
[
{
"content": "Given the joint density function \\( f(x,y,z,u) = \\frac{24}{(1+x+y+z+u)^5} \\) for \\( x > 0, y > 0, z > 0, u > 0 \\), find the probability \\( P(X+Y+Z+U \\ge 1) \\).",
"role": "user"
}
] | \dfrac{15}{16} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $45 million |
[
{
"content": "Use Green's Theorem to evaluate the line integral \\( \\int_{\\gamma} (x^2 - y)\\,dx + (x + y^2)\\,dy \\) where \\( \\gamma \\) is the ellipse parameterized by \\( x = a\\cos t, y = b\\sin t \\) for \\( 0 \\leq t \\leq 2\\pi \\) and \\( a, b > 0 \\).",
"role": "user"
}
] | 2\pi ab |
[
{
"content": "Given that \\( \\sum_{i=1}^n f(i) \\sim n \\log n \\) and \\( f \\) is a monotonically increasing function that is always positive, does it follow that \\( f(n) \\sim \\log n \\)?\n\nNote: \\( A(n) \\sim B(n) \\) means:\n\\[ \\lim_{n\\to\\infty } \\frac{A(n)}{B(n)}=1 \\]",
"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... | 6.73 m/s |
[
{
"content": "Given the circle \\( \\odot O: x^{2}+y^{2}=5 \\) and the parabola \\( C: y^{2}=2px \\) (with \\( p > 0 \\)), they intersect at point \\( A(x_{0}, 2) \\). \\( AB \\) is a diameter of \\( \\odot O \\). A line through point \\( B \\) intersects the parabola \\( C \\) at two points \\( D \\) and \\( E... | 2 |
[
{
"content": "Evaluate the integral \\( \\int_{\\mathbb{R}} e^{-itx} \\, dx \\). Discuss the convergence of this integral and explain how it relates to finding the density of a random variable given the characteristic function \\( \\phi(t) = \\frac{1}{4} + \\frac{1}{4}e^{-it} + \\frac{1}{2}\\frac{3}{4-e^{2it}} ... | 2\pi \delta(t) |
[
{
"content": "Given an arithmetic sequence \\(\\{a_{n}\\}\\) with common difference \\(d \\neq 0\\), and a geometric sequence \\(\\{b_{n}\\}\\) with common ratio \\(q\\) which is a positive rational number less than 1. If \\(a_{1}=d\\), \\(b_{1}=d^{2}\\), and \\(\\frac{a_{1}^{2}+a_{2}^{2}+a_{3}^{2}}{b_{1}+b_{2}... | \dfrac{1}{2} |
[
{
"content": "Find the minimum value of the expression \\( \\sqrt{2x^2+2x+1} +\\sqrt{2x^2-10x+13} \\). Determine the value of \\( \\alpha \\) such that the minimum value is \\( \\sqrt{\\alpha} \\).",
"role": "user"
}
] | 20 |
[
{
"content": "Determine the value of the parameter $k$ for which all solutions of the differential equation \\( u''(t) + k u(t) = 2 \\sin(10t) \\) remain bounded as \\( t \\to \\infty \\).",
"role": "user"
}
] | k \neq 100 |
[
{
"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... | $779.09 |
[
{
"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... | Bond Payable Dr $570,000
Premium on Bonds Payable Dr $17,100
Gain on Bond Redemption Cr $39,900
Cash Cr $547,200 |
[
{
"content": "Suppose that for any \\(-1 \\leq x \\leq 1\\), \\(|ax^2 + bx + c| \\leq 1\\). Find the maximum possible value of \\(|a| + |b| + |c|\\).",
"role": "user"
}
] | 3 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $2 |
[
{
"content": "Can Alice prevent Bob from making a 2018-digit number, constructed by taking turns with Alice, divisible by 3, given that each digit must be in a different residue class modulo 3 than the previous digit?",
"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... | 0.012 m |
[
{
"content": "Find the radius of convergence of the power series \\( \\sum_{n=1}^\\infty b_n z^n \\) derived from the power series \\( \\sum_{n=0}^\\infty a_n z^n \\), given that \\( \\lim_{n \\to \\infty} \\frac{a_n}{a_{n+1}} = z_0 \\) exists and \\( z_0 \\) is a pole on the unit circle.",
"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... | 9.31% |
[
{
"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... | Apr. 1, 2017:
Notes receivable 29,000
Accounts receivable 29,000
Jul. 1, 2017:
Notes receivable 31,000
Cash 31,000
Dec. 31, 2017:
Interest receivable 3,045
Interest revenue 3,045
Dec. 31, 2017:
Interest receivable 1,860
Interest revenue 1,860
Apr. 1, 2018:
Cash 33,060
Notes receivable 29,000
Interest receivable 3,045
Interest revenue 1,015
Apr. 1, 2018:
Accounts receivable 33,790
Notes receivable 31,000
Interest receivable 1,860
Interest revenue 930 |
[
{
"content": "Evaluate the limit: $$\\lim_{n \\to \\infty} \\frac{1}{n} \\int_{0}^{n} \\frac{x \\ln(1 + \\frac{x}{n})}{1 + x} \\, dx.$$",
"role": "user"
}
] | 2 \ln 2 - 1 |
[
{
"content": "Determine the set of positive real numbers \\(x\\) for which the series \\(\\sum_{n=1}^\\infty \\frac{x^{a(n)}}{n^3}\\) converges, where \\(a(n)\\) is the number of zeroes in the base 3 representation of \\(n\\).",
"role": "user"
}
] | (0, 25) |
[
{
"content": "Evaluate the integral \\( \\int_{0}^{\\infty} [x] \\cdot |\\sin(\\pi x)| \\, dx \\), where \\([x]\\) denotes the greatest integer less than or equal to \\(x\\).",
"role": "user"
}
] | \infty |
[
{
"content": "Let $\\Gamma$ be a discrete group and $\\text{Prob}(\\Gamma)$ be the space of all probability measures on $\\Gamma$ defined as $\\text{Prob}(\\Gamma)=\\{\\mu\\in l^{1}(\\Gamma): \\mu\\geq0,~\\sum\\limits_{t\\in\\Gamma}\\mu(t)=1\\}$. Define $F(\\mu, r)=\\{t\\in \\Gamma:~\\mu(t)>r\\}$. Determine whe... | 1 |
[
{
"content": "The set of all positive integers is divided into two disjoint subsets, $\\{f(1), f(2), \\cdots, f(n), \\cdots\\}$ and $\\{g(1), g(2), \\cdots, g(n), \\cdots\\}$, where $f(1)<f(2)<\\cdots<f(n)<\\cdots$ and $g(1)<g(2)<\\cdots<g(n)<\\cdots$ satisfy the condition $g(n)=f[f(n)]+1$ for $n \\geq 1$. Dete... | 388 |
[
{
"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... | Paleomagnetic studies showing the apparent wander of the magnetic poles, the discovery of earthquake and volcano alignment along distinct belts, and further palemagnetic studies revealing magnetic reversals in the ocean crust. |
[
{
"content": "Determine the number of equivalence relations \\(S\\) over the power set of natural numbers \\(\\mathcal P(\\mathbb N)\\) such that the equivalence class of \\(\\{8\\}\\) under \\(S\\) is \\(\\{A \\in \\mathcal P(\\mathbb N) \\mid A \\neq \\{1\\} \\wedge A \\neq \\{2\\}\\}\\).",
"role": "user"... | 2 |
[
{
"content": "Consider the set \\( A = \\{1, 2, 3, 4, 5\\} \\). A function \\( f: A \\to A \\) is chosen at random from the set of all nonempty relations on \\( A \\). What is the probability that \\( f \\) is a bijective function such that \\( f(x) \\neq x \\) for all \\( x \\in A \\) and \\( f(1) \\neq 2 \\)?... | \dfrac{11}{40} |
[
{
"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... | 848968.30 |
[
{
"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... | <img src="/cimages/multimages/16/2-methyl6550411838364394069.jpg" alt="Structure of 2-methylpropanal"> |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to\\infty} \\frac{ \\displaystyle\\int_1^x \\arctan(t^2)\\, dt}{x}$$ using a method other than L'Hopital's Rule.",
"role": "user"
}
] | \dfrac{\pi}{2} |
[
{
"content": "Let $x$ and $y$ be real numbers. If $x + y^3$, $x^2 + y^2$, and $x^3 + y$ are all integers, determine whether $x$ and $y$ must both be integers.",
"role": "user"
}
] | Yes |
[
{
"content": "Let $L$ be a field extension of $K$, and let $\\gamma, \\delta \\in L$ be algebraic over $K$ with $[K(\\gamma):K] = p$ and $[K(\\delta):K] = q$, where $p$ and $q$ are distinct primes. Determine the degree of the field extension $[K(\\gamma, \\delta):K]$. \\( \\boxed{?} \\)",
"role": "user"
}... | pq |
[
{
"content": "Consider an abelian group $G$ of order 34. Define the subset $S = \\{ g \\in G \\mid g = g^{-1} \\}$. Determine the number of elements in the subset $S$. Provide your answer as a single integer.",
"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... | $18,870 |
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