__src_index__ int64 0 172k | messages stringlengths 375 66.5k |
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1,776 | [{"role": "user", "content": "A regular polygon has sides of length 7 units and an exterior angle of 90 degrees. What is the perimeter of the polygon, in units?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about a regular polygon with sides of length 7 units and an exterior angle of 9... |
1,778 | [{"role": "user", "content": "The contrapositive of the proposition \"If $a > b$, then $a^2 > b^2$\" is ( ) \nA: If $a^2 > b^2$, then $a > b$, \nB: If $a \\leq b$, then $a^2 \\leq b^2$, \nC: If $a^2 \\leq b^2$, then $a \\leq b$, \nD: If $a > b$, then $a^2 \\leq b^2$."}, {"role": "assistant", "content": "<think>\n\... |
1,688 | [{"role": "user", "content": "Given the parabola $y=\\frac{1}{4}x^2$ and the circle $C: (x-1)^2+(y-2)^2=r^2$ $(r > 0)$ share a common point $P$. If the tangent line to the parabola at point $P$ also touches circle $C$, find the value of $r$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challengi... |
1,747 | [{"role": "user", "content": "For how many two-digit prime numbers is the sum of its digits 10?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so the problem is asking: how many two-d... |
1,795 | [{"role": "user", "content": "Scott has 7 pairs of shoes. Anthony has 3 times as many pairs of shoes as Scott, and Jim has 2 less pairs than Anthony. How many more pairs of shoes does Anthony have compared to Jim?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about Scott, Anthony, an... |
1,782 | [{"role": "user", "content": "Harry needs to buy 5 spellbooks that each cost a certain amount, three potion kits that each cost 20 silver, and one owl that costs 28 gold. There are 9 silver to a gold. Harry will pay a total of 537 silvers. How much does each spellbook cost in gold?"}, {"role": "assistant", "content": "... |
1,783 | [{"role": "user", "content": "Given $\\frac{\\log{a}}{p} = \\frac{\\log{b}}{q} = \\frac{\\log{c}}{r} = \\log{x}$, with all logarithms to the same base and $x \\neq 1$. If $\\frac{a^3b}{c^2} = x^y$, then find the value of $y$.\n- (A) $p + 3q - 2r$\n- (B) $3p + q - 2r$\n- (C) $2p + q - 3r$\n- (D) $2p - q + r$"}, {"role":... |
1,661 | [{"role": "user", "content": "Segments $AD=8$, $BE=10$, $CF=20$ are drawn from the vertices of triangle $ABC$, each perpendicular to a straight line $RS$, inclined at an angle of 45 degrees and not intersecting the triangle. Points $D$, $E$, and $F$ are the intersection points of $RS$ with the perpendiculars. If $x$ is... |
1,779 | [{"role": "user", "content": "An investment yields an interest payment of $225 each month. If the simple annual interest rate is 9%, what is the amount of the investment?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about finding the amount of an investment that yields $225 each month... |
1,765 | [{"role": "user", "content": "A right cylinder has a height of 10 inches and a radius of 3 inches. Calculate both the area of the curved surface and the total surface area of the cylinder, in square inches. Express your answers in terms of \\(\\pi\\)."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or... |
1,739 | [{"role": "user", "content": "(a) If \\( r = \\sqrt{2} + \\sqrt{3} \\), show that \\( \\sqrt{6} = \\frac{r^{2} - 5}{2} \\).\n\n(b) If \\( s = \\sqrt{215} + \\sqrt{300} \\), show that \\( s^{2} > 1015 \\)."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to p... |
1,781 | [{"role": "user", "content": "In the geometric sequence $\\{a_n\\}$, it is known that $a_1 = -1$ and the common ratio $q = 2$. The value of the sum of the first six terms $S_6$ of the sequence is ______."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the sum of the first six terms of a ... |
1,777 | [{"role": "user", "content": "In triangle $ABC$, let the sides opposite angles $A$, $B$, and $C$ be $a$, $b$, and $c$, respectively. Given that $a=4$, $B= \\frac{\\pi}{3}$, and the area of triangle $ABC$, $S_{\\triangle ABC} = 6\\sqrt{3}$, find the length of side $b$."}, {"role": "assistant", "content": "<think>\n\nOka... |
1,786 | [{"role": "user", "content": "A train travels 290 km in 4.5 hours, then continues for another 400 km in 5.5 hours. After that, it travels 350 km in 7 hours, and finally completes a 480 km trip in 6 hours. Calculate the overall average speed of the train during the entire journey."}, {"role": "assistant", "content": "<t... |
1,734 | [{"role": "user", "content": "The monotonically increasing interval of the function $y=(\\cos{x}+\\sin{x})\\cos{(x-\\frac{π}{2})}$ is ( )\nA: $[2kπ-\\frac{π}{8}, 2kπ+\\frac{3π}{8}]$ ($k∈\\mathbb{Z}$)\nB: $[kπ-\\frac{π}{8}, kπ+\\frac{3π}{8}]$ ($k∈\\mathbb{Z}$)\nC: $[kπ-\\frac{π}{4}, kπ+\\frac{π}{4}]$ ($k∈\\mathbb{Z}$)... |
1,704 | [{"role": "user", "content": "Given the expressions $(-2a)^6(-3a^3)+[2a^2]^3 \\div \\frac{1}{ \\frac{1}{ (-2)^2 3^2 (xy)^3 } }$ and $|-\\frac{1}{8}|+(\\pi^3)+(-\\frac{1}{2}^3-(\\frac{1}{3})^2)$, compute their respective values."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, a... |
1,789 | [{"role": "user", "content": "In a geometric sequence where all terms are positive, if $a_{6}=3$, then $a_{4}+a_{8}=$ ()\nA: has a minimum value of $6$\nB: has a maximum value of $6$\nC: has a maximum value of $9$\nD: has a minimum value of $3$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The probl... |
1,809 | [{"role": "user", "content": "Danielle's apartment has 6 rooms. Heidi's apartment has 3 times as many rooms as Danielle's apartment. Grant's apartment has 1/9 as many rooms as Heidi's apartment. How many rooms does Grant's apartment have?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is a... |
1,792 | [{"role": "user", "content": "Compare the numbers $\\frac{8}{32}$, $\\frac{6}{22}$, and $\\frac{10}{29}$ and order them from smallest to largest.\n$\\textbf{(A)}\\ \\frac{6}{22}<\\frac{8}{32}<\\frac{10}{29} \\quad$\n$\\textbf{(B)}\\ \\frac{10}{29}<\\frac{8}{32}<\\frac{6}{22} \\quad$\n$\\textbf{(C)}\\ \\frac{8}{32}<\\fr... |
1,773 | [{"role": "user", "content": "A business executive and his client are charging their dinner tab on the executive's expense account. The company will only allow them to spend a total of $75 for the meal. Assuming that they will pay 7% in sales tax for the meal and leave a certain percentage as a tip, the most their food... |
1,719 | [{"role": "user", "content": "Determine the slant asymptote for the rational function $$y = \\frac{3x^2 + 4x - 8}{x^2 - 4x + 3}.$$ If the slant asymptote can be described by the equation $y = mx + b$, find the sum $m + b$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it... |
1,788 | [{"role": "user", "content": "If point P is on the plane, and point Q is on the curve $x^2+(y+2)^2=1$, then the minimum value of $|PQ|$ is ( )"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem. The question says: If point P is on the plane, and point Q is on the curve \\( x^2 +... |
1,811 | [{"role": "user", "content": "Gunther just financed a John Deere tractor through the dealership. He has a certain monthly payment for 5 years, with no interest, and he financed the tractor for $9000. What is his monthly payment?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. Gunther financed a John De... |
1,797 | [{"role": "user", "content": "A couple who own an appliance store discover that if they advertise a sales discount of some percentage on every item in the store, at the end of one month the number of total items sold increases by 20%. Their gross income from sales for one month increases by 8%. What is the sales discou... |
1,770 | [{"role": "user", "content": "Let $h(x) = x^2 - 8x + 23$, and let $k(h(x)) = 3x + 4$. What is the sum of all possible values of $k(9)$?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, ... |
1,801 | [{"role": "user", "content": "A compound has a certain number of Potassium, 1 Bromine, and 3 Oxygen atoms. The molecular weight of the compound is 168. How many Potassium atoms are in the compound?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says a compound has some Potassium (K), 1 Bro... |
1,762 | [{"role": "user", "content": "Determine the standard equation of the curve based on the following conditions:\n(1) A parabola with a directrix equation $$x=-\\frac{3}{2};$$\n(2) A hyperbola with the focus on the x-axis that passes through points (2, 0) and $$(2\\sqrt{3}, \\sqrt{6}).$$"}, {"role": "assistant", "content"... |
1,822 | [{"role": "user", "content": "Given sets A={0, 1} and B={-1, 1}, find A∩B."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the intersection of sets A and B. First, let me remember what the intersection of two sets means. The intersection, denoted by A∩B, is the set of elements that are i... |
1,815 | [{"role": "user", "content": "Consider the inequality $4 \\leq |x+2| \\leq 8$. Find the set of $x$-values for which this inequality holds.\n$\\textbf{(A)}\\ -10\\leq x\\leq-6\\text{ or }2\\leq x\\leq 6\\qquad$\n$\\textbf{(B)}\\ -6\\leq x\\leq 6\\qquad$\n$\\textbf{(C)}\\ x\\leq-2\\text{ or }x\\geq 10\\qquad$\n$\\textbf{... |
1,740 | [{"role": "user", "content": "In acute triangle $\\triangle ABC$, $\\frac{b^2 - a^2 - c^2}{ac} = \\frac{\\cos(A + C)}{\\sin A \\cos A}$.\n(1) Find angle $A$;\n(2) If $a = \\sqrt{2}$, when $\\sin B + \\cos(\\frac{7\\pi}{12} - C)$ reaches its maximum value, find $B$ and $b$."}, {"role": "assistant", "content": "<think>\n... |
1,752 | [{"role": "user", "content": "Compute $1101_2 + 111_2 - 1010_2 + 1001_2$ and express your answer in base 2."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so I need to compute this bi... |
1,772 | [{"role": "user", "content": "For $-36 \\le x \\le 36,$ find the maximum value of $\\sqrt{36 + x} + \\sqrt{36 - x}.$"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so I need to find t... |
1,755 | [{"role": "user", "content": "Shifting the graph of the function $f(x)=\\sin (2x- \\frac {\\pi}{3})$ to the right by $\\frac {\\pi}{3}$ units results in the graph of the function $g(x)$. Then, an equation of a symmetry axis of $g(x)$ can be\nA: $x= \\frac {3\\pi}{4}$\nB: $x= \\frac {7\\pi}{6}$\nC: $x= \\frac {7\\pi}{12... |
1,814 | [{"role": "user", "content": "if the cost price of 81 chocolates is equal to the selling price of 45 chocolates , the gain percent is :"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem. So, the question says: \"If the cost price of 81 chocolates is equal to the selling price of... |
1,764 | [{"role": "user", "content": "Given non-zero vectors $\\overrightarrow{a}$, $\\overrightarrow{b}$, $\\overrightarrow{c}$ that satisfy $\\overrightarrow{a} + 2\\overrightarrow{b} + 3\\overrightarrow{c} = \\overrightarrow{0}$, and $\\overrightarrow{a} \\cdot \\overrightarrow{b} = \\overrightarrow{b} \\cdot \\overrightarr... |
1,825 | [{"role": "user", "content": "The value of $\\sin 210^\\circ$ is equal to ( )\n\nA: $-\\frac{\\sqrt{3}}{2}$\nB: $\\frac{\\sqrt{3}}{2}$\nC: $-\\frac{1}{2}$\nD: $\\frac{1}{2}$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the value of sin 210 degrees. Hmm, first, I remember that 210 deg... |
1,771 | [{"role": "user", "content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Given that $a > b$, $a=5$, $c=6$, and $\\sin B=\\dfrac{3}{5}$.\n\n1. Find the values of $b$ and $\\sin A$.\n2. Find the value of $\\sin (2A+\\dfrac{\\pi}{4})$."}, {"role": "assistant", "... |
1,692 | [{"role": "user", "content": "Let $O$ be the circumcenter of triangle $ABC$ with $|AB|=5$ , $|BC|=6$ , $|AC|=7$ . Let $A_1$ , $B_1$ , $C_1$ be the reflections of $O$ over the lines $BC$ , $AC$ , $AB$ , respectively. What is the distance between $A$ and the circumcenter of triangle $A_1B_1C_1$ ? $ \n\... |
1,829 | [{"role": "user", "content": "If $a$ and $d$ are constants and $(x + 3)(x + a) = x^2 + dx + 12$, then $d$ is?\n$\\textbf{(A)}\\ 4\\qquad \\textbf{(B)}\\ 5\\qquad \\textbf{(C)}\\ 6\\qquad \\textbf{(D)}\\ 7\\qquad \\textbf{(E)}\\ 8$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that (x... |
1,686 | [{"role": "user", "content": "\nConstruct the image of the square with vertices \\( A(0,0), B(0,2), C(2,2), D(2,0) \\) under the following transformations:\na) \\( w = i z \\)\nb) \\( w = 2 i z - 1 \\)\nc) \\( w = z^{2} \\)\nd) \\( w = z^{-1} \\)"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or chal... |
1,833 | [{"role": "user", "content": "A contest involves matching four celebrities with their baby photos, which are not labeled. Contestants have to guess the correct match for all four celebrities. What is the probability that a contestant guessing at random will correctly match all four celebrities with their respective bab... |
1,754 | [{"role": "user", "content": "A train 140 meters long crosses an electric pole in 2.3998080153587713 seconds, if its speed is a certain km/hr. What is the speed of the train?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about a train that's 140 meters long crossing an electric pole in... |
1,744 | [{"role": "user", "content": "\nLet \\( X = (X_t) \\) be a Borel function on \\([0, T]\\). Considering \\( t \\) as time, \\( X \\) as the observed process, and \\([0, T]\\) as the observation period for \\( X \\), P. Lévy proposed the following formula for calculating the time \\( l_X(x, T) \\), spent by the process \... |
1,830 | [{"role": "user", "content": "In the Cartesian coordinate system $xOy$, it is known that the initial sides of angles $\\alpha$ and $\\beta$ are the non-negative half-axis of $x$, and their terminal sides pass through points $A(1,2)$ and $B(5,1)$, respectively. The value of $\\tan (\\alpha-\\beta)$ is __________."}, {"r... |
1,837 | [{"role": "user", "content": "Mark has an egg farm. His farm supplies one store with 5 dozen eggs and another store with 30 eggs each day. How many eggs does he supply these two stores in a week?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about Mark's egg farm supplying two stores, ... |
1,835 | [{"role": "user", "content": "If $|a| = -a$, then the condition for the equation to hold is\n===================\nA: $a$ is a positive number\nB: $a$ is a negative number\nC: $a$ is zero or a negative number\nD: $a$ is zero or a positive number"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The proble... |
1,836 | [{"role": "user", "content": "If \\(p\\) and \\(q\\) are constants and \\((x + 3)(x + p) = x^2 + qx + 12\\), then \\(q\\) is\n**A)** 3 \n**B)** 5 \n**C)** 7 \n**D)** 9 \n**E)** 11"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that (x + 3)(x + p) equals x² + qx + 12, and we need t... |
1,718 | [{"role": "user", "content": "As in the figure, an \"L\" shape composed of three small squares can be taken out. Now, it is required that all the squares taken out are completely white. How many different ways are there to do this (the \"L\" shape is allowed to rotate)?"}, {"role": "assistant", "content": "<think>\n\nT... |
1,769 | [{"role": "user", "content": "For $f(x)=x^4+|x|,$ let $I_1=\\int_0^\\pi f(\\cos x)\\ dx,\\ I_2=\\int_0^\\frac{\\pi}{2} f(\\sin x)\\ dx.$ \r\n\r\nFind the value of $\\frac{I_1}{I_2}.$ "}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct ... |
1,750 | [{"role": "user", "content": "In the polar coordinate system, the ray $l:θ= \\frac{π}{6}$ intersects the circle $C:ρ=2$ at point $A$, and the equation of the ellipse $D$ is ${ρ}^{2}= \\frac{3}{1+2{\\sin }^{2}θ}$. Establish a rectangular coordinate system $xOy$ with the pole as the origin and the positive semi-axis of t... |
1,780 | [{"role": "user", "content": "From two packs of 52 cards each, two cards are drawn together at random. What is the probability of drawing one specific card, such as the Ace of Spades from the first deck, and one specific card from the second deck, such as the King of Hearts?"}, {"role": "assistant", "content": "<think>... |
1,748 | [{"role": "user", "content": "Let $l, l'$ be two lines in $3$ -space and let $A,B,C$ be three points taken on $l$ with $B$ as midpoint of the segment $AC$ . If $a, b, c$ are the distances of $A,B,C$ from $l'$ , respectively, show that $b \\leq \\sqrt{ \\frac{a^2+c^2}{2}}$ , equality holding if $l, l'$ ... |
1,842 | [{"role": "user", "content": "In a school of 850 boys, 40% are Muslims, 28% are Hindus, 10% are Sikhs, and the remaining belong to other communities. How many boys belong to other communities?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about finding the number of boys in a school wh... |
1,826 | [{"role": "user", "content": "Given that the point (1, 2) is transformed to the point (7, 6) under the transformation represented by the matrix A = $$\\begin{bmatrix} 1 & x \\\\ 2 & y\\end{bmatrix}$$, find:\n 1) Matrix A\n 2) The eigenvalues and their corresponding eigenvectors of Matrix A."}, {"role": "assistant", "... |
1,818 | [{"role": "user", "content": "How many positive integers less than 1000 are divisible by 2, 3, 5, and 7?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so the problem is asking: how m... |
1,787 | [{"role": "user", "content": "Thirty-six players are playing a game: they take turns drawing a random card from a 36-card deck. If a player draws the ace of diamonds, they win. If they draw any other card, they return it to the deck, and the next player takes their turn. This continues in a cycle: first player, then th... |
1,838 | [{"role": "user", "content": "If three geometric means are inserted between $4$ and $1296$, find the third term in the geometric sequence.\n$\\textbf{(A)}\\ 18\\qquad\\textbf{(B)}\\ 36\\qquad\\textbf{(C)}\\ 72\\qquad\\textbf{(D)}\\ 108\\qquad\\textbf{(E)}\\ \\text{None of these}$"}, {"role": "assistant", "content": "<t... |
1,831 | [{"role": "user", "content": "Suppose that $y^2$ varies inversely with $\\sqrt{z}$. If $y=3$ when $z=4$, find the value of $z$ when $y=6$. Express your answer in simplest fractional form."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct a... |
1,715 | [{"role": "user", "content": "Given functions $f\\left(x\\right)=ax^{2}-\\left(2-a\\right)x+1$ and $g\\left(x\\right)=x$, if for any real number $x$, at least one of $f\\left(x\\right)$ and $g\\left(x\\right)$ is a positive number, then the range of real number $a$ is ______."}, {"role": "assistant", "content": "<think... |
1,774 | [{"role": "user", "content": "The roots of\n\\[ z^5 = -\\frac{1}{\\sqrt{2}} + \\frac{i}{\\sqrt{2}} \\]\nare $\\text{cis } \\theta_1$, $\\text{cis } \\theta_2$, $\\dots$, $\\text{cis } \\theta_5$, where $0^\\circ \\le \\theta_k < 360^\\circ$ for all $1 \\le k \\le 5$. Find $\\theta_1 + \\theta_2 + \\dots + \\theta_5$. G... |
1,858 | [{"role": "user", "content": "Jesse has 21 bananas. If he shares them among 3 friends, each friend would get _____ bananas ."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. Jesse has 21 bananas and he wants to share them among 3 friends. The question is asking how many bananas each friend would get. Hm... |
1,853 | [{"role": "user", "content": "Given the function $f(x) = x \\sin x$, find $f'(π)$ \\_\\_\\_\\_\\_\\_."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the derivative of f(x) = x sin x at x = π. First, I remember that to find the derivative of a product of two functions, I should use the p... |
1,856 | [{"role": "user", "content": "a man buy a book in rs 50 & sale it rs 90 . what is the rate of profit ? ? ?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about finding the rate of profit when a man buys a book for Rs 50 and sells it for Rs 90. Hmm, first I need to remember how to calcul... |
1,840 | [{"role": "user", "content": "An $8 \\mathrm{~cm}$ cube has a $4 \\mathrm{~cm}$ square hole cut through its centre. What is the remaining volume, in $\\mathrm{cm}^{3}$?\n(A) 64\n(B) 128\n(C) 256\n(D) 384\n(E) 448"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem step by step. So... |
1,808 | [{"role": "user", "content": "Determine the quadrants wherein the solution set for the inequalities $y > 3x$ and $y > 6 - 2x$ is entirely contained.\n$\\textbf{(A)}\\ \\text{I and II}\\qquad \\textbf{(B)}\\ \\text{II and III}\\qquad \\textbf{(C)}\\ \\text{I and III}\\qquad \\textbf{(D)}\\ \\text{III and IV}\\qquad \\te... |
1,723 | [{"role": "user", "content": "A man walks $x$ miles due east, then turns $120^\\circ$ to his left and walks $6$ miles in the new direction. If he finishes at a point $2\\sqrt{3}$ miles from his starting point, find $x$.\nA. $3\\sqrt{3} - \\sqrt{3}$\nB. $3\\sqrt{3} + \\sqrt{3}$\nC. $2\\sqrt{3}$\nD. $6$\nE. Not uniquely ... |
1,791 | [{"role": "user", "content": "Positive numbers \\(a\\), \\(b\\), and \\(c\\) satisfy the condition \\(c^{2} + ab = a^{2} + b^{2}\\). Prove the inequality \\(c^{2} + ab \\leq ac + bc\\)."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and... |
1,828 | [{"role": "user", "content": "Simplify and write the result as a common fraction: $$\\sqrt{\\sqrt[3]{\\sqrt{\\frac{1}{4096}}}}$$"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so I ne... |
1,854 | [{"role": "user", "content": "Ancient Chinese mathematician Monk Yixing used the \"Nine-Fold Shadow Algorithm\" to establish a table of the correspondence between the shadow length $l$ and the solar zenith angle $\\theta \\left(0^{\\circ}\\leqslant \\theta \\leqslant 180^{\\circ}\\right)$ in the \"Dayan Calendar.\" Thi... |
1,737 | [{"role": "user", "content": "What is the ratio of the volume of a cube with edge length 8 inches to the volume of a cube with edge length 20 centimeters? Express your answer as a decimal."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct ... |
1,756 | [{"role": "user", "content": "Find the number of integers $n$ such that $n$ does not divide $f(n)$, where $f(n) = n - p$, with $p$ being the smallest prime divisor of $n$, for all integers $2 \\le n \\le 60$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult ... |
1,794 | [{"role": "user", "content": "In the standard formulation of a flavored drink, the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is different, and the ratio of flavoring to water is half that of the standard formulation. A large bottle... |
1,790 | [{"role": "user", "content": "In the rectangular coordinate system $xOy$, point $A$ is a moving point on the ellipse $\\frac{x^{2}}{16}+ \\frac{y^{2}}{4}=1$, and point $P$ is on the line $OA$ such that $\\overrightarrow{OA}\\cdot \\overrightarrow{OP}=6$. Find the maximum value of the projection of line segment $OP$ on ... |
1,804 | [{"role": "user", "content": "Evaluate the sum \\[\\frac{1}{3^1} + \\frac{3}{3^2} + \\frac{5}{3^3} + \\frac{7}{3^4} + \\cdots + \\frac{2k-1}{3^k} + \\cdots \\]"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to... |
1,850 | [{"role": "user", "content": "A British tourist in Spain wants to exchange pounds for Euros. If 4500 Euros = 3900 pounds, how much Euros will the tourist receive for exchanging 3000 pounds?\n(A) 3200 Euros\n(B) 3500 Euros\n(C) 3461.54 Euros\n(D) 3730 Euros\n(E) 3910 Euros"}, {"role": "assistant", "content": "<think>\n\... |
1,848 | [{"role": "user", "content": "Determine the relationship between the three numbers $a=0.31^2$, $b=\\log_2{0.31}$, and $c=2^{0.31}$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to figure out the relationship between a, b, and c where a is 0.31 squared, b is the logarithm base 2 of 0.31, and c... |
1,860 | [{"role": "user", "content": "Given the complex number $z=m+2i$, and $(2+i)z$ is a purely imaginary number, the real number $m=$ ( ).\nA: $1$\nB: $2$\nC: $-1$\nD: $-2$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that given the complex number \\( z = m + 2i \\), and \\( (2 + i)z \\)... |
1,865 | [{"role": "user", "content": "The equation $x^{2}-4x+m=0$ has two distinct real roots for $x$. What is the range of values for $m$?\n\nA: $m \\gt 2$\n\nB: $m \\lt 2$\n\nC: $m \\gt 4$\n\nD: $m \\lt 4$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about a quadratic equation \\( x^2 - 4x ... |
1,733 | [{"role": "user", "content": "Each of the 1000 gnomes has a hat, blue on the outside and red on the inside (or vice versa). If a gnome is wearing the red hat, he can only lie, and if he is wearing the blue hat, he can only tell the truth. Throughout one day, each gnome told every other gnome, \"You are wearing a red ha... |
1,867 | [{"role": "user", "content": "Convert the point \\( \\left( 10, \\frac{5 \\pi}{3} \\right) \\) in polar coordinates to rectangular coordinates."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to convert the polar coordinates (10, 5π/3) to rectangular coordinates. Hmm, polar coordinates are given... |
1,871 | [{"role": "user", "content": "In a school of 1200 students, 35% are Muslims, 25% are Hindus, 15% are Sikhs, 10% are Christians, 5% are Buddhists, and the remaining students belong to other religious communities. How many students belong to the other religious communities?"}, {"role": "assistant", "content": "<think>\n\... |
1,857 | [{"role": "user", "content": "In the polar coordinate system, the polar coordinates of two points $A$ and $B$ are $A(1, \\frac{\\pi}{6})$ and $B(2, -\\frac{\\pi}{2})$, respectively. The distance between points $A$ and $B$ is equal to $\\_\\_\\_\\_\\_\\_$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see.... |
1,863 | [{"role": "user", "content": "The minimum positive period of the function $y=\\cos^2x$ is ( ) \nA: $2\\pi$ \nB: $\\pi$ \nC: $\\frac{\\pi}{2}$ \nD: $\\frac{\\pi}{4}$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The question is asking for the minimum positive period of the function \\( y = \\cos^... |
1,832 | [{"role": "user", "content": "Find the number of positive integers \\(k\\) for which the equation\n\\[3kx - 18 = 9k\\]\nhas an integer solution for \\(x\\).\n- (A) 3\n- (B) 2\n- (C) 5\n- (D) 4"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a dir... |
1,851 | [{"role": "user", "content": "for any even integer p , 300 multiplied by p is square of an integer . what is the least value of p ?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem. The question says: \"For any even integer p, 300 multiplied by p is the square of an integer. Wh... |
1,881 | [{"role": "user", "content": "Mike picked 8 pears and Jason picked 7 pears from the pear tree. Fred picked 6 apples from the apple tree. Sarah picked 12 apples from the apple tree. How many pears and apples were picked in total?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for ... |
1,806 | [{"role": "user", "content": "In the expansion of $(\\frac{3}{{x}^{2}}+x+2)^{5}$, the coefficient of the linear term in $x$ is ____."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so ... |
1,880 | [{"role": "user", "content": "Given two numbers \\( M \\) and \\( N \\), find the percent that \\( M \\) is greater than \\( N \\) in reference to the sum of \\( M \\) and \\( N \\).\nA) \\( \\frac{100(M-N)}{M} \\)\nB) \\( \\frac{100(M-N)}{N} \\)\nC) \\( \\frac{100(M-N)}{M+N} \\)\nD) \\( \\frac{100N}{M+N} \\)\nE) \\( \... |
1,887 | [{"role": "user", "content": "Joel’s garden is 64 square feet large. He wants to use half of the garden for fruits and half of the garden for vegetables. He wants to use a quarter of the fruit section for strawberries. How many square feet of the garden will be used for strawberries?"}, {"role": "assistant", "content":... |
1,870 | [{"role": "user", "content": "A train 270 meters long is moving at a certain speed. It will cross a man coming from the opposite direction at a speed of 2 km per hour in 36 seconds. What is the speed of the train in kmph?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem step by... |
1,875 | [{"role": "user", "content": "(Convert 4 points) Convert the binary number $101101_2$ to decimal."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to convert the binary number 101101₂ to decimal. Hmm, binary to decimal. I remember that each digit in a binary number represents a power of 2, starti... |
1,885 | [{"role": "user", "content": "Bucket P has thrice the capacity as bucket Q. It takes some turns for bucket P to fill the empty drum. It takes 60 turns for both the buckets P and Q, having each turn together, to fill the empty drum. How many turns does it take for bucket P alone to fill the drum?"}, {"role": "assistant"... |
1,891 | [{"role": "user", "content": "Given a regression equation $$\\hat y = 2 + 3x$$, when the variable $x$ increases by one unit, then ( ) \nA: $y$ increases by an average of 2 units \nB: $y$ increases by an average of 3 units \nC: $y$ decreases by an average of 2 units \nD: $y$ decreases by an average of 3 units"}, {"... |
1,845 | [{"role": "user", "content": "Given that $\\overrightarrow{a}$ is an arbitrary vector forming an angle of $60^{\\circ}$ with the unit vector $\\overrightarrow{b}$, then the minimum value of the function $f(\\lambda)=\\left|\\lambda \\overrightarrow{a}- \\overrightarrow{b}\\right| \\cdot \\frac{\\left|\\left( \\sqrt{3} ... |
1,841 | [{"role": "user", "content": "Three distinct integers are selected at random between $1$ and $2020$, inclusive. Which of the following is a correct statement about the probability $p$ that the product of the three integers is odd?\n$\\textbf{(A)}\\ p<\\dfrac{1}{8}\\qquad\\textbf{(B)}\\ p=\\dfrac{1}{8}\\qquad\\textbf{(C... |
1,890 | [{"role": "user", "content": "In the Cartesian coordinate system, the distance from the point $\\left(3,-2\\right)$ to the origin is ______."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the distance from the point (3, -2) to the origin in the Cartesian coordinate system. Hm... |
1,894 | [{"role": "user", "content": "Rachel makes a certain amount as a waitress in a coffee shop. In one hour, she serves 20 different people and they all leave her a $1.25 tip. She made $37 in that hour. How much does she make per hour without tips?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The proble... |
1,878 | [{"role": "user", "content": "Given $x, y \\in R^{+}$, and they satisfy the equation $\\frac{x}{3} + \\frac{y}{4} = 1$, find the maximum value of $xy$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that x and y are positive real numbers, and they satisfy the equation (x/3) + (y/4) = ... |
1,864 | [{"role": "user", "content": "Add the following two numbers: $800,000,000,000 + 299,999,999,999$.\nA) $1,000,000,000,000$\nB) $1,099,999,999,999$\nC) $1,100,000,000,000$\nD) $900,000,000,000$\nE) $2,099,999,999,999$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to add 800,000,000,000 and 299,9... |
1,892 | [{"role": "user", "content": "What is the least common multiple of 9, 12, and 15?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the least common multiple (LCM) of 9, 12, and 15. Hmm, LCM is the smallest number that all three numbers divide into without leaving a remainder. I remember t... |
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