__src_index__ int64 0 172k | messages stringlengths 375 66.5k |
|---|---|
831 | [{"role": "user", "content": "Two trains 315 m and 270 m long run at the speed of 80 km/hr and 50 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about two trains moving in oppo... |
821 | [{"role": "user", "content": "Calculate the value of the following series expressed as a common fraction: $$\\frac{1}{4^{1}}+\\frac{1}{4^{2}}+\\frac{1}{4^{3}}+\\frac{1}{4^{4}}+\\frac{1}{4^{5}}+\\frac{1}{4^{6}}.$$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to calculate the sum of this series... |
823 | [{"role": "user", "content": "A company's stock index today is 2, and the index increases by 0.02% every day. What is the approximate value of this company's stock index after 100 days? (Round to three decimal places)."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about a stock index t... |
845 | [{"role": "user", "content": "Given that the directrix of the parabola $y^2 = 2px$ (where $p > 0$) passes through the point $(-1,1)$, find the coordinates of the focus of the parabola."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about a parabola given by the equation \\( y^2 = 2px \\... |
853 | [{"role": "user", "content": "The terminal side of the angle $-870^{\\circ}$ is in the quadrant $(\\quad)$\nA: First Quadrant\nB: Second Quadrant\nC: Third Quadrant\nD: Fourth Quadrant"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking which quadrant the terminal side of the angle -8... |
813 | [{"role": "user", "content": "Let $P$ be a point on the ellipse $C: \\dfrac{x^{2}}{16} + \\dfrac{y^{2}}{9} = 1$, $F_{1}$ and $F_{2}$ be the left and right foci of the ellipse $C$, respectively. If $\\overrightarrow {PF_{1}} \\cdot \\overrightarrow {PF_{2}} = 5$, then the area of $\\triangle PF_{1}F_{2}$ is ( ).\n\nA: $... |
842 | [{"role": "user", "content": "Given that $a$ and $b$ are real numbers, then \"a > 1, b > 2\" is a condition for \"a + b > 3 and ab > 2\" to be\nA: A sufficient but not necessary condition\nB: A necessary but not sufficient condition\nC: A sufficient and necessary condition\nD: Neither sufficient nor necessary condition... |
790 | [{"role": "user", "content": "A collection of 300 books, consisting of novels, biographies, and science books, went on sale. 3/5 of the novels, 2/3 of the biographies, and 7/10 of the science books were sold. If the novels were sold for $4 each, biographies for $7 each, and science books for $6 each, and there are 30 n... |
839 | [{"role": "user", "content": "Naomi drives to the beauty parlor in 60 minutes during normal traffic conditions. On the way back from the parlor, her average speed is half the average speed as it was on the way to the parlor. During her first round trip, she encounters a 15-minute traffic delay and stops for a 10-minute... |
863 | [{"role": "user", "content": "Given the function $f(x)=x^{2}$, then $\\lim_{\\triangle x \\to 0} \\frac{f(\\triangle x)-f(0)}{\\triangle x}=$ \\_\\_\\_\\_\\_\\_."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the limit as Ξx approaches 0 of [f(Ξx) - f(0)] divided by Ξx, where f(x) is x ... |
827 | [{"role": "user", "content": "Given that $x \\in \\left[0, \\frac{\\pi}{3}\\right]$, let vector $\\overrightarrow{m} = (\\sin x, \\cos x)$ and $\\overrightarrow{n} = \\left(\\frac{\\sqrt{3}}{2}, \\frac{1}{2}\\right)$.\n\n(1) If $\\overrightarrow{m} \\parallel \\overrightarrow{n}$, find the value of $x$.\n\n(2) If $\\ov... |
721 | [{"role": "user", "content": "Determine the number of angles between \\(0\\) and \\(2\\pi\\), other than integer multiples of \\(\\frac{\\pi}{2}\\), such that \\( \\sin \\theta \\), \\( \\cos \\theta \\), and \\( \\cot \\theta \\) form a geometric sequence in some order."}, {"role": "assistant", "content": "<think>\n\n... |
870 | [{"role": "user", "content": "Jessica has 3 dozen red marbles. Sandy has 4 times more red marbles than Jessica. How many red marbles does Sandy have?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says Jessica has 3 dozen red marbles. First, I need to remember that a dozen is 12, so 3 doze... |
819 | [{"role": "user", "content": "The spinner used by Jane and her brother now has six congruent sectors, numbered 1 through 6. They each spin the spinner once. If the non-negative difference of their numbers is less than 2, Jane wins. Otherwise, her brother wins. What is the probability that Jane wins? Express your answer... |
858 | [{"role": "user", "content": "Given $f(x)$ and $g(x)$ are respectively even and odd functions defined on $\\mathbb{R}$, and $f(x) - g(x) = x^3 + x^2 + 1$, then $f(1) + g(1) = \\ $\n\nA: $-3$\n\nB: $-1$\n\nC: $1$\n\nD: $3$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that f(x) is an ... |
865 | [{"role": "user", "content": "Matthew, the baker, usually takes some time to assemble ingredients, 1.5 hours to bake the cakes, and another 1 hour to decorate each cake with cinnamon sprinkles. One day, his oven failed to reach the correct temperature and it took twice as long for the cakes to bake as they usually take... |
749 | [{"role": "user", "content": "If $16^8 = 8^x$, what is the value of $2^{-x}$? Express your answer as a common fraction."}, {"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 sol... |
728 | [{"role": "user", "content": "Find all pairs of positive numbers \\((x, y)\\) that satisfy the system of equations:\n\\[\n\\left\\{\n\\begin{array}{l}\n2 x - \\sqrt{x y} - 4 \\sqrt{\\frac{x}{y}} + 2 = 0 \\\\\n2 x^{2} + x^{2} y^{4} = 18 y^{2}.\n\\end{array}\n\\right.\n\\]"}, {"role": "assistant", "content": "<think>\n\n... |
838 | [{"role": "user", "content": "Given that the solution set of the inequality $ax^{2}+bx+c\\leqslant 0$ is $\\{x\\left|\\right.x\\leqslant -3$ or $x\\geqslant 4\\}$, then the solution set of the inequality $bx^{2}+2ax-c-3b\\leqslant 0$ is ______."}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to solve th... |
868 | [{"role": "user", "content": "New York is two-thirds as populated as all of New England. If New England has 2100000 people, calculate the combined population of both states."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says New York is two-thirds as populated as all of New England. New E... |
866 | [{"role": "user", "content": "A certain percentage of the members of a study group are women, and 40 percent of those women are lawyers. The probability that a randomly selected member is a woman lawyer is 0.32. What percentage of the study group are women?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's tr... |
871 | [{"role": "user", "content": "The equation of the directrix of the parabola $x^{2}=2y$ is \\_\\_\\_\\_\\_\\_."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the equation of the directrix for the parabola given by \\( x^2 = 2y \\). Hmm, first, I should remember the standard form of a par... |
876 | [{"role": "user", "content": "The domain of the function $f(x) = \\ln(x - 1)$ is ( )\nA: $\\{x | x > 1\\}$\nB: $\\{x | x < 1\\}$\nC: $\\{x | x > 0\\}$\nD: $\\{x | x < 0\\}$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The question is about finding the domain of the function f(x) = ln(x - 1). Hmm, do... |
812 | [{"role": "user", "content": "In $\\triangle ABC$, $AB = AC = 3.6$, point $D$ lies on $AB$ with $AD = 1.2$, and point $E$ lies on the extension of $AC$. The area of $\\triangle AED$ is equal to the area of $\\triangle ABC$. Find the length of $AE$.\n\n(A) 4.8 \n(B) 5.4 \n(C) 7.2 \n(D) 10.8 \n(E) 12.6"}, {"role": "a... |
780 | [{"role": "user", "content": "Given an ellipse $C$: $\\frac{x^2}{16}+\\frac{y^2}{4}=1$, with the left and right foci being $F_{1}$ and $F_{2}$, respectively. Line $l$ intersects the ellipse at points $A$ and $B$, where the chord $AB$ is bisected by the point $(\\sqrt{3},\\frac{\\sqrt{3}}{2})$. \n$(1)$ Find the equatio... |
874 | [{"role": "user", "content": "The average of 10 numbers was calculated as a certain value. It is discovered later on that while calculating the average, one number, namely 66, was incorrectly read as 26. The correct average is 22. What was the initially calculated average?"}, {"role": "assistant", "content": "<think>\n... |
745 | [{"role": "user", "content": "**Q.** Show that for any given positive integers $k, l$ , there exists infinitely many positive integers $m$ , such that $i) m \\geqslant k$ $ii) \\text{gcd}\\left(\\binom{m}{k}, l\\right)=1$ *Suggested by pigeon_in_a_hole*"}, {"role": "assistant", "content": "<think>\n\nThis is a compl... |
886 | [{"role": "user", "content": "In the plane rectangular coordinate system $xOy$, the point symmetric to point $(2,5)$ with respect to the $y$-axis is:\n\nA: $(-2,5)$\n\nB: $(2,-5)$\n\nC: $(-2,-5)$\n\nD: $(5,2)$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The question is asking for the point symmetri... |
849 | [{"role": "user", "content": "Marcy keeps a certain amount of water by her desk. She takes a sip every five minutes, and each sip is 40 ml. It takes her 250 minutes to drink the whole bottle of water. How many liters of water does Marcy keep by her desk?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. ... |
879 | [{"role": "user", "content": "Miki has a dozen oranges of the same size and a dozen pears of the same size. Miki extracts 12 ounces of pear juice from 4 pears and 6 ounces of orange juice from 3 oranges. She decides to make a pear-orange juice blend using 8 pears and 6 oranges. What percent of the blend is pear juice?\... |
862 | [{"role": "user", "content": "Find the value of the expression \\(\\frac{a^{2}}{b c}+\\frac{b^{2}}{a c}+\\frac{c^{2}}{a b}\\) if \\(a + b + c = 0\\)."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the value of the expression \\(\\frac{a^{2}}{b c} + \\frac{b^{2}}{a c} + \\frac{c^{2}}{a b... |
800 | [{"role": "user", "content": "Find the value of the following expression: \n\\(\\cos \\left(\\frac{3}{2} \\pi + 4 \\alpha \\right) + \\sin (3 \\pi - 8 \\alpha) - \\sin (4 \\pi - 12 \\alpha) = 4 \\cos 2 \\alpha \\cos 4 \\alpha \\sin 6 \\alpha\\)."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or chal... |
820 | [{"role": "user", "content": "(1) In the expansion of $(1-x)^5 + (1-x)^6 + (1-x)^7 + (1-x)^8$, find the coefficient of the term containing $x^3$; \n(2) If in the expansion of $(2-x)^6$, the second term is less than the first term but not less than the third term, find the range of values for $x$."}, {"role": "assistan... |
854 | [{"role": "user", "content": "A full stationary oil tank that is a right circular cylinder has a certain radius and a height of 25 feet. Oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder with a radius of 4 feet and a height of 10 feet. The oil level dropped 0.016 f... |
883 | [{"role": "user", "content": "In a class of 54 students, a systematic sample of size 6 is to be taken based on their student ID numbers (1β54). If the number 5 is the first to be drawn in the first part, what is the highest student ID number in the sample?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try... |
791 | [{"role": "user", "content": "Let \\( P \\) be a point inside triangle \\( ABC \\) such that\n\\[ \\overrightarrow{PA} + 3 \\overrightarrow{PB} + 2 \\overrightarrow{PC} = \\mathbf{0}. \\]\nFind the ratio of the area of triangle \\( ABC \\) to the area of triangle \\( APB \\)."}, {"role": "assistant", "content": "<think... |
778 | [{"role": "user", "content": "How many three-digit numbers have at least one $3$ and at least one $4$?\nA) 46\nB) 48\nC) 50\nD) 52\nE) 54"}, {"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... |
877 | [{"role": "user", "content": "If the equation $\\frac{x^{2}}{k-3} + \\frac{y^{2}}{k+3} = 1$ represents a hyperbola with foci on the $y$-axis, then the range of the real number $k$ is $\\_\\_\\_\\_\\_\\_\\_.$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about finding the range of k suc... |
798 | [{"role": "user", "content": "To reduce the academic burden on students, the \"double reduction\" policy has been implemented in compulsory education schools nationwide starting from the autumn of 2021. To understand the parents' awareness of the \"double reduction\" policy, a school conducted a questionnaire evaluatio... |
893 | [{"role": "user", "content": "If $\\log_{5}a + \\log_{5}b = 2$, then the minimum value of $a + b$ is $\\underline{\\hspace{1cm}}$.\nA: $25$\nB: $10$\nC: $5$\nD: $2 \\sqrt {5}$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that log base 5 of a plus log base 5 of b equals 2, and we nee... |
897 | [{"role": "user", "content": "When 632-AB1=41, what number should go in B?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is 632 - AB1 = 41, and we need to find the number that goes in B. Hmm, first, I need to figure out what AB1 is. Wait, AB1 is a three-digit number where A and B are digi... |
898 | [{"role": "user", "content": "if 20 % of a number = 200 , then 120 % of that number will be ?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that 20% of a number is 200, and we need to find 120% of that same number. Hmm, first, I need to figure out what the original number is. Let me ... |
753 | [{"role": "user", "content": "If the positive integers $x$ and $y$ satisfy $(2x-5)(2y-5)=25$, then the value of $x+y$ 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 I need to s... |
843 | [{"role": "user", "content": "Set A contains all the odd numbers between 1 and 100 inclusive. Set B contains all the odd numbers between 103 and 200 inclusive. What is the difference between the sum of elements of Set B and the sum of the elements of Set A?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's tr... |
744 | [{"role": "user", "content": "Show that for any integers \\( a \\), \\( b \\), \\( c \\), not all zero, and such that \\( |a|, |b|, |c| < 10^6 \\), we have \\( |a + b \\sqrt{2} + c \\sqrt{3}| > 10^{-21} \\). However, show that we can find such \\( a \\), \\( b \\), \\( c \\) with \\( |a + b \\sqrt{2} + c \\sqrt{3}| < 1... |
833 | [{"role": "user", "content": "Let $r$ and $s$ denote the two real roots of $x^2 - 3x\\sqrt{2} + 2 = 0$. Determine $r^6 + s^6$."}, {"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... |
900 | [{"role": "user", "content": "A new regulation requires that all truck licenses consist of the letters A, M, or S followed by any six digits. What is the number of groups of letters and numbers available for truck licenses?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about figuring o... |
889 | [{"role": "user", "content": "Proposition p: $|x| \\geq 1$, Proposition q: $x^2 + x - 6 \\geq 0$, then \"not p\" is a ( ) condition for \"not q\" to hold.\nA: Necessary but not sufficient condition\nB: Sufficient but not necessary condition\nC: Necessary and sufficient condition\nD: Neither sufficient nor necessary con... |
894 | [{"role": "user", "content": "Let the universal set $A = \\{x | x \\leq 2x + 1 \\leq 5\\}$, and $B = \\{x | 0 < x \\leq 3\\}$. Then, $A \\cap B = \\_\\_\\_\\_\\_\\_$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the intersection of sets A and B. First, I should figure out what set A i... |
878 | [{"role": "user", "content": "Given the equations $a = b+3$, $b = c-4$, $c = d+5$, and $d = e-6$, determine which of the five quantities $a, b, c, d, e$ is the largest.\nA) $a$\nB) $b$\nC) $c$\nD) $d$\nE) $e$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to figure out which of the five quantit... |
899 | [{"role": "user", "content": "Lisa is a member of the photography club at school. Every weekend the club will go anywhere to take photos. Leslie took 10 photos of animals to share with the club. She also took 3 times as many photos of flowers as animals and took 10 fewer scenery than the flowers. If Lisa took 15 fewer ... |
789 | [{"role": "user", "content": "Given a circle \\( \\odot O \\), point \\( A \\) lies outside the circle, and two tangents \\( AM \\) and \\( AN \\) are drawn from \\( A \\) to touch the circle at points \\( M \\) and \\( N \\) respectively. Point \\( P \\) is chosen on the extension of segment \\( OM \\) such that \\( P... |
912 | [{"role": "user", "content": "How many matches will be held during a 10-person round-robin tennis tournament where each player plays every other player exactly once?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about a 10-person round-robin tennis tournament where each player plays ev... |
913 | [{"role": "user", "content": "Michelle needs a drying rack for each three pounds of pasta she makes, and it takes a certain number of cups of flour to make each pound of pasta dough. She owns three racks right now. Michelle will need 1 more drying rack if she makes pasta using three 8-cup bags of flour. How many cups o... |
792 | [{"role": "user", "content": "Determine all pairs of integers \\((x, y)\\) satisfying \\(x^{2} = y^{2}\\left(x + y^{4} + 2y^{2}\\right)\\)."}, {"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.\nWe... |
822 | [{"role": "user", "content": "Let $a, b, c$ be positive real numbers such that $a + b + c = 2.$ Find the minimum value of\n\\[\\frac{1}{a + 3b} + \\frac{1}{b + 3c} + \\frac{1}{c + 3a}.\\]"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct a... |
916 | [{"role": "user", "content": "If the terminal side of angle $Ξ±$ passes through point $P(1, -\\sqrt{3})$, then the value of $\\sin Ξ±$ is equal to __________."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that the terminal side of angle Ξ± passes through the point P(1, -β3), and we need... |
885 | [{"role": "user", "content": "The standard equation of circle C, whose center is on the x-axis and which is tangent to the line $l: y = 2x + 1$ at point P(0, 1), is \\_\\_\\_\\_\\_\\_."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and ... |
873 | [{"role": "user", "content": "What is the coefficient of $x^4$ in the expansion of $$(x - 3\\sqrt{2})^8?$$"}, {"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 the coeffic... |
752 | [{"role": "user", "content": "The \\( n \\) points \\( P_{1}, P_{2}, \\ldots, P_{n} \\) are placed inside or on the boundary of a disk of radius 1 in such a way that the minimum distance \\( d_{n} \\) between any two of these points has its largest possible value \\( D_{n} \\). Calculate \\( D_{n} \\) for \\( n=2 \\) t... |
914 | [{"role": "user", "content": "Two years ago, Ram put $1,000 into a savings account. At the end of the first year, his account had accrued some interest bringing his total balance to $1,100. The next year, his account balance increased by 20%. At the end of the two years, Ram's account balance increased by 32% from his ... |
901 | [{"role": "user", "content": "Add $5_8 + 13_8.$ Express your answer in base $8.$"}, {"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 add two numbers in base 8: 5 base 8 plus 1... |
918 | [{"role": "user", "content": "a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 15000 . a ' s share is ?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to ... |
904 | [{"role": "user", "content": "Determine the sum of the prime factors of $2310$.\n$\\textbf{(A)}\\ 20\\qquad\\textbf{(B)}\\ 27\\qquad\\textbf{(C)}\\ 28\\qquad\\textbf{(D)}\\ 34\\qquad\\textbf{(E)}\\ 35$"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to prov... |
867 | [{"role": "user", "content": "Let $A=\\{x|a_1x^2+b_1x+c_1>0 \\ (a_1, b_1, c_1 \\in \\mathbb{R}, a_1b_1c_1 \\neq 0)\\}$, and $B=\\{x|a_2x^2+b_2x+c_2>0 \\ (a_2, b_2, c_2 \\in \\mathbb{R}, a_2b_2c_2 \\neq 0)\\}$. Then $A=B$ if and only if $$\\frac {a_{1}}{a_{2}}= \\frac {b_{1}}{b_{2}}= \\frac {c_{1}}{c_{2}}$$ holds. This ... |
808 | [{"role": "user", "content": "Show that there are no seven lines in the plane such that there are at least six points which lie on the intersection of just three lines and at least four points which lie on the intersection of just two lines."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challengi... |
788 | [{"role": "user", "content": "For which values of the parameter \\( a \\) are both roots of the equation \\( (1+a) x^2 - 3a x + 4a = 0 \\) greater than 1?"}, {"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 thin... |
861 | [{"role": "user", "content": "Using a compass and a ruler, construct a point such that the tangents drawn from it to two given circles are equal to the given segments."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I... |
929 | [{"role": "user", "content": "Factorize:<br/>$(1)7x^{2}-63$;<br/>$(2)x^{3}+6x^{2}y+9xy^{2}$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's tackle these two factorization problems one by one. Starting with the first one: \\(7x^2 - 63\\). \n\nFirst, I need to remember that factoring usually starts with look... |
934 | [{"role": "user", "content": "At Northstar High School, the 120 students who participate in the Math Club usually meet to discuss various topics and enjoy some snacks. This year, Daniel and Emily are in charge of baking the cookies. They follow a recipe that makes a batch of 18 cookies using the following ingredients:\... |
932 | [{"role": "user", "content": "Divide this number by 2.5, subtract 10.5 from it, and multiply that by 0.3 to get 5.85. Find this number."}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to solve this problem step by step. The question says: \"Divide this number by 2.5, subtract 10.5 from it, and multiply ... |
887 | [{"role": "user", "content": "As shown in the figure, there is a toy clock. For each full circle that the hour hand makes, the minute hand makes 9 circles. If initially the two hands coincide, what is the degree turned by the hour hand when they next coincide?"}, {"role": "assistant", "content": "<think>\n\nThis is a c... |
909 | [{"role": "user", "content": "Given that the first four terms of a positive geometric sequence $\\{a\\_n\\}$ have a sum of $9$ and a product of $\\frac{81}{4}$, determine the sum of the reciprocals of these terms.\nA: $\\frac{3}{2}$\nB: $\\frac{9}{4}$\nC: $1$\nD: $2$"}, {"role": "assistant", "content": "<think>\n\nOkay... |
919 | [{"role": "user", "content": "Let \\[g(x) =\n\\begin{cases}\n4x^2 - 5 & \\text{if } x \\leq 5, \\\\\nbx + 3 & \\text{if } x > 5.\n\\end{cases}\n\\]\nFind $b$ if the graph of $y=g(x)$ is continuous."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide ... |
938 | [{"role": "user", "content": "A train speeds past a pole in some seconds and a platform 500 m long in 100 seconds. Its length is 500 m. How many seconds does it take for the train to speed past the pole?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem step by step. First, let'... |
902 | [{"role": "user", "content": "Let $\\alpha$ and $\\beta$ be two planes, and $m$ and $n$ be two lines. There are the following four propositions: \n(1) If $m \\perp n$, $m \\perp \\alpha$, and $n \\parallel \\beta$, then $\\alpha \\perp \\beta$. \n(2) If $m \\perp \\alpha$, $n \\parallel \\alpha$, then $m \\perp n$. ... |
836 | [{"role": "user", "content": "Let $m$ be a positive integer. Evaluate $b \\equiv (5^{2m} + 6)^{-1} \\pmod{11}$."}, {"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 the in... |
936 | [{"role": "user", "content": "If the expansion of the binomial $$(x^{2}- \\frac {1}{x})^{n}$$ has a total of 6 terms, then the coefficient of the term containing $x^4$ is \\_\\_\\_\\_\\_."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that the expansion of the binomial \\((x^2 - \\fra... |
942 | [{"role": "user", "content": "A massive number of placards are placed in a huge basket at the entrance of a stadium. Every person entering the stadium collects placards one for each hand. People started entering the stadium at 2 pm at a constant rate of X people per minute. After a certain amount of time, people compla... |
948 | [{"role": "user", "content": "Bianca earned 5 points for each bag of cans she recycled. If she had 17 bags, but didn't recycle 8 of them, how many points would she have earned?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about Bianca earning points for recycling cans. She gets 5 poin... |
891 | [{"role": "user", "content": "Given the line $ax + by - 1 = 0 (a > 0, b > 0)$ passes through the center of symmetry of the curve $y = 1 + \\sin(\\pi x) (0 < x < 2)$, find the minimum value of $\\frac{1}{a} + \\frac{2}{b}$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to solve this problem step by ste... |
888 | [{"role": "user", "content": "How many rational terms are in the expansion of\n\na) $(\\sqrt{2}+\\sqrt[4]{3})^{100}$\n\nb) $(\\sqrt{2}+\\sqrt[3]{3})^{300}$?"}, {"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 th... |
920 | [{"role": "user", "content": "Let $L$ be the number formed by $2022$ digits equal to $1$ , that is, $L=1111\\dots 111$ .\nCompute the sum of the digits of the number $9L^2+2L$ ."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and ... |
950 | [{"role": "user", "content": "Determine the value of $x$ for which the expression $\\frac{x-5}{6x}$ is equal to zero."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the value of x where the expression (x - 5)/(6x) equals zero. Hmm, right. So, when is a fraction equal to zero? I remember... |
875 | [{"role": "user", "content": "Let $\\mathbf{a}, \\mathbf{b}, \\mathbf{c}$ be vectors in $\\mathbb{R}^3$, and let $D$ be the determinant of the matrix with columns $\\mathbf{a}, 2\\mathbf{b}, \\mathbf{c}$. Find the determinant of the matrix formed by columns $\\mathbf{a} \\times \\mathbf{b}, 2(\\mathbf{b} \\times \\math... |
884 | [{"role": "user", "content": "Three fair coins are to be tossed once. For each tail that results, one fair die is to be rolled. What is the probability that the sum of the die rolls is odd? (Note that if no die is rolled, the sum is 0.)\nA. $\\frac{7}{16}$\nB. $\\frac{1}{2}$\nC. $\\frac{43}{72}$\nD. $\\frac{5}{8}$\nE. ... |
923 | [{"role": "user", "content": "What is the value of $\\frac{2023^3 - 2 \\cdot 2023^2 \\cdot 2024 + 3 \\cdot 2023 \\cdot 2024^2 - 2024^3 + 1}{2023 \\cdot 2024}$?"}, {"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... |
882 | [{"role": "user", "content": "Find the remainder when $x^6 - 2x^5 - 3x^4 + 4x^3 + 5x^2 - x - 2$ is divided by $(x-3)(x^2-1)$."}, {"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 ... |
864 | [{"role": "user", "content": "Inside a square with side length 2, there are seven polygons each with an area of at least 1.\n\nProve that there exist two polygons such that the area of their intersection is at least \\( \\frac{1}{7} \\)."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging q... |
935 | [{"role": "user", "content": "Find the real roots of\n\\[x^4 - 2x^3 - x + 2 = 0.\\]"}, {"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 the real roots of this quartic equ... |
943 | [{"role": "user", "content": "Kadin makes a larger snowman by stacking four snowballs with radii of 2 inches, 4 inches, 5 inches, and 6 inches. Assuming all snowballs are perfect spheres, calculate the total volume of snow used only for the snowballs with radii greater than 3 inches. Express your answer in terms of $\\... |
905 | [{"role": "user", "content": "Let $$y = 72 + 108 + 144 + 180 + 324 + 396 + 3600.$$ Determine which of the following statements are true?\n\nA. $y$ is a multiple of $6$.\nB. $y$ is a multiple of $12$.\nC. $y$ is a multiple of $18$.\nD. $y$ is a multiple of $36$.\n\nAnswer as a list of letters in alphabetical order, sepa... |
908 | [{"role": "user", "content": "Let $L$ be a subset in the coordinate plane defined by $L = \\{(41x + 2y, 59x + 15y) | x, y \\in \\mathbb Z \\}$ , where $\\mathbb Z$ is set of integers. Prove that for any parallelogram with center in the origin of coordinate and area $1990$ , there exist at least two points of $L$... |
947 | [{"role": "user", "content": "In statistical inference, when a certain condition is met, we can be 95% confident that event A is related to event B; when another condition is met, it is considered that there is insufficient evidence to show that events A and B are related."}, {"role": "assistant", "content": "<think>\n... |
958 | [{"role": "user", "content": "Carrie wants to buy a new iPhone. The new iPhone costs $800. She can trade in her Samsung Galaxy for $240. She can make $80 per week babysitting. How many weeks does she have to work before she can purchase the iPhone?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. Carrie... |
962 | [{"role": "user", "content": "Melissa scored 120.0 points in all her games total. If she played 10.0 games, how many points did she score in each game."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says Melissa scored 120.0 points in total over 10.0 games, and we need to find out how many... |
851 | [{"role": "user", "content": "In the expression \\((x+y+z)^{2026}+(x-y-z)^{2026}\\), the brackets were expanded and like terms combined. How many terms of the form \\(x^{a} y^{b} z^{c}\\) with a non-zero coefficient resulted?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and... |
951 | [{"role": "user", "content": "Let \\\\(a\\\\) and \\\\(b\\\\) be in \\\\((0, +\\infty)\\\\) and \\\\(a \\neq b\\\\). Prove that \\\\(a^{3}+b^{3} > a^{2}b+ab^{2}\\\\)."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to prove that for positive real numbers a and b, where a isn't equal to b, the in... |
963 | [{"role": "user", "content": "Given $i$ is the imaginary unit, the value of $(1+i)^2$ is ( )\nA: $i$\nB: $-i$\nC: $2i$\nD: $-2i$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the value of (1 + i) squared, where i is the imaginary unit. Hmm, I need to remember how to square a... |
852 | [{"role": "user", "content": "How many 0's are located to the right of the decimal point and before the first non-zero digit in the terminating decimal representation of $\\frac{1}{2^7 \\cdot 5^3}$?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.