__src_index__ int64 0 172k | messages stringlengths 375 66.5k |
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735 | [{"role": "user", "content": "The measure of each exterior angle of a regular polygon is $20$ degrees. What is the sum of the measures of the interior angles, in degrees?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer... |
669 | [{"role": "user", "content": "On a 12-hour clock, an elapsed time of three hours looks the same as an elapsed time of 15 hours. Because of this, we can say that three hours is \"clock equivalent\" to its square number of hours. What is the least whole number of hours that is greater than 3 hours and is \"clock equivale... |
741 | [{"role": "user", "content": "How many sets of exactly four consecutive positive integers have a sum of 34?\n(A) 1 (B) 2 (C) 3 (D) 4 (E) None of the above\nA) 1\nB) 2\nC) 3\nD) 4\nE) None of the above"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem. The question is asking:... |
697 | [{"role": "user", "content": "Determine the nearest integer to\n(a) $\\frac{19}{15}+\\frac{19}{3}$\n(b) $\\frac{85}{42}+\\frac{43}{21}+\\frac{29}{14}+\\frac{15}{7}$\n(c) $-\\frac{11}{10}-\\frac{1}{2}-\\frac{7}{5}+\\frac{2}{3}$"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, an... |
677 | [{"role": "user", "content": "A positive number is called $n$-primable if it is divisible by $n$ and each of its digits is a one-digit prime number. How many 5-primable positive integers are there that are less than 1000?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it ... |
722 | [{"role": "user", "content": "In another hyperbola, the center is at $(1, -3),$ one focus is at $(1 + 3\\sqrt{5}, -3),$ and one vertex is at $(4, -3).$ The equation of this hyperbola can be written as\n\\[\\frac{(x - h)^2}{a^2} - \\frac{(y - k)^2}{b^2} = 1.\\]\nCalculate $h + k + a + b.$"}, {"role": "assistant", "conte... |
738 | [{"role": "user", "content": "What is the sum of the coordinates of the midpoint of the segment with endpoints $(10, -3, 6)$ and $(4, 7, -2)$ in three-dimensional space?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer.... |
670 | [{"role": "user", "content": "You have infinitely many boxes, and you randomly put 3 balls into them. The boxes are labeled \\(1, 2, \\ldots\\). Each ball has a probability \\(\\frac{1}{2^n}\\) of being put into box \\(n\\). The balls are placed independently of each other. What is the probability that some box will co... |
742 | [{"role": "user", "content": "15 persons can build a wall 90 m long in 42 days. In how many days can 40 persons complete a similar wall 60 m long?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about 15 people building a 90-meter wall in 42 days, and we need to find out how many days 40... |
626 | [{"role": "user", "content": "The square $ABCD$ is inscribed in a circle with center $O$ . Let $E$ be the midpoint of $AD$ . The line $CE$ meets the circle again at $F$ . The lines $FB$ and $AD$ meet at $H$ . Prove $HD = 2AH$ "}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challeng... |
734 | [{"role": "user", "content": "Given the set $M=\\{(x,y) | x^2+y^2=1, x\\in \\mathbb{Z}, y\\in \\mathbb{Z}\\}$, and $N=\\{(x,y) | (x-1)^2+y^2=1\\}$, then the number of elements in $M \\cap N$ is ( ).\n\nA: 0\n\nB: 1\n\nC: 2\n\nD: 4"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to solve this problem ste... |
756 | [{"role": "user", "content": "Calculate $4 \\cdot 6 \\cdot 8 + 24 \\div 4.$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to calculate 4 times 6 times 8 plus 24 divided by 4. Hmm, first, I remember that in math problems, we have to follow the order of operations, which is PEMDAS: Parentheses, ... |
743 | [{"role": "user", "content": "If $a$, $b$, and $c$ are real numbers, then \"$a \\gt b$\" is ( ) \"$ac^{2} \\gt bc^{2}$\".\n\nA: Sufficient but not necessary condition\n\nB: Necessary but not sufficient condition\n\nC: Necessary and sufficient condition\n\nD: Neither necessary nor sufficient condition"}, {"role": "ass... |
610 | [{"role": "user", "content": "What is the smallest four-digit positive integer, with all different digits, that is divisible by the square of each of its digits?"}, {"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 ... |
761 | [{"role": "user", "content": "It is 78 miles to Grandma's house. Mr. Welch drove 35 miles. He stopped to buy a pie for dessert. Then he drove 18 miles and stopped to put gas in the car. How many more miles until he reaches Grandma's house?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is ... |
754 | [{"role": "user", "content": "The coordinates of the focus of the parabola $y = -\\frac{1}{8}x^2$ are which of the following?\n\nA: $(0, \\frac{1}{32})$\n\nB: $(\\frac{1}{32}, 0)$\n\nC: $(0, -2)$\n\nD: $(-2, 0)$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the focus of the parabola gi... |
597 | [{"role": "user", "content": "In an acute-angled triangle \\(ABC\\), the altitudes are \\(AD\\), \\(BE\\), and \\(CF\\). Prove that the perimeter of triangle \\(DEF\\) does not exceed half the perimeter of triangle \\(ABC\\)."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and... |
758 | [{"role": "user", "content": "There are 45 students in a certain exam in the Zhonghuan Cup. Among them, 35 students are good at English, 31 students are good at Chinese, and 24 students are good at both subjects. How many students are not good at either subject?"}, {"role": "assistant", "content": "<think>\n\nOkay, let... |
746 | [{"role": "user", "content": "In $\\triangle ABC$, $\\angle C=90^{\\circ}$, $\\tan A=\\frac{\\sqrt{3}}{3}$, then $\\cos B=$____."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find cos B in a right-angled triangle ABC where angle C is 90 degrees, and tan A is √3/3. Hmm, right-angled at C, so... |
757 | [{"role": "user", "content": "A train 120-meters long is traveling at 45 km/hr and can cross a bridge of 255 meters in a certain amount of time. How many seconds does it take for the train to cross the bridge?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about a train crossing a bridg... |
725 | [{"role": "user", "content": "Define $\\%M$ by the formula $\\%M = 0.4(M) + 2$. Calculate $\\%(\\%(\\%40))$."}, {"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 calculate this... |
747 | [{"role": "user", "content": "Given the sets $A = \\{x \\mid mx - 1 = 0\\}$, $B = \\{2, 3\\}$, and $A \\subseteq B$, find the possible values of $m$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about finding the possible values of \\( m \\) such that the set \\( A = \\{x \\mid mx - 1... |
667 | [{"role": "user", "content": "What is the value of the expression \\(x^{2000} + x^{1999} + x^{1998} + 1000x^{1000} + 1000x^{999} + 1000x^{998} + 2000x^{3} + 2000x^{2} + 2000x + 3000\\) (where \\(x\\) is a real number), if \\(x^{2} + x + 1 = 0\\)? Vasya calculated the answer to be 3000. Is Vasya correct?"}, {"role": "as... |
682 | [{"role": "user", "content": "Given a sequence $\\{a\\_n\\}$ with the sum of its first $n$ terms denoted as $S\\_n$, where $a\\_1=2$, and $a\\_{n+1}=S\\_n+2 (n∈ℕ^*)$,\n\n1. Find the general term formula for the sequence $\\{a\\_n\\}$;\n2. If a sequence $\\{c\\_n\\}$ satisfies $c\\_n= \\frac {a_{n}}{(a_{n}-1)^{2}}$ and ... |
769 | [{"role": "user", "content": "Anais has 30 more toys than Kamari. Kamari has 65 toys in his box. How many toys are there altogether?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says Anais has 30 more toys than Kamari. Kamari has 65 toys. We need to find the total number of toys they hav... |
695 | [{"role": "user", "content": "Find the product of all constants $t$ such that the quadratic $x^2 + tx - 12$ can be factored in the form $(x+a)(x+b)$, where $a$ and $b$ are integers."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and cor... |
768 | [{"role": "user", "content": "Mona brought 20 cookies to share in class. Jasmine brought fewer cookies than Mona. Rachel brought 10 more cookies than Jasmine. Mona, Jasmine, and Rachel brought altogether 60 cookies to share in class. How many cookies did Jasmine bring?"}, {"role": "assistant", "content": "<think>\n\nOk... |
764 | [{"role": "user", "content": "Given points A and B with coordinates (2, -2) and (4, 3) respectively, and vector $\\overrightarrow{a} = (2k-1, 7)$, and $\\overrightarrow{a} \\parallel \\overrightarrow{AB}$, find the value of $k$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the value o... |
617 | [{"role": "user", "content": "Given the sequences \\(\\{a_n\\}\\) and \\(\\{b_n\\}\\) where \\(a_1 = b_1 = 10\\), the recursive formulas are defined as:\n\\[\n\\begin{cases}\na_{n+1} = \\frac{1}{a_n b_n} \\\\\nb_{n+1} = a_n^4 b_n\n\\end{cases} \\quad (n \\in \\mathbb{Z}^+)\n\\]\nFind \\(a_n\\) and \\(b_n\\)."}, {"role"... |
772 | [{"role": "user", "content": "Given the arithmetic sequence 7, x, 11, y, z, find the values of x, y, and z."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the values of x, y, and z in the arithmetic sequence 7, x, 11, y, z. First, I remember that in an arithmetic sequence, the differenc... |
767 | [{"role": "user", "content": "The angle that has the same terminal side as a $40^\\circ$ angle is ( )\nA: $k \\cdot 360^\\circ - 40^\\circ$, $k \\in \\mathbb{Z}$\nB: $k \\cdot 180^\\circ - 40^\\circ$, $k \\in \\mathbb{Z}$\nC: $k \\cdot 360^\\circ + 40^\\circ$, $k \\in \\mathbb{Z}$\nD: $k \\cdot 180^\\circ + 40^\\circ$... |
632 | [{"role": "user", "content": "We want to create a square-based, open-top box from a circular piece of paper as shown in the figure. Determine the ratio of dimensions \\( a \\) and \\( b \\) seen in the figure such that the volume of the box is maximized."}, {"role": "assistant", "content": "<think>\n\nThis is a complex... |
760 | [{"role": "user", "content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively. If angles $A$, $B$, $C$ form an arithmetic sequence and $a=1$, $S_{\\triangle ABC}= \\frac{ \\sqrt{3}}{2}$, then $b=$ \\_\\_\\_\\_\\_\\_."}, {"role": "assistant", "content": "<think>\n\nOkay, le... |
644 | [{"role": "user", "content": "We consider the two sequences $\\left(a_{n}\\right)_{n \\geq 0}$ and $\\left(b_{n}\\right)_{n \\geq 0}$ of integers, defined by $a_{0}=b_{0}=2$ and $a_{1}=b_{1}=14$ and by\n\n$$\n\\begin{aligned}\na_{n} & =14 a_{n-1}+a_{n-2} \\\\\nb_{n} & =6 b_{n-1}-b_{n-2}\n\\end{aligned}\n$$\n\nfor $n \\... |
785 | [{"role": "user", "content": "In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. He attempts all 60 questions and secures 150 marks. How many questions did he attempt correctly?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this ... |
771 | [{"role": "user", "content": "Given that $f(x)$ is a monotonically increasing function defined on $(0,+\\infty)$, the solution set to the inequality $f(x) > f[8(x-2)]$ is $(\\quad)$:\nA: $(0,+\\infty)$\nB: $(0,2)$\nC: $(2,+\\infty)$\nD: $(2, \\frac{16}{7})$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's tr... |
779 | [{"role": "user", "content": "Rebecca runs a hair salon. She charges $30 for haircuts, $40 for perms, and $60 for dye jobs, but she has to buy a box of hair dye for $10 to dye every head of hair. Today, she has four haircuts, some perms, and two dye jobs scheduled. If she makes $50 in tips, she will have $310 at the en... |
702 | [{"role": "user", "content": "\nIn a mini-football tournament, bets are accepted on four teams. Bets on the first team have odds of $1: 5$ (if the first team wins, the player receives the amount they bet on this team plus five times that amount, i.e., six times the bet amount, and if they lose, the money is not returne... |
762 | [{"role": "user", "content": "Among the following propositions, the correct one is ( ).\nA. Two lines perpendicular to the same line are parallel;\nB. If a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other;\nC. If a line intersects one of two parallel lines, then it al... |
786 | [{"role": "user", "content": "Given that $i$ is the imaginary unit, the complex number $\\frac{5}{2-i}-i=$ ( )\nA: $i-2$\nB: $2+i$\nC: $-2$\nD: $2$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to solve this problem: (5)/(2 - i) - i, and choose the correct answer from the options A to D. Alr... |
763 | [{"role": "user", "content": "Suppose $x^{5}=a\\_n+a\\_1(x-1)+a\\_2(x-1)^{2}+a\\_3(x-1)^{3}+a\\_4(x-1)^{4}+a\\_5(x-1)^{5}$, find the value of $a\\_4$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is to find the coefficient \\( a_4 \\) in the expansion of \\( x^5 \\) as a polynomial in \\... |
774 | [{"role": "user", "content": "When Greenville State University decided to move its fine arts collection to a new library, it had to package the collection in 20-inch by 20-inch boxes with a certain height. The university pays $0.70 for every box, and it needs 3.06 million cubic inches to package the collection. The min... |
773 | [{"role": "user", "content": "Find the range of values for $k$ in the hyperbola $\\frac{x^2}{4} - \\frac{y^2}{k} = 1$ given that its eccentricity $e \\in (1, 2)$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the range of values for \\( k \\) in the hyperbola \\( \\frac{x^2}{4} - \\fra... |
770 | [{"role": "user", "content": "Given the parabola $E: y^2 = 2px$ ($p>0$) with focus $F$, and $OF$ (where $O$ is the origin) as one diagonal of the rhombus $OBFC$, the other diagonal $BC$ has a length of 2, and $B$, $C$ are on the parabola $E$, then $p=$ （ ）\nA: $2 \\sqrt {2}$\nB: 2\nC: $\\sqrt {2}$\nD: 1"}, {"role": "... |
648 | [{"role": "user", "content": "Given $f(x) = \\sin x$, for any $x_{1} \\in [0, \\frac{\\pi}{2}]$, there exists $x_{2} \\in [0, \\frac{\\pi}{2}]$ such that $f(x_{1}) - 2f(x_{2}+\\theta) = -1$ holds. Then the possible values of $\\theta$ are:\n\nA: $\\frac{3\\pi}{13}$\n\nB: $\\frac{5\\pi}{13}$\n\nC: $\\frac{7\\pi}{13}$\n\... |
687 | [{"role": "user", "content": "Let \\( m = \\underbrace{555555555}_{\\text{9 digits}} \\) and \\( n = \\underbrace{1111111111}_{\\text{10 digits}} \\).\n\nWhat is \\( \\gcd(m, n) \\)?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and co... |
643 | [{"role": "user", "content": "How many ten digit positive integers with distinct digits are multiples of $11111$ ? $ \\textbf{(A)}\\ 0\n\\qquad\\textbf{(B)}\\ 1264\n\\qquad\\textbf{(C)}\\ 2842\n\\qquad\\textbf{(D)}\\ 3456\n\\qquad\\textbf{(E)}\\ 11111\n$ "}, {"role": "assistant", "content": "<think>\n\nThis is a compl... |
781 | [{"role": "user", "content": "Philip is a dedicated painter whose output varies by day. On Mondays and Tuesdays, he creates 3 paintings each day. On Wednesdays, he slows down a bit and only produces 2 paintings. Thursdays and Fridays are his most creative days; he makes 5 paintings each day. He takes weekends off. Howe... |
723 | [{"role": "user", "content": "The polynomial $h(x) = x^3 - 2x^2 + 3x - 4$ has three distinct roots. Let $p(x) = x^3 + ax^2 + bx + c$ be a cubic polynomial with leading coefficient $1$ such that the roots of $p(x)$ are the squares of the roots of $h(x)$. Find the ordered triple $(a,b,c)$."}, {"role": "assistant", "conte... |
766 | [{"role": "user", "content": "Solve for $x$: $$\\log_3 \\frac{4x+12}{6x-4} +\\log_3\\frac{6x-4}{2x-3}=2$$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to solve this logarithmic equation: log base 3 of (4x + 12)/(6x - 4) plus log base 3 of (6x - 4)/(2x - 3) equals 2. Hmm, first, I remember tha... |
795 | [{"role": "user", "content": "Diane shows Sarah a game that deciphers at what age she will marry based on her name and current age. Sarah is 9 years old. The game consists of adding the number of letters in the player's name plus some multiple of the player's age. According to the game, Sarah will get married at the ag... |
783 | [{"role": "user", "content": "$(1)$ Simplify: $2m+3n-3m+5n$;<br/>$(2)$ Below is the process of Little Le's simplification of polynomials. Please read carefully and complete the corresponding tasks.<br/>Solution: $2(m^{2}+m^{2}n)-(2m^{2}-mn^{2})$,<br/>$=2m^{2}+2m^{2}n-2m^{2}+mn^{3}\\ldots $, first step,<br/>$=3m^{2}n\\l... |
793 | [{"role": "user", "content": "Sue borrowed some books and 6 movies. She returned 8 books. She then returned a third of the movies to the library and checked out 9 more books. Sue now has 20 movies and books. How many books did Sue initially borrow?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figu... |
693 | [{"role": "user", "content": "Given two intersecting circles with radius \\( r \\) and centers \\( O_{1} \\) and \\( O_{2} \\), the distance between the centers is \\( O_{1}O_{2} = 1 \\). A ray starting from the midpoint \\( O \\) of the common chord and making an angle \\( \\alpha \\) with the common chord intersects ... |
750 | [{"role": "user", "content": "Given the function $f(x) = \\ln(x) - x$.\n1. Find the intervals of monotonicity and the maximum value of $f(x)$.\n2. Let the sequence $\\{ a_n \\}$ be defined by $a_n = 1 + \\frac{1}{2^n}$ for $n \\in \\mathbb{N}^*$. Use the conclusion from part 1 to prove: $a_1 \\cdot a_2 \\cdot a_3 \\cdo... |
794 | [{"role": "user", "content": "what is the average of first 21 multiples of 7 ?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the average of the first 21 multiples of 7. Hmm, first, I need to remember what the first 21 multiples of 7 are. Let me think. The first multiple of 7... |
787 | [{"role": "user", "content": "In the parallelogram $ABCD$, given $A(4,1,3)$, $B(2,-5,1)$, and $C(3,7,-5)$, the coordinates of vertex $D$ are ____."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the coordinates of vertex D in parallelogram ABCD. First, I remember that in a parallelogram,... |
797 | [{"role": "user", "content": "The y-coordinate of the intersection point between the tangent line to the curve $y = x^3 + 11$ at point $P(1, 12)$ and the y-axis is ( ).\n\nA: -9\nB: -3\nC: 9\nD: 15"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the y-coordinate of the interse... |
730 | [{"role": "user", "content": "Given $m=(\\sqrt{3}\\sin \\omega x,\\cos \\omega x)$, $n=(\\cos \\omega x,-\\cos \\omega x)$ ($\\omega > 0$, $x\\in\\mathbb{R}$), $f(x)=m\\cdot n-\\frac{1}{2}$ and the distance between two adjacent axes of symmetry on the graph of $f(x)$ is $\\frac{\\pi}{2}$.\n\n$(1)$ Find the intervals of... |
755 | [{"role": "user", "content": "In triangle $ABC$, it is known that $AB=2$, $AC=3$, and $A= \\frac{\\pi}{3}$. \n(1) Find the length of $BC$. \n(2) Find the value of $\\cos(A-C)$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correc... |
784 | [{"role": "user", "content": "Given real numbers \\( x \\) and \\( y \\) that satisfy \\[ \\frac{x^{2}}{9}+\\frac{y^{2}}{4}=1 \\], find the maximum value of the function \\( U = x + y \\)."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the maximum value of U = x + y given that x and y s... |
777 | [{"role": "user", "content": "When $x = \\theta$, the function $f(x) = 3\\sin x - \\cos x$ attains its minimum value. Determine the value of $\\sin \\theta$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that when \\( x = \\theta \\), the function \\( f(x) = 3\\sin x - \\cos x \\) at... |
809 | [{"role": "user", "content": "A boy has 12 oranges. He gives one-third of this number to his brother, a fraction of the remainder to his friend, and keeps the rest for himself. His friend gets 2 oranges. What is the ratio of the number of oranges given to his friend to the remainder after giving some to his brother?"},... |
713 | [{"role": "user", "content": "There are 19 candy boxes arranged in a row, with the middle box containing $a$ candies. Moving to the right, each box contains $m$ more candies than the previous one; moving to the left, each box contains $n$ more candies than the previous one ($a$, $m$, and $n$ are all positive integers).... |
801 | [{"role": "user", "content": "At the beginning of the year 2020, a city implemented the \"Old Item Recycling Plan,\" providing a platform for the reuse of old items. By the end of 2020, 40,000 old items were collected. With increased publicity, the number of old items collected in the whole year of 2022 reached 90,000.... |
714 | [{"role": "user", "content": "Problem 3.\nLet $f:\\left[ 0,\\frac{\\pi }{2} \\right]\\to \\left[ 0,\\infty \\right)$ an increasing function .Prove that:\n(a) $\\int_{0}^{\\frac{\\pi }{2}}{\\left( f\\left( x \\right)-f\\left( \\frac{\\pi }{4} \\right) \\right)}\\left( \\sin x-\\cos x \\right)dx\\ge 0.$ (b) Exist $... |
815 | [{"role": "user", "content": "Find the surface area of a brick with dimensions of 8 cm x 6 cm x some height. The surface area is 152 square centimeters. What is the height of the brick?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the height of a brick when the surface area is given. ... |
726 | [{"role": "user", "content": "Matt's five cousins are coming to visit. There are four identical rooms that they can stay in. If any number of the cousins can stay in one room, how many different ways are there to put the cousins in the rooms?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challeng... |
816 | [{"role": "user", "content": "Given that the real axis length of the hyperbola $\\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1 (a > 0, b > 0)$ is $2\\sqrt{2}$, and the imaginary axis length is $2$, determine the equations of the asymptotes of the hyperbola. The options are:\nA: $y = \\pm \\sqrt{2}x$\nB: $y = \\pm 2x$\nC: $y =... |
796 | [{"role": "user", "content": "A fair 8-sided die with faces numbered from 1 to 8 is rolled. What is the probability that the number rolled is a divisor of 12?"}, {"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 ... |
811 | [{"role": "user", "content": "Let $f(x)$ be an even function. Is $f(f(x))$ odd, even, or neither?\nEnter \"odd\", \"even\", or \"neither\"."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that f(x) is an even function, and we need to figure out if f(f(x)) is odd, even, or neither. Hmm,... |
804 | [{"role": "user", "content": "Regarding the roots of the quadratic equation in $x$: $x^{2}-\\left(k-3\\right)x-k+1=0$, which of the following statements is correct?\n\nA: It has two distinct real roots.\n\nB: It has two equal real roots.\n\nC: It has no real roots.\n\nD: It cannot be determined."}, {"role": "assistant"... |
825 | [{"role": "user", "content": "Kelly gives away 91 Nintendo games. How many did she have initially if she still has 92 games left?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says Kelly gives away 91 Nintendo games, and after that, she still has 92 games left. We need to find out how man... |
818 | [{"role": "user", "content": "Lars owns a bakeshop. She can bake some loaves of bread within an hour and 30 baguettes every 2 hours. If she bakes 6 hours a day, she makes 150 breads. How many loaves of bread can she bake within an hour?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this ... |
765 | [{"role": "user", "content": "Given that the set of points $\\{(x,y)|(m+3)x+y=3m-4\\} \\cap \\{(x,y)|7x+(5-m)y-8=0\\} = \\varnothing$, find the area of the triangle formed by the line $(m+3)x+y=3m+4$ and the coordinate axes.\n\nA: $2$\nB: $4$\nC: $\\frac {128}{7}$\nD: $2$ or $\\frac {128}{7}$"}, {"role": "assistant", "... |
676 | [{"role": "user", "content": "Professor Antônio discovered an interesting property related to the integer $x$ that represents his age. He told his students that $x^{2}=\\overline{a b a c}$ and that $x=\\overline{a b}+\\overline{a c}$. What is the professor's age?\n\nNote: We are using a bar to distinguish the decimal r... |
817 | [{"role": "user", "content": "Find the value range for $\\sqrt{224}$. The options are:\n$\\text{(A)}\\ 14 \\qquad \\text{(B)}\\ \\text{less than }14 \\qquad \\text{(C)}\\ \\text{between }14\\text{ and }15 \\qquad \\text{(D)}\\ \\text{between }15\\text{ and }16 \\qquad \\text{(E)}\\ \\text{between }16\\text{ and }17$\n$... |
776 | [{"role": "user", "content": "Denis has identical ten-ruble coins, identical two-ruble coins, and identical one-ruble coins (more than 20 coins of each type). In how many ways can Denis pay exactly 16 rubles for a pie without receiving change? It is not necessary to use coins of each type."}, {"role": "assistant", "con... |
824 | [{"role": "user", "content": "Let \\( g(x) = \\frac{x^2 + 1}{x^2 - 1} \\). Then for \\( x^2 \\neq 1 \\), \\( g(-x) \\) is:\n- **(A)** \\( \\frac{1}{g(x)} \\)\n- **(B)** \\( -g(x) \\)\n- **(C)** \\( \\frac{1}{g(-x)} \\)\n- **(D)** \\( -g(-x) \\)\n- **(E)** \\( g(x) \\)\n- **(A)** \\( \\frac{1}{g(x)} \\)\n- **(B)** \\( -... |
748 | [{"role": "user", "content": "The coefficients of the quadratic equation \\( a x^{2} + b x + c = 0 \\) satisfy the condition \\( 2a + 3b + 6c = 0 \\). Prove that this equation has a root in the interval \\( (0, 1) \\)."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is ... |
810 | [{"role": "user", "content": "The solution set of the quadratic inequality $ax^{2}+bx+c \\gt 0$ is $\\{x| -2 \\lt x \\lt 1\\}$. Then the solution set of the inequality $cx^{2}+ax+b\\geqslant 0$ is ( ).\n\nA: $\\{x| -2\\leqslant x\\leqslant 1\\}$\n\nB: $\\{x| -\\frac{1}{2}\\leqslant x\\leqslant 1\\}$\n\nC: $\\{x| x\\leq... |
829 | [{"role": "user", "content": "There is 80 mg of caffeine in a cup of coffee. Lisa does not want to drink more than 200 mg of caffeine per day. She drinks a certain number of cups of coffee and ends up drinking 40 milligrams of coffee over her goal. How many cups of coffee did Lisa drink?"}, {"role": "assistant", "conte... |
799 | [{"role": "user", "content": "A store increases the price of an item by 20%, then by another 10%, and then by 15%. After that, the store offers a 5% discount on the total price and charges a 7% tax on the discounted price. If we want to bring the item price back to its original value, what would be the required percent... |
830 | [{"role": "user", "content": "The marked price of a book was 40% less than the suggested retail price. Bob purchased the book for 40% off the marked price during a special promotion. What percent of the suggested retail price did Bob pay?\n$\\mathrm{(A)\\ }20\\%\\qquad\\mathrm{(B)\\ }25\\%\\qquad\\mathrm{(C)\\ }36\\%\\... |
736 | [{"role": "user", "content": "Given the function $f(x)=\\ln x- \\frac {1}{4}x+ \\frac {3}{4x}-1$. \n(I) Find the intervals of monotonicity for the function $f(x)$. \n(II) Let $g(x)=-x^{2}+2bx-4$, if for any $x_{1}\\in(0,2)$, $x_{2}\\in[1,2]$, the inequality $f(x_{1})\\geqslant g(x_{2})$ always holds, find the range o... |
803 | [{"role": "user", "content": "What is the remainder when $5^0 + 5^1 + 5^2 + \\cdots + 5^{999}$ is divided by 7?\nA) 1\nB) 2\nC) 3\nD) 4"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the remainder when the sum \\(5^0 + 5^1 + 5^2 + \\cdots + 5^{999}\\) is divided by 7. Hmm, so... |
802 | [{"role": "user", "content": "Find the quadratic polynomial, with real coefficients, which has $5 + 2i$ as a root, and where the coefficient of $x^2$ is 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 thi... |
806 | [{"role": "user", "content": "It is known that all 'krakozyabrs' have either horns or wings (or both). From the results of a global census of 'krakozyabrs,' it was found that 20% of the 'krakozyabrs' with horns also have wings, and 25% of the 'krakozyabrs' with wings also have horns. How many 'krakozyabrs' are left in ... |
844 | [{"role": "user", "content": "John buys 3 reels of 100m fishing line. He cuts it into 10m sections. How many sections does he get?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. John buys 3 reels of 100m fishing line each. So first, I need to figure out the total length of fishing line he has. Each ... |
814 | [{"role": "user", "content": "Given two skew lines $a$ and $b$ that form an angle of $60^{\\circ}$, and lines $OA$ and $OB$ are parallel to $a$ and $b$ respectively, find the measure of $\\angle AOB$ and the angle formed by lines $OA$ and $OB$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure o... |
705 | [{"role": "user", "content": "In triangle \\(ABC\\), angle \\(C\\) equals \\(30^\\circ\\), and angle \\(A\\) is acute. A line perpendicular to side \\(BC\\) is drawn, cutting off triangle \\(CNM\\) from triangle \\(ABC\\) (point \\(N\\) lies between vertices \\(B\\) and \\(C\\)). The areas of triangles \\(CNM\\) and \\... |
840 | [{"role": "user", "content": "Marty plans to paint a fence and can choose from five different colors: blue, green, yellow, black, or white. He can also choose from four different painting tools: a brush, a roller, a sponge, or a spray gun. How many different combinations of color and painting tool can Marty choose?"}, ... |
751 | [{"role": "user", "content": "\\(1-\\cos (2 \\alpha - \\pi) + \\cos (4 \\alpha - 2 \\pi) = 4 \\cos 2 \\alpha \\cos \\left(\\frac{\\pi}{6} + \\alpha\\right) \\cos \\left(\\frac{\\pi}{6} - \\alpha\\right)\\)."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to... |
832 | [{"role": "user", "content": "David swims the 100-meter freestyle in 48 seconds. He swims the 100-meter backstroke 4 seconds slower than he swims the 100-meter freestyle without considering the external factors. When considering wind resistance, the backstroke takes an extra 2 seconds. He swims the 100-meter butterfly ... |
718 | [{"role": "user", "content": "(a) Determine the largest possible value $M$ that $x + y + z$ can take if $x$, $y$, and $z$ are positive real numbers satisfying\n\n$$\n16 x y z = (x + y)^2 (x + z)^2\n$$\n\n(b) Show that there are infinitely many triples $(x, y, z)$ of positive rational numbers such that\n\n$$\n16 x y z =... |
847 | [{"role": "user", "content": "The Sumata family took a vacation by car. Each day they drove 250 miles. They drove 1250 miles in total. How many days did their vacation last?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about the Sumata family's vacation. They drove 250 miles each day,... |
848 | [{"role": "user", "content": "What is the arithmetic square root of $36$?\n\nA: $6$\n\nB: $\\pm 6$\n\nC: $\\sqrt {6}$\n\nD: $\\pm \\sqrt {6}$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The question is asking for the arithmetic square root of 36. Hmm, first I need to remember what the arithmetic sq... |
841 | [{"role": "user", "content": "Given the proposition p: For all $x$ in $\\mathbb{R}$, $x^2 - 3x + 3 > 0$, then $\\neg p$ is."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about finding the negation of the proposition p, which states that for all real numbers x, x squared minus 3x plus 3... |
733 | [{"role": "user", "content": "Let \\(x,\\) \\(y,\\) \\(z,\\) and \\(w\\) be real numbers such that\n\\[\\frac{(x - y)(z - w)}{(y - z)(w - x)} = \\frac{3}{7}.\\]\nFind the sum of all possible values of\n\\[\\frac{(x - z)(y - w)}{(x - y)(z - w)}.\\]"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or cha... |
834 | [{"role": "user", "content": "\nDetermine how much money the Romanov family will save by using a multi-tariff meter over three years.\n\nThe cost of the meter is 3500 rubles. The installation cost is 1100 rubles. On average, the family's electricity consumption is 300 kWh per month, with 230 kWh used from 23:00 to 07:0... |
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