__src_index__ int64 0 172k | messages stringlengths 375 66.5k |
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1,429 | [{"role": "user", "content": "In three years from now, Tully will be a certain multiple of Kate's age. Tully was 60 years old a year ago, and Kate is now 29 years old. What is the ratio of Tully's age to Kate's age in three years from now?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out th... |
1,400 | [{"role": "user", "content": "9 - 3 ÷ what number / 3 + 3 equals 3?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem. The question is: 9 - 3 ÷ what number / 3 + 3 equals 3? Hmm, first, I need to make sure I understand the problem correctly. It says \"9 - 3 ÷ what number / 3 + 3... |
1,428 | [{"role": "user", "content": "A technician makes a round-trip to and from a certain service center by the same route. The technician completes the drive to the center and then completes some percent of the drive from the center. The technician has completed 70 percent of the round-trip. What percent of the drive from t... |
1,380 | [{"role": "user", "content": "Evaluate $3000^3 - 2998\\cdot3000^2 - 2998^2\\cdot3000 + 2998^3$."}, {"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 evaluate this expression: 3... |
1,323 | [{"role": "user", "content": "Given a line $l$ passing through the focus $F(1,0)$ of the parabola $y^2=2px$ ($p>0$) intersecting the parabola at points $M$ and $N$,\n(Ⅰ) Write the standard equation of the parabola and the equation of its directrix;\n(Ⅱ) $O$ is the origin of coordinates, and the lines $MO$ and $NO$ inte... |
1,433 | [{"role": "user", "content": "a train is running at a speed of 40 km / hr and it crosses a post in 25.2 seconds . what is the length of the train ?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about a train running at 40 km/h and crossing a post in 25.2 seconds. We need to find the le... |
1,420 | [{"role": "user", "content": "Given the sequence $\\{a_n\\}$ that satisfies $(a_1 = \\frac{3}{2}, a_{n+1} = 3a_n - 1)$,\n\n(1) If sequence $\\{b_n\\}$ satisfies $(b_n = a_n - \\frac{1}{2})$, prove that $\\{b_n\\}$ is a geometric sequence.\n\n(2) Find the sum of the first $n$ terms of the sequence $\\{a_n\\}$, denoted a... |
1,443 | [{"role": "user", "content": "A new building needed 9 windows. The builder had already installed 6 of them. It takes a certain amount of time to install each window, and it will take him 18 hours to install the rest. How long does it take to install one window?"}, {"role": "assistant", "content": "<think>\n\nOkay, let'... |
1,431 | [{"role": "user", "content": "There are 20 parts in total, among which 16 are good and 4 are defective. If we randomly pick 3 parts from these 20, find the number of different ways in which at least one good part is included."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about finding ... |
1,434 | [{"role": "user", "content": "The universal set is the set of real numbers \\\\(R\\\\), \\\\(M=\\\\{x|-2\\leqslant x\\leqslant 2\\\\}\\\\), \\\\(N=\\\\{x|x < 1\\\\}\\\\), then \\\\((\\complement_{R}M)\\cap N=\\\\) \\\\()\nA: \\\\(\\\\{x|x < -2\\\\}\\\\)\nB: \\\\(\\\\{x|-2 < x < 1\\\\}\\\\)\nC: \\\\(\\\\{x|x < 1\\\\}\\... |
1,419 | [{"role": "user", "content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively. Given vectors $\\overrightarrow{m}=(b, \\sqrt {3}a)$, $\\overrightarrow{n}=(\\cos B,\\sin A)$, and $\\overrightarrow{m} \\parallel \\overrightarrow{n}$.\n(1) Find the measure of angle $B$;\n(2) ... |
1,372 | [{"role": "user", "content": "Ancient Greek mathematicians from the Pythagorean school studied various polygonal numbers, such as triangular numbers 1, 3, 6, 10, ..., with the $n$-th triangular number being $\\frac{n(n+1)}{2} = \\frac{1}{2}n^{2} + \\frac{1}{2}n$. Let the $n$-th $k$-sided polygon number be denoted as $N... |
1,407 | [{"role": "user", "content": "Given $l_1: 2x+my-2=0$, $l_2: mx+2y-1=0$, and $l_1 \\perp l_2$, the value of $m$ is ( )\n\nA: 2 \nB: 1 \nC: 0 \nD: Does not exist"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that two lines, l₁ and l₂, are perpendicular, and we need to find the valu... |
1,332 | [{"role": "user", "content": "Two boards, one five inches wide and the other seven inches wide, are nailed together to form an X. The angle at which they cross is 45 degrees. If this structure is painted and the boards are separated, what is the area of the unpainted region on the five-inch board? Assume that the nail ... |
1,363 | [{"role": "user", "content": "A solution contains some parts of water for every 7 parts of lemonade syrup. To make the solution contain 30% lemonade syrup, 2.1428571428571423 parts of the solution should be removed and replaced with water. How many parts of water are there in the original solution?"}, {"role": "assista... |
1,403 | [{"role": "user", "content": "The diagram shows part of a scale of a measuring device. The arrow indicates an approximate reading of\n$\\text{(A)}\\ 5.05 \\qquad \\text{(B)}\\ 5.10 \\qquad \\text{(C)}\\ 5.15 \\qquad \\text{(D)}\\ 5.20 \\qquad \\text{(E)}\\ 5.25$"}, {"role": "assistant", "content": "<think>\n\nOkay, let... |
1,446 | [{"role": "user", "content": "2 birds and 6 storks were sitting on the fence. 3 more birds came to join them. How many more storks than birds are sitting on the fence?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says there are 2 birds and 6 storks sitting on the fence. Then 3 more birds... |
1,430 | [{"role": "user", "content": "Find the greatest common divisor (GCD) of 8251 and 6105."}, {"role": "assistant", "content": "<think>\n\nOkay, so I need to find the greatest common divisor (GCD) of 8251 and 6105. Hmm, let's see. I remember that the Euclidean algorithm is a good method for finding the GCD of two numbers. ... |
1,378 | [{"role": "user", "content": "Mary is baking a cake using a recipe that calls for a ratio of 5:3:1 for flour, sugar, and salt. The recipe requires a total of 30 ounces of ingredients. She already added 12 ounces of flour. How many more ounces of flour than sugar does she need to add now, if she hasn't added any sugar y... |
1,450 | [{"role": "user", "content": "A group of 5 friends went into a restaurant. The chef already had 20 chicken wings cooked but cooked 25 more for the group. If they each got the same amount, how many would each person get?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. So there's a problem here about 5 f... |
1,417 | [{"role": "user", "content": "A train of a certain length is running with a speed of 55 km/hr. In 10.45077684107852 seconds, it will pass a man who is running at 7 km/hr in the direction opposite to that in which the train is going. What is the length of the train?"}, {"role": "assistant", "content": "<think>\n\nOkay, ... |
1,449 | [{"role": "user", "content": "Jenny wants to read 3 books in the next 10 days. She can read a certain number of words per hour. The first book has 200 words, the second book has 400 words, and the third book has 300 words. She should spend, on average, 54 minutes per day reading. How many words can she read per hour?"}... |
1,454 | [{"role": "user", "content": "Robbie is tracking his nutrition intake per week. He eats some cups of rice in the morning, 2 cups of rice in the afternoon, and 5 cups of rice in the evening. If a cup of rice has 10 grams of fat, Robbie gets 700 grams of fat in a week. How many cups of rice does he eat in the morning?"},... |
1,319 | [{"role": "user", "content": "In triangle $\\triangle ABC$, $AC > BC$, and $F$ is the midpoint of $AB$. Through $F$, a diameter $DE$ is drawn in the circumcircle of $\\triangle ABC$ such that $C$ and $E$ are on the same side of $AB$. A line is drawn through $C$ parallel to $AB$, intersecting $DE$ at $L$. Prove that $(A... |
1,456 | [{"role": "user", "content": "Among the four rational numbers $-\\frac{2}{3}$, $-1$, $0$, $1$, the smallest one is ( )\n\nA: $-\\frac{2}{3}$\n\nB: $-1$\n\nC: $0$\n\nD: $1$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The question is asking which of the four rational numbers—-2/3, -1, 0, 1—is the sma... |
1,459 | [{"role": "user", "content": "In a 60-item exam, Liza got 90% of the items correctly. Her best friend, Rose, got 2 more correct answers than her. How many incorrect answers did Rose have?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about Liza and Rose taking a 60-item exam. Liza got ... |
1,445 | [{"role": "user", "content": "Given that $m$ is a root of the equation $x^{2}-2x-7=0$, find $m^{2}-2m+1$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that m is a root of the equation x² - 2x - 7 = 0, and we need to find m² - 2m + 1. Hmm, first, if m is a root of that equation, that... |
1,457 | [{"role": "user", "content": "In the arithmetic sequence $\\{a_{n}\\}$, $a_{1}=2$ and $a_{3} + a_{5}=10$. Find the value of $a_{7}$.\n(A) $5$\n(B) $8$\n(C) $10$\n(D) $14$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the value of \\( a_7 \\) in an arithmetic sequence where \\( a_1 = 2 ... |
1,458 | [{"role": "user", "content": "Shane wants to take as many photos as possible this year. He takes 146 photos in the first 2 months of the year. In January, he takes some photos every day. In February, he took 21 photos each week. How many photos did Shane take each day in January?"}, {"role": "assistant", "content": "<t... |
1,383 | [{"role": "user", "content": "Given an even function $y=2\\sin(\\omega x+\\varphi)$ ($\\omega>0$, $0<\\varphi<\\pi$), the graph intersects with the line $y=2$ at two points whose x-coordinates are $x_1$ and $x_2$. If the minimum value of $|x_2-x_1|$ is $\\pi$, then on which of the following intervals is the function mo... |
1,436 | [{"role": "user", "content": "Given a random variable $X \\sim N(3, \\sigma^2)$, if $P(X > m) = 0.3$, then $P(X > 6-m) =$ \\_\\_\\_\\_\\_\\_."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that X is a normal random variable with mean 3 and variance σ², so X ~ N(3, σ²). We're told that... |
1,312 | [{"role": "user", "content": "If the function $f(x)=x^{2}-m\\cos x+m^{2}+3m-8$ has a unique zero, then the set of real numbers $m$ that satisfy this condition is \\_\\_\\_\\_\\_\\_."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and cor... |
1,460 | [{"role": "user", "content": "To prove the proposition \"In $\\triangle ABC$, if $\\angle A \\neq \\angle B$, then $AC \\neq BC$\" using proof by contradiction, one should first assume that\n\nA: $AC > BC$\n\nB: $AC < BC$\n\nC: $\\angle A = \\angle B$\n\nD: $AC = BC$"}, {"role": "assistant", "content": "<think>\n\nOkay... |
1,451 | [{"role": "user", "content": "There are 30 people in a club. 12 of them are left-handed. 20 of them like jazz music. 3 of them are right-handed and dislike jazz music. How many club members are left-handed and like jazz music? Assume people are either left-handed or right-handed, but not both."}, {"role": "assistant", ... |
1,421 | [{"role": "user", "content": "Some familiar internet slang terms include \"$yyds$\", \"involution\", \"lying flat\", etc. Let $f(x) = f'(x)$ be the equation defining the real root $x$ as the \"lying flat point\" of the function $f(x)$. If the \"lying flat points\" of the functions $g(x) = e^x - x$, $h(x) = \\ln x$, and... |
1,462 | [{"role": "user", "content": "Calculate the sum of $5.67 + (-3.92)$ as a decimal."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to calculate the sum of 5.67 and -3.92. Hmm, adding a negative number is the same as subtracting its positive value, right? So 5.67 + (-3.92) should be the same as 5.... |
1,361 | [{"role": "user", "content": "Given that the sequence $\\{a\\_n\\}$ is an arithmetic sequence, $a\\_1+a\\_5=-20$, $a\\_3+a\\_8=-10$.\n1. Find the general term of the sequence $\\{a\\_n\\}$.\n2. For what value of $n$ does the sum of the first $n$ terms of the sequence $\\{a\\_n\\}$, denoted as $S\\_n$, reach its minimum... |
1,475 | [{"role": "user", "content": "A student got 74% in math and 81% in history. The student needs to get 70% in the third subject to achieve a certain overall average. What is the desired overall average percentage?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem. So, the student ... |
1,351 | [{"role": "user", "content": "Suppose that all four of the numbers \\[3 - 2\\sqrt{2}, \\; -3-2\\sqrt{2}, \\; 1+\\sqrt{7}, \\; 1-\\sqrt{7}\\]are roots of the same nonzero polynomial with rational coefficients. What is the smallest possible degree of the polynomial?"}, {"role": "assistant", "content": "<think>\n\nThis is... |
1,360 | [{"role": "user", "content": "Given a $99 \\times 99$ grid where each cell is colored either black or white, you are allowed to recolor all the cells of any column or any row simultaneously to the color that is the majority in that column or row before recoloring. Is it always possible to make all the cells of the grid... |
1,455 | [{"role": "user", "content": "Compute $1-2+3-4+ \\dots -100$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to compute the sum 1 - 2 + 3 - 4 + ... - 100. Hmm, so it's alternating signs, starting with positive for the first term, negative for the second, and so on, up to the 100th term, which i... |
1,411 | [{"role": "user", "content": "Given that $\\{a_n\\}$ is a geometric sequence with $a_1=3$ and $a_4=24$, and the sequence $\\{b_n\\}$ satisfies: $b_1=0$, $b_n+b_{n+1}=a_n$, \n(1) Prove that $a_n=3\\times2^{n-1}$; \n(2) Prove that $b_n=2^{n-1}+(-1)^n$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex o... |
1,473 | [{"role": "user", "content": "Given the function $f(x) = 2^{x-1}$, its inverse function is denoted as $y = f^{-1}(x)$. If $f^{-1}(a) + f^{-1}(b) = 4$, then $ab =$ ?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about finding the product ab given that the sum of the inverse function eva... |
1,479 | [{"role": "user", "content": "the average marks of a class of 30 students is 40 and that of another class of 50 students is 90 . find the average marks of all the students ?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about finding the average marks of all the students when we have t... |
1,469 | [{"role": "user", "content": "What is the base five equivalent of $235_{10}$?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the base five equivalent of 235 in base ten. Hmm, base five... So, base five means each digit represents a power of 5, right? Like, the rightmost digit is 5^0, th... |
1,359 | [{"role": "user", "content": "x and y started a business by investing Rs. 36000 and Rs. 42000 respectively. After some months, z joined in the business with an investment of Rs. 48000. The total profit was Rs. 13860, and z's share in the profit was Rs. 4032. How many months after x and y started the business did z join... |
1,423 | [{"role": "user", "content": "Let $\\omega$ be a nonreal root of $x^2 = 1.$ Compute\n\\[(1 - \\omega + \\omega^2)^6 + (1 + \\omega - \\omega^2)^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 abo... |
1,463 | [{"role": "user", "content": "a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 10 % . what was its profit on the items sold i... |
1,371 | [{"role": "user", "content": "Which of the following statements is incorrect?\n\nA: The line passing through points $M(x_{1}, y_{1})$ and $N(x_{2}, y_{2})$ can be represented by the equation $\\frac{{y-y_{1}}}{{y_{2}-y_{1}}}=\\frac{{x-x_{1}}}{{x_{2}-x_{1}}}$.\n\nB: The equation of the line passing through the point $P(... |
1,480 | [{"role": "user", "content": "Given that $x = \\ln(\\pi)$, $y = \\log_5(2)$, and $z = e^{- \\frac {1}{2}}$, determine the relationship between $x$, $y$, and $z$.\nA: $x < y < z$\nB: $z < x < y$\nC: $z < y < x$\nD: $y < z < x$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to figure out the rela... |
1,448 | [{"role": "user", "content": "What is $\\frac{0.\\overline{81}}{0.\\overline{36}}$? Express your answer as a common fraction in lowest terms."}, {"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.\n... |
1,489 | [{"role": "user", "content": "Sandy gets some marks for each correct sum and loses 2 marks for each incorrect sum. Sandy attempts 30 sums and obtains 60 marks. Sandy got 24 sums correct. How many marks does Sandy get for each correct sum?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out thi... |
1,477 | [{"role": "user", "content": "The function $f(x) = \\sin^2x - \\cos^2x$, where $x \\in \\mathbb{R}$, has a minimum positive period and a maximum value of ( )\nA: $\\pi$, 1\nB: $\\pi$, 2\nC: $2\\pi$, 1\nD: $2\\pi$, 2"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about the function \\( f... |
1,438 | [{"role": "user", "content": "To paint a cube on all sides requires 60 grams of paint. How much paint will be needed to paint a \"snake\" formed by 2016 such cubes? The beginning and end of the snake are shown in the illustration, and the remaining cubes are replaced by ellipses."}, {"role": "assistant", "content": "<t... |
1,439 | [{"role": "user", "content": "Given that the positive numbers $a$, $b$, and $c$ satisfy the inequality $\\frac{1}{a} + \\frac{4}{b} + \\frac{9}{c} \\leqslant \\frac{36}{a + b + c}$, find the value of $\\frac{2b + 3c}{a + b + c} =$ _____."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging q... |
1,466 | [{"role": "user", "content": "In the sequence $\\{a_n\\}$, $a_{n+1}= \\frac {a_n}{1+3a_n}$, $a_1=2$, then $a_{10}=$ ______."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the 10th term of this sequence where each term is defined by a recursive formula: \\( a_{n+1} = \\frac{a_n}{1 + 3a_n... |
1,467 | [{"role": "user", "content": "A biased coin has a probability of $\\frac{3}{4}$ of landing heads and $\\frac{1}{4}$ of landing tails. A player must choose between playing Game A or Game C. In Game A, the player tosses the coin four times and wins if all four outcomes are the same. In Game C, the player tosses the coin ... |
1,404 | [{"role": "user", "content": "Given the equation of line $l$ as $ax + by + c = 0$, where $a$, $b$, and $c$ form an arithmetic sequence. Determine the maximum distance from the origin $O$ to line $l$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provid... |
1,492 | [{"role": "user", "content": "If $\\sin(\\pi + \\alpha) = \\frac{3}{5}$ and $\\alpha$ is an angle in the third quadrant, find the value of $\\tan \\alpha$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that sin(π + α) = 3/5 and α is in the third quadrant. We need to find tan α. Hmm, ... |
1,441 | [{"role": "user", "content": "In rectangle $ABCD$, where $AB=10$ and $AD=12$, point $M$ is located on $\\overline{AD}$ such that $AM = 9$ meters. Calculate the area of $\\triangle AMC$.\n$\\text{(A) }30 \\qquad \\text{(B) }35 \\qquad \\text{(C) }40 \\qquad \\text{(D) }45 \\qquad \\text{(E) }50$"}, {"role": "assistant",... |
1,490 | [{"role": "user", "content": "If the one-variable quadratic equation $bx^{2}+2bx+4=0$ has two equal real roots with respect to $x$, then the value of $b$ is ( )\n\nA: $0$\n\nB: $4$\n\nC: $0$ or $4$\n\nD: $0$ or $-4$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about a quadratic equati... |
1,496 | [{"role": "user", "content": "Calculate the result of $(1-2)(3-4)(5-6)\\ldots(2011-2012)$.\n\nA: $-1$\n\nB: $1$\n\nC: $-2011$\n\nD: $4024$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem. The question is asking for the product of a series of terms: (1-2)(3-4)(5-6)...(2011-2012... |
1,482 | [{"role": "user", "content": "Given a function $f(x) = 3\\sin(\\omega x + \\frac{\\pi}{6})$ where $\\omega > 0$, and the period of $f(x)$ is $\\pi$, identify which of the following statements is true:\n\nA: The graph of $f(x)$ passes through the point $(0, \\frac{1}{2})$. \nB: $f(x)$ is a decreasing function on the in... |
1,504 | [{"role": "user", "content": "A rectangular box has a volume of 1728 cubic inches. How many cubic feet are in the volume of this box?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about converting cubic inches to cubic feet. The box has a volume of 1728 cubic inches, and we need to fin... |
1,500 | [{"role": "user", "content": "Suppose there is a process of deductive reasoning with the following structure: \"Major premise: ______, minor premise: The quadrilateral ABCD is a rectangle; conclusion: The diagonals of the quadrilateral ABCD are equal.\" What should be filled in the blank for the major premise?"}, {"rol... |
1,497 | [{"role": "user", "content": "Compute $\\cos 30^\\circ$."}, {"role": "assistant", "content": "<think>\n\nGot it, let's see. I need to compute cos 30 degrees. Hmm, I remember from trigonometry that there are special angles with known cosine values, like 0°, 30°, 45°, 60°, 90°, etc. 30° is one of those special angles, so... |
1,397 | [{"role": "user", "content": "Given the polynomial \\( g(x) = x^5 + x^4 + x^3 + x^2 + x + 1 \\), find the remainder when the polynomial \\( g(x^{12}) \\) is divided by \\( g(x) \\).\n\n(A) 6\n\n(B) \\( 5 - x \\)\n\n(C) \\( 4 - x + x^2 \\)\n\n(D) \\( 3 - x + x^2 - x^3 \\)\n\n(E) \\( 2 - x + x^2 - x^3 + x^4 \\)"}, {"role... |
1,347 | [{"role": "user", "content": "Let $\\Delta ABC$ be an isosceles triangle with $AB = AC$. How many squares in the same plane as $\\Delta ABC$ share two vertices with the triangle?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correc... |
1,414 | [{"role": "user", "content": "In the Cartesian coordinate system $(xOy)$, line $l$ passes through point $(1,0)$ with an inclination angle of $\\alpha$. Establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of the $x$-axis as the polar axis. The polar equation of curve $C$... |
1,503 | [{"role": "user", "content": "The complex number $z$ satisfies $zi=2-i$, then the point corresponding to the conjugate complex number $\\overline {z}$ is in the ( ) quadrant.\nA: first\nB: second\nC: third\nD: fourth"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that the complex nu... |
1,494 | [{"role": "user", "content": "Given a cylinder with a base radius of $r$ and a height of $4r$, if the lateral area of the cylinder is equal to the surface area of a sphere with radius $R$, then $\\dfrac{R}{r}=$ ______."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is ... |
1,426 | [{"role": "user", "content": "Emily chooses a real number uniformly from the interval $[0,1000]$, and Max chooses a number uniformly from the interval $[0,3000]$. What is the probability that Max's number is at least twice as large as Emily's number?\nA) $\\frac{1}{4}$ \nB) $\\frac{1}{3}$\nC) $\\frac{1}{2}$\nD) $\\frac... |
1,491 | [{"role": "user", "content": "Reggie and his brother are having a basketball shooting contest with different types of shots and bonus points. They each get to take 25 shots. Layups are worth 1 point, dunks are worth 1 point, free throws are worth 2 points, three-pointers are worth 3 points, alley-oops are worth 4 point... |
1,510 | [{"role": "user", "content": "Jerry paid off some of his debts. Two months ago, he paid some amount while last month, he paid $3 more. His debt was $50 in all, and he still has to pay $23. How much did Jerry pay two months ago?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out how much Jerry... |
1,444 | [{"role": "user", "content": "Given a parabola $y^2 = 4x$ with focus $F$, a chord passing through $F$ intersects the parabola at points $A$ and $B$. Perpendicular lines to the $y$-axis are drawn from $A$ and $B$, with foot points $C$ and $D$ respectively. The minimum value of $|AC| + |BD|$ is ______."}, {"role": "assis... |
1,424 | [{"role": "user", "content": "Let $x,$ $y,$ and $z$ be nonnegative real numbers such that $x + y + z = 1.$ Find the maximum value of $x^2 + y^2 + z^4.$"}, {"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 a... |
1,521 | [{"role": "user", "content": "A bag contains red, white, and black balls of the same size. The probability of drawing a red ball is 0.42, and the probability of drawing a white ball is 0.28. What is the probability of drawing a black ball?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is ... |
1,519 | [{"role": "user", "content": "Compute: $12 \\cdot \\frac{1}{15} \\cdot 30.$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to compute 12 multiplied by 1/15 multiplied by 30. Hmm, let's break this down step by step. First, maybe I should handle the multiplication in the order that's easiest. Som... |
1,464 | [{"role": "user", "content": "Given the equations $xy = 8$ and $x^2 + y^2 = 34$, the points of intersection of these two curves are joined in succession. What figure is formed by these points?\n$\\textbf{(A)}\\ \\text{a straight line}\\qquad \\textbf{(B)}\\ \\text{an equilateral triangle} \\qquad \\textbf{(C)}\\ \\text... |
1,522 | [{"role": "user", "content": "Olaf is sailing across the ocean with 25 men, including himself. He needs 1/2 a gallon of water per day per man. The boat can go 200 miles per day and he needs to travel 4,000 miles. How many gallons of water does he need?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. Ol... |
1,391 | [{"role": "user", "content": "The function \\( f(x) = \\frac{x+1}{x} + \\frac{x+2}{x+1} + \\cdots + \\frac{x+2023}{x+2022} \\) has a center of symmetry at \\((a, b)\\). What is the value of \\(2a + b\\)?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to pr... |
1,512 | [{"role": "user", "content": "Given the function $f(x)=\\sin (2x- \\frac {π}{6})$, its graph $C\\_1$ is translated to the left by $\\frac {π}{4}$ units to obtain the graph $C\\_2$. Determine the analytical expression of the function $g(x)$ corresponding to $C\\_2$."}, {"role": "assistant", "content": "<think>\n\nOkay, ... |
1,476 | [{"role": "user", "content": "Determine the domain of the real-valued function $$f(x) = \\sqrt{6 - \\sqrt{7 - \\sqrt{x}}}.$$"}, {"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 t... |
1,528 | [{"role": "user", "content": "Tim's cat had kittens. He gave 3 to Jessica and 6 to Sara. He now has 9 kittens. How many kittens did he have to start with?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about Tim's cat having kittens, and he gave some away, then he has 9 left. We need to... |
1,516 | [{"role": "user", "content": "The harmonic mean of $1$ and $2023$ is closest to which integer?\nA) 1\nB) 2\nC) 2024\nD) 4046"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the harmonic mean of 1 and 2023, and we need to find which integer it's closest to. The options are A) 1... |
1,405 | [{"role": "user", "content": "Points \\( G \\) and \\( N \\) are chosen on the interiors of sides \\( E D \\) and \\( D O \\) of unit square \\( D O M E \\), so that pentagon \\( GNOME \\) has only two distinct side lengths. The sum of all possible areas of quadrilateral \\( NOME \\) can be expressed as \\( \\frac{a-b ... |
1,525 | [{"role": "user", "content": "Which of the following quadratic equations has no real roots?\n\nA: $x^{2}+x+3=0$\n\nB: $x^{2}+2x+1=0$\n\nC: $x^{2}-2=0$\n\nD: $x^{2}-2x-3=0$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The question is asking which of the given quadratic equations has no real roots. I ... |
1,468 | [{"role": "user", "content": "As shown in the figure, \\(AD\\) is the angle bisector of \\(\\triangle ABC\\) with \\(AB < AC\\). On \\(AC\\), point \\(E\\) is chosen such that \\(CE = AB\\). Let \\(M\\) and \\(N\\) be the midpoints of \\(BC\\) and \\(AE\\), respectively. Prove that \\(MN \\parallel AD\\)."}, {"role": "... |
1,533 | [{"role": "user", "content": "In a division sum, the remainder is 0. A student mistook the divisor by 12 instead of 21 and obtained some quotient. The correct quotient is 20. What quotient did the student obtain by mistake?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem step ... |
1,507 | [{"role": "user", "content": "Randomly select a number $x$ in the interval $[0,2]$. The probability of the event \"$-1 \\leqslant \\log_{\\frac{1}{2}}(x+ \\frac{1}{2}) \\leqslant 1$\" occurring is ( ).\n\nA: $\\frac{3}{4}$\n\nB: $\\frac{2}{3}$\n\nC: $\\frac{1}{3}$\n\nD: $\\frac{1}{4}$"}, {"role": "assistant", "content"... |
1,484 | [{"role": "user", "content": "The total corn yield in centners, harvested from a certain field area, is expressed as a four-digit number composed of the digits 0, 2, 3, and 5. When the average yield per hectare was calculated, it was found to be the same number of centners as the number of hectares of the field area. D... |
1,531 | [{"role": "user", "content": "the average age of a class of 20 students is 21 years . the average increased by 1 when the teacher ' s age also included . what is the age of the teacher ?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about finding the age of a teacher when the average a... |
1,488 | [{"role": "user", "content": "Given: $\\cos\\alpha + \\sin\\alpha = \\frac{2}{3}$, then the value of $\\frac{\\sqrt{2}\\sin(2\\alpha - \\frac{\\pi}{4}) + 1}{1 + \\tan\\alpha}$ is \\_\\_\\_\\_\\_\\_."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide... |
1,530 | [{"role": "user", "content": "If y is 60% greater than x, then x is what percentage less than y?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says, \"If y is 60% greater than x, then x is what percentage less than y?\" Hmm, I need to figure out the percentage that x is less than y. Let m... |
1,470 | [{"role": "user", "content": "Let\n\\[g(x) = (\\arcsin x)^3 - (\\arccos x)^3.\\]\nFind the range of $g(x)$ where all functions are in radians."}, {"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.\... |
1,539 | [{"role": "user", "content": "Daria just got a new credit card so she could buy some furniture. Daria has $500 saved ready to pay for the furniture she buys. She bought a couch for $750, a table for a certain amount, and a lamp for $50. After she pays the initial $500, she still owes $400 before interest. How much did ... |
1,543 | [{"role": "user", "content": "If $10^{\\log_{10}16} = 10y + 6$, determine the value of $y$.\n- $\\textbf{(A)}\\ 0$\n- $\\textbf{(B)}\\ \\frac{1}{2}$\n- $\\textbf{(C)}\\ 1$\n- $\\textbf{(D)}\\ 2$\n- $\\textbf{(E)}\\ \\frac{3}{2}$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is: If \\(10^{... |
1,465 | [{"role": "user", "content": "In a regular hexagon with a side length of 3, three semicircles are inscribed such that their diameters coincide with alternating sides of the hexagon. What is the area of the shaded region inside the hexagon but outside all of the semicircles?\nA. $ 12\\sqrt{3} - \\frac{25\\pi}{8} $\nB. $... |
1,536 | [{"role": "user", "content": "Calculate: $(\\sqrt{2}-1)^{0}-(\\frac{1}{3})^{-1}-\\sqrt{8}-\\sqrt{(-2)^{2}}$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to calculate this expression: (√2 - 1)^0 - (1/3)^-1 - √8 - √((-2)^2). Hmm, let's break it down step by step. First, I remember that any num... |
1,447 | [{"role": "user", "content": "Some Christmas lights are arranged using magical wires. Each light can be either green or yellow. Each wire connects two lights and has a magical property: when someone touches a wire connecting two lights, each light changes color from green to yellow or from yellow to green.\n\na) In the... |
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