__src_index__ int64 0 172k | messages stringlengths 375 66.5k |
|---|---|
1,095 | [{"role": "user", "content": "In the diagram, \\( AOB \\) is a sector of a circle with \\( \\angle AOB = 45^\\circ \\). \\( OY \\) is drawn perpendicular to \\( AB \\) and intersects \\( AB \\) at \\( X \\). What is the length of \\( XY \\)? Assume that \\( OY \\) is a radius of the circle and \\( OY = 10 \\) units."},... |
1,185 | [{"role": "user", "content": "When five is added to three more than a certain number, the result is 19. What is the number?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem. The question says: \"When five is added to three more than a certain number, the result is 19. What is t... |
1,040 | [{"role": "user", "content": "The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 17 terms of the arithmetic progression?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that the sum of the fourth and twelfth term of an arithmetic pro... |
1,182 | [{"role": "user", "content": "A driver travels for 3 hours at 50 miles per hour. Her car's fuel efficiency is 30 miles per gallon. She is paid $0.60 per mile, and her only expense is gasoline, which costs $2.50 per gallon. Calculate the driver’s net rate of pay in dollars per hour after accounting for the gasoline expe... |
1,183 | [{"role": "user", "content": "Given the complex number $z= \\frac {3+2i}{2-3i}$, then the conjugate of $z$, $\\overline {z}=$ ( )\nA: $1$\nB: $-1$\nC: $i$\nD: $-i$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the conjugate of the complex number z, which is given as (3 + 2i)/(2 - 3i). ... |
1,194 | [{"role": "user", "content": "At Minyoung's house, there are four times as many chickens as ducks, and 17 fewer rabbits than ducks. If there are 8 rabbits in Minyoung's house, how many chickens, ducks, and rabbits are there in total in Minyoung's house?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to... |
1,204 | [{"role": "user", "content": "Calculate:<br/>$(1)\\left(+17\\right)+\\left(-12\\right)$;<br/>$(2)-\\frac{1}{7}-(-\\frac{6}{7})$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's tackle these two problems one by one. First, problem (1) is (+17) + (-12). Hmm, adding a negative number is the same as subtracting... |
1,187 | [{"role": "user", "content": "What is the sum of the number of faces, edges, and vertices of a square pyramid that has a square base? Additionally, find the number of diagonals in the square base."}, {"role": "assistant", "content": "<think>\n\nOkay, let's tackle this problem step by step. First, the question is asking... |
1,097 | [{"role": "user", "content": "Calculate the value of \\[\\cot(\\cot^{-1} 4 + \\cot^{-1} 9 + \\cot^{-1} 17 + \\cot^{-1} 33).\\]"}, {"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... |
1,191 | [{"role": "user", "content": "A boy is travelling from his home to school at 4 km/hr and reached 7 min late. The next day he traveled at 8 km/hr and reached 8 min early. What is the distance between home and school?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem step by step.... |
1,203 | [{"role": "user", "content": "The sum of two nonzero real numbers is $3$ times their product. What is the sum of the reciprocals of the two numbers?\nA) 1 \nB) 2 \nC) 3 \nD) 4 \nE) 6"}, {"role": "assistant", "content": "<think>\n\nGot it, let's try to solve this problem step by step. The question says: \"The sum of... |
1,198 | [{"role": "user", "content": "\"In Zhaotong, known as the city of apples and books, Zhaotong apples have become the \"golden fruit\" for farmers in Zhaolu Dam area to increase their income and become rich. With the continuous expansion of the apple planting base, the apple yield has increased. The apple yield in Zhaoya... |
1,193 | [{"role": "user", "content": "Calculate:<br/>$(1)2\\sqrt{2}+\\sqrt{27}-\\sqrt{8}$;<br/>$(2)(2\\sqrt{12}-3\\sqrt{\\frac{1}{3}})×\\sqrt{6}$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's tackle these two problems one by one. Starting with the first one: (1) 2√2 + √27 - √8. Hmm, I need to simplify each radic... |
1,124 | [{"role": "user", "content": "In the Cartesian coordinate system with origin $O$, point $A(4, -3)$ is the right-angle vertex of $\\triangle OAB$, given that $|AB| = 2|OA|$, and the ordinate of point $B$ is greater than $0$.\n\n$(1)$ Find the coordinates of $\\overrightarrow{AB}$;\n\n$(2)$ Find the equation of the circl... |
1,108 | [{"role": "user", "content": "Five students, A, B, C, D, and E, are arranged to participate in the volunteer service activities of the Shanghai World Expo. Each person is engaged in one of the four jobs: translation, tour guide, etiquette, or driver. Each job must have at least one person participating. A and B cannot ... |
1,167 | [{"role": "user", "content": "The domain of the function $f(x)$ is $\\mathbb{R}$, $f(0)=2$, and for any $x\\in\\mathbb{R}$, $f(x)+f'(x) > 1$. The solution set for the inequality $e^{x}\\cdot f(x) > e^{x}+1$ is ________.\nA: $\\{x|x > 0\\}$\nB: $\\{x|x < 0\\}$\nC: $\\{x|x < -1\\}$ or $\\{x|x > 1\\}$\nD: $\\{x|x < -1\\}$... |
1,159 | [{"role": "user", "content": "Given the moving straight line ${l_{0}}:ax+by+c-2=0 (a > 0, c > 0)$ that always passes through point $P(1,m)$, and the maximum distance from point $Q(4,0)$ to the moving straight line ${l_{0}}$ is $3$, find the minimum value of $\\frac{1}{2a}+\\frac{2}{c}$.\nA: $\\frac{9}{2}$\nB: $\\frac{9... |
1,142 | [{"role": "user", "content": "Given that the power function $f(x)=({{m^2}-2m+2}){x^{5k-2{k^2}}}({k∈Z})$ is an even function and monotonically increasing on $\\left(0,+\\infty \\right)$.\n$(1)$ Find the analytical expression of the function $f\\left(x\\right)$;\n$(2)$ If $f\\left(2x-1\\right) \\lt f\\left(2-x\\right)$, ... |
1,171 | [{"role": "user", "content": "Jason borrowed money from his sister to buy a new bicycle. His sister agreed to let him work off his debt by helping in her cafe, where his first hour is paid at $\\$1$, the second hour at $\\$2$, up until the tenth hour which is paid at $\\$10$, after which the rate cycle starts again fro... |
1,186 | [{"role": "user", "content": "The minimum value of the function $f(x)=\\frac{{e}^{x}}{x}+x-\\ln x$ is ( ).\n\nA: $e$\n\nB: $e+1$\n\nC: $1$\n\nD: $e-1$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to find the minimum value of the function \\( f(x) = \\frac{e^x}{x} + x - \\ln x \\). Hmm, first, I need ... |
1,212 | [{"role": "user", "content": "A train of length 250 m crosses a bridge of some length in 20 seconds. The speed of the train is 72 km/hr. What is the length of the bridge?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about a train crossing a bridge. I need to find the length of the bri... |
1,136 | [{"role": "user", "content": "Solve the system of equations\n\n$$\n\\left\\{\\begin{array}{l}\n5 x^{2}+14 x y+10 y^{2}=17 \\\\\n4 x^{2}+10 x y+6 y^{2}=8\n\\end{array}\\right.\n$$"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correc... |
1,209 | [{"role": "user", "content": "What is the smallest positive whole number divisible by five different prime numbers?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The question is asking for the smallest positive whole number that's divisible by five different prime numbers. Hmm, right. So first, I nee... |
1,217 | [{"role": "user", "content": "What least number must be subtracted from 9671 so that the remaining number is divisible by 2?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking: What least number must be subtracted from 9671 so that the remaining number is divisible by 2? Hmm, right. ... |
1,218 | [{"role": "user", "content": "The area of a square is twice the number of inches in its perimeter. Find the length, in inches, of a side of the square."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says the area of a square is twice the number of inches in its perimeter. I need to find th... |
1,189 | [{"role": "user", "content": "Given the function $f(x)= \\begin{cases} (5-a)x-3,x < 1 \\\\ \\log _{a}x,x\\geqslant 1 \\end{cases}$, find the range of values for the real number $a$ that makes this function an increasing function on $\\mathbb{R}$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure... |
1,139 | [{"role": "user", "content": "Solve the following system of equations:\n\n$$\n\\begin{aligned}\n& x^{2}+y^{2}-2 z^{2}=2 a^{2} \\\\\n& x+y+2 z=4\\left(a^{2}+1\\right) \\\\\n& z^{2}-x y=a^{2}\n\\end{aligned}\n$$"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult... |
1,196 | [{"role": "user", "content": "if both 112 and 33 are factors of the number a * 43 * 62 * 1311 , then what is the smallest possible value of a ?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that both 112 and 33 are factors of the number a * 43 * 62 * 1311. We need to find the smalles... |
1,151 | [{"role": "user", "content": "Given that the center of the ellipse $(C)$ is at the origin, one focus is at $F(0, \\sqrt {3})$, and the ellipse $(C)$ passes through the point $P( \\frac {1}{2}, \\sqrt {3})$.\n(I) Find the equation of the ellipse $(C)$;\n(II) A line with a slope not equal to $0$ passing through the point... |
1,228 | [{"role": "user", "content": "The area of a rectangular field is equal to 300 square meters. Its perimeter is some meters and the length of this rectangle is 15 meters. What is the perimeter of this rectangular field?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says the area of a rectan... |
1,084 | [{"role": "user", "content": "Given ellipse $C_{1}$ and parabola $C_{2}$ have a common focus $F(1,0)$, the center of $C_{1}$ and the vertex of $C_{2}$ are both at the origin. A line $l$ passing through point $M(4,0)$ intersects the parabola $C_{2}$ at points $A$ and $B$ (where point $A$ is in the fourth quadrant).\n$(1... |
1,221 | [{"role": "user", "content": "Find \\(\\lim _{x \\rightarrow \\infty} \\frac{4 x^{3}+x^{2}-2}{3 x^{2}+5 x-2}\\)."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the limit as x approaches infinity of (4x³ + x² - 2)/(3x² + 5x - 2). Hmm, limits at infinity for rational functions. I remember... |
1,216 | [{"role": "user", "content": "Given the function $f(x)= \\begin{cases} x+2 & (x\\leqslant -1) \\\\ x^{2} & (-1 < x < 2) \\\\ 2x & (x\\geqslant 2)\\\\ \\end{cases}$.\n\n(1) Find the values of $f(-4)$, $f(3)$, and $f(f(-2))$.\n(2) If $f(a)=10$, find the value of $a$."}, {"role": "assistant", "content": "<think>\n\nOkay, ... |
1,146 | [{"role": "user", "content": "Given a geometric progression with $n$ terms, where the first term is $a$ and the common ratio is $r$, let $P$ be the product of the squares of these $n$ terms, $S$ their sum, and $S'$ the sum of their reciprocals. Express $P$ in terms of $S$, $S'$, and $n$.\nA. $(S \\cdot S')^{\\frac{n}{2... |
1,202 | [{"role": "user", "content": "A certain meter records voltage between some values inclusive. The average value of 3 recordings on the meter was 6 volts, and the smallest possible recording was 2 volts. What is the lowest value the meter can record?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figu... |
1,164 | [{"role": "user", "content": "In a regular hexagon $ABCDEF$, diagonal $AC$ is drawn. Given that each interior angle of a regular hexagon is 120 degrees, what is the measure of angle $CAB$?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct ... |
1,213 | [{"role": "user", "content": "Determine the correct statement about the function $f(x) = \\frac{2x-1}{x-3} (x \\neq 3)$.\n\nA: The function $f(x)$ has a maximum or minimum value in its domain.\nB: The function $f(x)$ is strictly increasing in its domain.\nC: The graph of the function $f(x)$ is symmetrical about the poi... |
1,192 | [{"role": "user", "content": "For the equation $x^{2}+ax+b=0$ with respect to $x$, the following four propositions are given:<br/>A: $x=1$ is a root of the equation<br/>B: The sum of the two roots of the equation is $2$<br/>C: $x=3$ is a root of the equation<br/>D: The two roots of the equation have opposite signs<br/>... |
1,080 | [{"role": "user", "content": "In the arithmetic sequence $\\left\\{ a_n \\right\\}$, it is known that the common difference $d=2$, and $a_2$ is the geometric mean of $a_1$ and $a_4$.\n\n(1) Find the general formula for the sequence $\\left\\{ a_n \\right\\}$.\n\n(2) Let $b_n = a_{\\frac{n(n+1)}{2}}$, and denote $T_n = ... |
1,229 | [{"role": "user", "content": "Find the equation of the line that passes through the point P(1,1) and is perpendicular to the line 2x - y = 0. Represent the answer in the general form of the equation of a line."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the equation of a line that pa... |
1,237 | [{"role": "user", "content": "The denominator of a fraction is 4 more than twice the numerator. If the fraction is equivalent to \\( \\frac{3}{7} \\), what is the numerator of the fraction?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says the denominator of a fraction is 4 more than twi... |
1,236 | [{"role": "user", "content": "The average marks of 25 students in a class is 100. A student's mark is wrongly noted as a certain value instead of 10. The correct average marks is 98. What was the wrongly noted mark of the student?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this proble... |
1,117 | [{"role": "user", "content": "Linda is hiking in the Rockies. She walks northward three miles, then turns $45$ degrees eastward and walks five miles. How far is she from her starting point? Express your answer in simplest radical form."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging que... |
1,231 | [{"role": "user", "content": "What is the least number that should be added to some number, so the sum of the number is completely divisible by 23? The answer is 4. What is the original number?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem. The question says: \"What is the l... |
1,239 | [{"role": "user", "content": "When it is 3 o'clock, the hour hand and the minute hand coincide."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says, \"When it is 3 o'clock, the hour hand and the minute hand coincide.\" Wait, is that true? I need to check if at 3 o'clock, the hour and minut... |
1,245 | [{"role": "user", "content": "Given sets $A=\\{1,2,4\\}$ and $B=\\{2,4,5\\}$, then $A\\cup B=$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the union of sets A and B. First, I remember that the union of two sets, denoted by A ∪ B, is the set of all elements that are in A, in B, or in... |
1,132 | [{"role": "user", "content": "Given the functions $f(x)=5+\\log_{\\frac{1}{2}}(-x^{2}+2x+7)$, $x\\in[0,3]$, and $g(x)=9^{x}-2m\\cdot 3^{x}$, $x\\in[0,1]$.\n$(1)$ Find the monotonic intervals and extreme values of $f(x)$.\n$(2)$ Let the range of $f(x)$ be $M$ and the range of $g(x)$ be $N$. Is there a real number $m$ su... |
1,247 | [{"role": "user", "content": "Among the following statements, the correct one(s) is/are \\_\\_\\_\\_\\_\\_\n\\\\(①\\\\) If a point is randomly thrown into a circle, and the probability of the point falling on any point inside the circle is equal, then the mathematical model of this random experiment is the classical pr... |
1,098 | [{"role": "user", "content": "The difference between the longest and shortest diagonals of the regular n-gon equals its side. Find all possible n."}, {"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 ... |
1,210 | [{"role": "user", "content": "The polynomial equation \\[x^3 + ax + b = 0,\\] where $a$ and $b$ are rational numbers, has $3-\\sqrt{5}$ as a root. It also has an integer root. What is it?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct a... |
1,238 | [{"role": "user", "content": "Compute $\\dbinom{8}{3}$."}, {"role": "assistant", "content": "<think>\n\nGot it, let's see. I need to compute the binomial coefficient C(8,3), which is also written as \"8 choose 3\". I remember that the formula for combinations is C(n,k) = n! / (k!(n - k)!), where \"n!\" means n factoria... |
1,246 | [{"role": "user", "content": "Given $1 \\lt x \\lt 4$, simplify: $\\sqrt{{(1-x)}^2}+|x-4|=$____."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is to simplify √[(1 - x)²] + |x - 4| given that 1 < x < 4. Hmm, right. So first, I need to remember that the square root of a square is the absolu... |
1,252 | [{"role": "user", "content": "Sara initially has 4,892.5 black marbles. Fred gives her an additional 2,337.8 black marbles. How many black marbles does Sara have now?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. Sara starts with 4,892.5 black marbles. Then Fred gives her 2,337.8 more. I need to find... |
1,253 | [{"role": "user", "content": "Factor the expression: $63x^2 + 28x$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to factor the expression 63x² + 28x. Hmm, factoring usually means finding the greatest common factor (GCF) first, right? So I should look at the coefficients and the variables to f... |
1,261 | [{"role": "user", "content": "A small village has a total population of $520$. The data is shown on a graph which divides this population into four equal groups represented by rectangles. However, the labels specifying males and females are unreaded. If it is known that one rectangle represents all males in the village... |
1,170 | [{"role": "user", "content": "Given a right triangle \\( ABC \\) where the hypotenuse \\( BC \\) is divided into \\( n \\) equal parts, with \\( n \\) being an odd number. Let the segment containing the midpoint of the hypotenuse make an angle \\( \\alpha \\) with vertex \\( A \\). The hypotenuse \\( BC \\) has length ... |
1,259 | [{"role": "user", "content": "If 25% of x is 30 less than 20% of a certain number, then x is 680. What is the number?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem step by step. The question says: \"If 25% of x is 30 less than 20% of a certain number, then x is 680. What is ... |
1,200 | [{"role": "user", "content": "In an isosceles triangle with a lateral side of 100 and a base of 60, a circle is inscribed. Find the distance between the points of tangency located on the lateral sides."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to prov... |
1,262 | [{"role": "user", "content": "Marcus has two containers. The first container was $\\frac{4}{5}$ full of juice, and the second container was empty. He poured all the juice from the first container into the second container, at which point the second container was $\\frac{2}{3}$ full of juice. What is the ratio of the vo... |
1,257 | [{"role": "user", "content": "The equation $x^2+y^2+2ax-4y+(a^2+a)=0$ represents a circle. The range of values for $a$ is ( )\n\nA: $[4,+\\infty)$\n\nB: $(4,+\\infty)$\n\nC: $(-\\infty,4]$\n\nD: $(-\\infty,4)$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about finding the range of va... |
1,211 | [{"role": "user", "content": "The school organizes student representatives to visit and comfort the elderly who have lost their only child. Now, there are 5 bags of gifts, numbered 1, 2, 3, 4, 5, to be distributed among 4 elderly people, with each person receiving at least one bag. If the two bags given to the same per... |
1,269 | [{"role": "user", "content": "We have that $3a + 2 = 2$ and $b - 2a = 3.$ What is the value of $b$?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the value of \\( b \\) given two equations: \\( 3a + 2 = 2 \\) and \\( b - 2a = 3 \\). Hmm, first, maybe I should solve for \\( a \\) using ... |
1,248 | [{"role": "user", "content": "A fruit seller has mangoes, apples, and oranges. He sells mangoes at the rate of Rs. 14 per kg and loses 15%. He sells apples at Rs. 20 per kg and loses 10%. He sells oranges at Rs. 30 per kg and makes a profit of 5%. What should be the price per kg of each type of fruit if he wants to mak... |
1,258 | [{"role": "user", "content": "The midpoint of a line segment is located at $(3, 7)$. If one of the endpoints is $(0, 11)$, what is the other endpoint? Express your answer as an ordered pair."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direc... |
1,201 | [{"role": "user", "content": "Given a complex number $z$ that satisfies $|z|= \\sqrt{2}$, and the imaginary part of $z^{2}$ is $2$.\n\n(1) Find the complex number $z$;\n\n(2) Let $A$, $B$, and $C$ be the points corresponding to $z$, $z^{2}$, and $z-z^{2}$ in the complex plane, respectively. Find the area of $\\triangle... |
1,223 | [{"role": "user", "content": "Paula Parrot starts on a number line at 0 and wants to reach 2. She can hop only $\\frac{1}{4}$ of the distance to her goal in each hop. Each subsequent hop is $\\frac{1}{4}$ of the remaining distance to the goal. How far has she hopped after four hops? Express your answer as a common frac... |
1,271 | [{"role": "user", "content": "Hoseok's average score in Korean, English, and Science is 89. If Hoseok's average score increases by 1 after taking the Social studies test, what is the score of Social studies?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about Hoseok's average scores. F... |
1,273 | [{"role": "user", "content": "You work for a manufacturing plant that pays you $12.50 an hour plus a certain amount for each widget you make. You need to produce 1000 widgets in a 40-hour week to earn $660 (before payroll deductions). How much do you earn per widget?"}, {"role": "assistant", "content": "<think>\n\nOkay... |
1,230 | [{"role": "user", "content": "Janet filmed a new movie that is a certain percentage longer than her previous 2-hour long movie. Her previous movie cost $50 per minute to film, and the newest movie cost twice as much per minute to film as the previous movie. The total amount of money required to film Janet's entire newe... |
1,268 | [{"role": "user", "content": "For real numbers $u,$ the point\n\\[(x,y) = (3^u - 4, 9^u - 7 \\cdot 3^u - 2)\\]is plotted. All the plotted points lie on what kind of curve?\n\n(A) Line\n(B) Circle\n(C) Parabola\n(D) Ellipse\n(E) Hyperbola"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this... |
1,206 | [{"role": "user", "content": "Find the number of ordered pairs $(a, b)$ of complex numbers such that\n\\[a^5b^3 + a^2b^7 = 0\\]\n\\[a^3b^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 ... |
1,220 | [{"role": "user", "content": "Find the standard equation of the hyperbola that passes through the point (2, 1) and has asymptotes tangent to the circle $x^2 + (y-2)^2 = 1$.\n\nA: $\\frac {x^{2}}{ \\frac {11}{3}} - \\frac {y^{2}}{11} = 1$\n\nB: $\\frac {x^{2}}{2} - y^{2} = 1$\n\nC: $\\frac {y^{2}}{ \\frac {11}{3}} - ... |
1,256 | [{"role": "user", "content": "If $\\sin 2\\theta - 1 + i(\\sqrt{2}\\cos \\theta + 1)$ is a purely imaginary number, find the value(s) of $\\theta$ ($\\ \\ \\ \\ \\ \\ \\ \\ $).\n\nA: $2k\\pi - \\frac{\\pi}{4} (k \\in \\mathbb{Z})$\nB: $2k\\pi + \\frac{\\pi}{4} (k \\in \\mathbb{Z})$\nC: $2k\\pi \\pm \\frac{\\pi}{4} (k \... |
1,260 | [{"role": "user", "content": "Show that every graph admits an acyclic orientation."}, {"role": "assistant", "content": "<think>\n\nOkay, so I need to show that every graph admits an acyclic orientation. Hmm, let's start by recalling what an acyclic orientation is. An acyclic orientation of a graph is an assignment of d... |
1,150 | [{"role": "user", "content": "If the sum of the digits of a positive integer $a$ equals 6, then $a$ is called a \"good number\" (for example, 6, 24, 2013 are all \"good numbers\"). List all \"good numbers\" in ascending order as $a_1$, $a_2$, $a_3$, …, if $a_n = 2013$, then $n =$ ( )\nA: 50\nB: 51\nC: 52\nD: 53"}, {"r... |
1,281 | [{"role": "user", "content": "Given that $\\cos \\alpha = -\\frac{1}{5}$ and $\\sin \\alpha = \\frac{2\\sqrt{6}}{5}$, determine the quadrant in which the terminal side of $\\alpha$ lies.\nA. First quadrant\nB. Second quadrant\nC. Third quadrant\nD. Fourth quadrant"}, {"role": "assistant", "content": "<think>\n\nOkay, l... |
1,226 | [{"role": "user", "content": "a) Prove that for all real numbers $k,l,m$ holds : $$ (k+l+m)^2 \\ge 3 (kl+lm+mk) $$ When does equality holds?\n\nb) If $x,y,z$ are positive real numbers and $a,b$ real numbers such that $$ a(x+y+z)=b(xy+yz+zx)=xyz, $$ prove that $a \\ge 3b^2$ . When does equality holds?\n"}, {... |
1,234 | [{"role": "user", "content": "If a quadrilateral has diagonals that are equal in length and perpendicular to each other, which of the following classifications must it fall under?\n$\\textbf{(A)}\\ \\text{rhombus} \\qquad\\textbf{(B)}\\ \\text{rectangle} \\qquad\\textbf{(C)}\\ \\text{square} \\qquad\\textbf{(D)}\\ \\te... |
1,286 | [{"role": "user", "content": "In a set of data $3$, $5$, $1$, $4$, $6$, $5$, the mode and median are respectively ( ).\n\nA: $5$, $4.5$\n\nB: $4.5$, $4$\n\nC: $4$, $4.5$\n\nD: $5$, $5$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the mode and median of the data set: 3, 5, 1... |
1,276 | [{"role": "user", "content": "The average of 6 numbers is 30. The average of the first 4 numbers is a certain value, and the average of the last 3 numbers is 35. The fourth number is 25. What is the average of the first 4 numbers?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this proble... |
1,222 | [{"role": "user", "content": "Lizzie's group, the Hilltown team, the Green Valley crew, the Riverbank squad, and the Meadowlane gang embarked on a mission to clean up some farmlands. The total area of the given farmlands spans 28,500.0 square feet. \n\nOn the first day, Lizzie's group managed to clean an area of 3,534 ... |
1,294 | [{"role": "user", "content": "Kelly had 56 apples. She needs to pick some more apples to have a certain number of apples altogether. If she needs to pick 49 more apples, how many apples will she have altogether?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says Kelly had 56 apples. She n... |
1,290 | [{"role": "user", "content": "If $|m|=|-7|$, then $m=$____."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says if the absolute value of m equals the absolute value of -7, then what is m? Hmm, first I need to remember what absolute value means. Absolute value is the distance from zero on t... |
1,197 | [{"role": "user", "content": "Children are dividing a bag of marbles among themselves. The first child took one marble and a tenth of the remaining marbles, then the second took two marbles and a tenth of the remaining, then the third took three marbles and a tenth of the remaining, and so on, until the last child took... |
1,241 | [{"role": "user", "content": "Given vectors $\\overrightarrow{a}=(\\cos x,\\sin x)$, $\\overrightarrow{b}=(-\\cos x,\\cos x)$, $\\overrightarrow{c}=(-1,0)$.\n(I) If $x= \\frac {\\pi}{6}$, find the angle between vectors $\\overrightarrow{a}$ and $\\overrightarrow{c}$.\n(II) When $x\\in[ \\frac {\\pi}{2}, \\frac {9\\pi}{... |
1,287 | [{"role": "user", "content": "The price of a book was $400. If the book's price is decreased by a certain percentage and then increased by 40%, the final price of the book is $476. What was the percentage decrease in the book's price?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this pr... |
1,148 | [{"role": "user", "content": "Below is the graph of \\( y = a \\cos (bx + c) \\) for some positive constants \\( a \\), \\( b \\), and \\( c \\). The graph first reaches a zero at \\( x = 0 \\). Determine the smallest possible value of \\( c \\)."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or chal... |
1,208 | [{"role": "user", "content": "Andrea wants to fill in four sections of her backyard with sod that must be purchased in 3 x 4-foot rectangles. If the four sections have the following dimensions: \n\n1) 35 x 42 feet \n2) 55 x 86 feet \n3) 20 x 50 feet\n4) 48 x 66 feet \n\nHow many rectangles of sod does she need to buy?"... |
1,300 | [{"role": "user", "content": "Stacy has 2 more than triple as many berries as Steve. Steve has one half as many berries as Skylar. If Skylar has 20 berries, how many berries does Stacy have?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about Stacy, Steve, and Skylar and how many berri... |
1,232 | [{"role": "user", "content": "What is the sign of the $n$-th term in the expansion of the product\n\n$$(1-a)(1-b)(1-c)(1-d) \\ldots=1-a-b+a b-c+a c+b c-a b c-d+\\ldots$$\n\nfor $n = 0, 1, 2, \\ldots$?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provi... |
1,305 | [{"role": "user", "content": "Jane bought 2 skirts for $13 each. She also bought 3 blouses for $6 each. She paid the cashier $100. How much change did she receive?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. Jane bought some skirts and blouses, and I need to figure out how much change she got from ... |
1,272 | [{"role": "user", "content": "Given a parabola $y=ax^2+bx+c$ passing through point P $(1,1)$, and it is tangent to the line $y=x-3$ at point Q $(2,-1)$, find the values of the real numbers $a$, $b$, and $c$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult t... |
1,303 | [{"role": "user", "content": "At the beginning of the academic term, John's goal was to earn a 'B' on at least $75\\%$ of his $60$ tests for the semester. He earned a 'B' on $32$ of the first $40$ tests. If he is to achieve his goal, on at most how many of the remaining tests can he earn a grade lower than a 'B'?\nA. 5... |
1,297 | [{"role": "user", "content": "The ratio of $a$ to $b$ is $5:4$, the ratio of $c$ to $d$ is $2:1$, and the ratio of $d$ to $b$ is $1:8$. What is the ratio of $a$ to $c$?\nA) 10:1\nB) 5\nC) 4:1\nD) 16:3\nE) 20:3"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this ratio problem. So, we need ... |
1,266 | [{"role": "user", "content": "In the rectangular coordinate system $(xOy)$, a polar coordinate system is established with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis. The polar coordinate equation of a certain circle is given by: $ρ^2 - 4ρ\\cos θ + 2 = 0$.\n\n(I) Convert the po... |
1,235 | [{"role": "user", "content": "17. Let \\(\\xi_{1}, \\ldots, \\xi_{n}\\) be independent and identically distributed random variables with a continuous distribution function \\(F=F(x)\\). Given that \\(\\mathrm{P}\\left(\\xi_{i}=\\xi_{j}\\right)=0\\) for \\(i \\neq j\\), show the following:\n\n(a) Prove that the distribu... |
1,310 | [{"role": "user", "content": "In a certain group, the number of people and the time spent on household chores (in hours) in a week are shown in the table below. Which of the following statements about the \"time spent on chores\" data is correct?\n\n| Time Spent on Chores (hours) | 2 | 3 | 4 |\n|-----------------... |
1,251 | [{"role": "user", "content": "Given a triangle \\( \\triangle ABC \\) with \\( \\angle ABC = 80^\\circ \\), \\( \\angle ACB = 70^\\circ \\), and \\( BC = 2 \\). A perpendicular line is drawn from \\( A \\) to \\( BC \\), and another perpendicular line is drawn from \\( B \\) to \\( AC \\). The two perpendicular lines i... |
1,306 | [{"role": "user", "content": "There are 300 seniors at Morse High School, and 40% of them have cars. Of the remaining grades (freshmen, sophomores, and juniors), only 10% of them have cars. If 15% of all the students at Morse have cars, how many students are in those other 3 lower grades?"}, {"role": "assistant", "cont... |
1,307 | [{"role": "user", "content": "The solution set of the inequality $x^2 + 2x < 3$ is expressed as ______. (The answer should be expressed in the form of a set)"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to solve the inequality \\( x^2 + 2x < 3 \\). Hmm, first, maybe I should rearrange it so t... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.