__src_index__ int64 0 172k | messages stringlengths 375 66.5k |
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366 | [{"role": "user", "content": "Two employees X and Y are paid a total of Rs. 560 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that two employees, X and Y, are paid a total of Rs. 5... |
390 | [{"role": "user", "content": "If $\\alpha$ and $\\beta$ are the two distinct solutions to the equation $x^2 = 2x + 1$, what is the value of $(\\alpha-\\beta)^2$?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that α and β are the two distinct solutions to the equation x² = 2x + 1, and... |
395 | [{"role": "user", "content": "Find the number greater than 1.1 among the five numbers 1.4, 9/10, 1.2, 0.5 and 13/10, and find the number of that numbers."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking to find the number greater than 1.1 among the five numbers: 1.4, 9/10, 1.2, 0.5... |
386 | [{"role": "user", "content": "Three teams planted trees. The first team planted $a$ trees, the second team planted twice as many trees as the first team plus 8 more, and the third team planted 6 fewer trees than half of what the second team planted. How many trees did the three teams plant in total? And calculate the t... |
402 | [{"role": "user", "content": "In the function $y=\\frac{1}{x-2}$, the range of the independent variable $x$ is ( ).\n\nA: $x \\gt 2$\n\nB: $x\\geqslant 2$\n\nC: $x\\neq 2$\n\nD: $x \\lt 2$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The question is about finding the range of the independent variabl... |
276 | [{"role": "user", "content": "Find the sum \\( S_{n} = \\sin \\alpha \\cdot \\sin ^{2} \\frac{\\alpha}{2} + 2 \\sin \\frac{\\alpha}{2} \\cdot \\sin ^{2} \\frac{\\alpha}{4} + \\cdots + 2^{n-1} \\cdot \\sin \\frac{\\alpha}{2^{n-1}} \\cdot \\sin ^{2} \\frac{\\alpha}{2^{n}} \\)."}, {"role": "assistant", "content": "<think>... |
343 | [{"role": "user", "content": "What is the units digit of the product of all the odd positive integers between 20 and 120?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so the problem... |
356 | [{"role": "user", "content": "The cash realized on selling a 14% stock is Rs. 109.25. The cash amount before brokerage is Rs. 109. What is the percentage of the brokerage?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem step by step. So, the question is about finding the perce... |
361 | [{"role": "user", "content": "What is the sum of the different prime factors of $247520$?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so I need to find the sum of the different pri... |
344 | [{"role": "user", "content": "Given a parabola $x^{2}=2py\\ (p > 0)$ with focus $F$ and directrix intersecting the hyperbola $x^{2}-y^{2}=1$ at points $A$ and $B$. If $\\triangle ABF$ is an equilateral triangle, find the value of $P$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging ques... |
300 | [{"role": "user", "content": "Arrange the positive integers according to the pattern shown below: \n1 2 5 10 17… \n4 3 6 11 18… \n9 8 7 12 19… \n16 15 14 13 20… \n25 24 23 22 21… \n… \nWhat is the number in the 2007th row and 2008th column? (Answer with a specific number.)"}, {"role"... |
331 | [{"role": "user", "content": "What is the largest result we can find when we divide a 2-digit number by the sum 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 to think about it.\nWell, so the pr... |
412 | [{"role": "user", "content": "At the park, Naomi saw people riding 7 regular bikes and 11 children's bikes. Regular bikes have 2 wheels and kid's bikes have a certain number of wheels. Naomi saw 58 wheels at the park. How many wheels does a kid's bike have?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's se... |
367 | [{"role": "user", "content": "Given the function $f(x)=e^{x}-e^{1-x}-ax$, if $x_{1}$ and $x_{2}$ are two zeros of the function $g(x)=e^{x}+e^{1-x}-a$, and $f(x_{1})+f(x_{2})=-4$, then the real number $a$ is $\\left(\\ \\ \\right)$\n\nA: $2$\n\nB: $3$\n\nC: $4$\n\nD: $5$"}, {"role": "assistant", "content": "<think>\n\nO... |
291 | [{"role": "user", "content": "In a certain number quiz, the test score of a student with seat number $n$ ($n=1,2,3,4$) is denoted as $f(n)$. If $f(n) \\in \\{70,85,88,90,98,100\\}$ and it satisfies $f(1)<f(2) \\leq f(3)<f(4)$, then the total number of possible combinations of test scores for these 4 students is \\_\\_\... |
408 | [{"role": "user", "content": "Two wheels are spun, one with three sections and another with five sections. The first wheel has two sections labeled as even numbers and one as an odd number. The second wheel has three sections labeled as even numbers and two as odd numbers. What is the probability that the sum of the nu... |
309 | [{"role": "user", "content": "Steve has an isosceles triangle with base 8 inches and height 10 inches. He wants to cut it into eight pieces that have equal areas, as shown below. To the nearest hundredth of an inch what is the number of inches in the greatest perimeter among the eight pieces? [asy]\nsize(150);\ndefault... |
316 | [{"role": "user", "content": "If \\( n \\) is a positive integer, the notation \\( n! \\) (read \" \\( n \\) factorial\") represents the product of the integers from 1 to \\( n \\) inclusive. For example, \\( 5! = 1 \\times 2 \\times 3 \\times 4 \\times 5 = 120 \\). Which of the following is equal to a perfect square?\... |
398 | [{"role": "user", "content": "In a circular garden with center $O$, there are two points $A$ and $B$ on the circle such that the measure of $\\angle AOB$ is $60^\\circ$. The radius of the garden is $15$ cm. Calculate the length of the arc $AB$ on the boundary of the garden. Provide your answer in terms of $\\pi$."}, {"... |
414 | [{"role": "user", "content": "Let vector $\\vec{a} = (4, m)$, $\\vec{b} = (1, -2)$, and $\\vec{a} \\perp \\vec{b}$. Find the magnitude of $\\vec{a} + 2\\vec{b}$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that vector a is (4, m), vector b is (1, -2), and they are perpendicular. We... |
422 | [{"role": "user", "content": "Mrs. Wong had 30 Valentines. She gave 8 Valentines to her children, 5 Valentines to her neighbors, and 3 Valentines to her coworkers. How many Valentines does she have left?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. Mrs. Wong started with 30 Valentines. She gave some... |
400 | [{"role": "user", "content": "How many positive divisors do 9240 and 10800 have in common?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking how many positive divisors 9240 and 10800 have in common. Hmm, right. So, to find the number of common positive divisors, I think I need to fi... |
401 | [{"role": "user", "content": "Rich likes to take long walks through town. He walks some distance from his house to the sidewalk, then 200 feet down the sidewalk to the end of the road. Then he makes a left and walks double his total distance so far until he reaches the next intersection. Then he walks half the total di... |
394 | [{"role": "user", "content": "Let $y = ax^{2} + (b-2)x + 3$. \n$(1)$ If the solution set of the inequality $y > 0$ with respect to $x$ is $\\{x | -1 < x < 3\\}$, find the solution set of $y \\geq 4$. \n$(2)$ If $x = 1$ and $y = 2$, $a > 0$, $b > 0$, find the minimum value of $\\frac{1}{a} + \\frac{4}{b}$."}, {"role":... |
416 | [{"role": "user", "content": "Conducting regression analysis on two variables $y$ and $x$, we obtain a set of sample data: $(x_1, y_1), (x_2, y_2), \\ldots, (x_n, y_n)$. Among the following statements, the incorrect one is:\nA. The regression equation obtained from the sample data is $y = ax + b$ and must pass through ... |
418 | [{"role": "user", "content": "Kiarra is twice as old as Bea. Job is 3 times older than Bea. Figaro is 7 years older than Job. Harry is half as old as Figaro. If Harry is 26, how old is Kiarra?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out how old Kiarra is. The problem says Harry is 26, ... |
383 | [{"role": "user", "content": "Given that all terms of a geometric sequence $\\{a_n\\}$ are positive numbers, and $3a_1$, $\\frac{1}{2}a_3$, $2a_2$ form an arithmetic sequence, calculate the value of $$\\frac{a_{20}+a_{19}}{a_{18}+a_{17}}$$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challengin... |
423 | [{"role": "user", "content": "Among the following expressions, which one is a fractional equation? ( )\nA: $\\dfrac{x^2+1}{2}=\\dfrac{5}{3}$\nB: $\\dfrac{1}{3x-1}+\\dfrac{4x}{3x+1}$\nC: $\\dfrac{x}{2x-1}-\\dfrac{3}{2x+1}=1$\nD: $\\dfrac{3-x}{4}+2=\\dfrac{x-4}{3}$"}, {"role": "assistant", "content": "<think>\n\nOkay,... |
419 | [{"role": "user", "content": "Rohan spends a certain percentage of his salary on food, 20% on house rent, 10% on entertainment, and 10% on conveyance. His savings at the end of a month are Rs. 2500, and his monthly salary is Rs. 12500. What percentage of his salary does he spend on food?"}, {"role": "assistant", "conte... |
352 | [{"role": "user", "content": "Let $T = \\{7^k | k \\in \\mathbb{Z}, 0 \\le k \\le 1000 \\}$. Given that $7^{1000}$ ends with the digits $0001$ and has $202$ digits, how many elements of $T$ end with the digit $1$?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is diffi... |
387 | [{"role": "user", "content": "The probability of an event $A$ occurring is $v=0.1$. We conduct $n=998$ trials. Which is more likely; that $A$ occurs 100 times, or that it occurs 99 times?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out whether it's more likely for event A to occur 100 time... |
426 | [{"role": "user", "content": "The linear regression equation $\\overline{y}=bx+a$ represents a line that must pass through a fixed point $(\\,)$\nA: $(0,0)$\nB: $(\\bar{x},0)$\nC: $(0,\\bar{y})$\nD: $(\\bar{x},\\bar{y})$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The question is about the linear r... |
431 | [{"role": "user", "content": "The amount of time that three people worked on a special project was in the ratio of 1 to 2 to 3. The hardest working person worked 40 hours more than the person who worked the least. How many hours did the project take in total?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's ... |
420 | [{"role": "user", "content": "Simplify $\\dfrac{150}{6000} \\cdot 75.$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to simplify (150/6000) multiplied by 75. Hmm, first, maybe I should simplify the fraction 150/6000 before multiplying by 75. Let me start by reducing 150/6000. Both numerator an... |
371 | [{"role": "user", "content": "Non-zero vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ satisfy $|\\overrightarrow{b}|=2$, $\\angle(\\overrightarrow{a}, \\overrightarrow{b}) = 30^{\\circ}$, and for all $\\lambda > 0$, $|\\overrightarrow{a}-\\lambda \\overrightarrow{b}|\\geqslant |\\overrightarrow{a}- \\overright... |
397 | [{"role": "user", "content": "A function has the following properties: (1) its minimum positive period is $4\\pi$; (2) $x= \\frac{\\pi}{3}$ is a symmetrical axis of its graph; (3) it is a decreasing function in the interval $(\\frac{2\\pi}{3}, \\frac{5\\pi}{6})$. Determine the function from the options below:\nA: $y=\\... |
433 | [{"role": "user", "content": "From five cards marked with the numbers 0, 1, 2, 3, and 4, one card is drawn and its number is noted. The card is then put back and another card is drawn and its number is also noted. The number of different ways the sum of the numbers on the two drawn cards can exactly equal 4 is ( ).\n\n... |
406 | [{"role": "user", "content": "Given a function $f(x)$ such that for any $x \\in \\mathbb{R}$, $f(x+2)+f(x-2)=2f(2)$, and if the graph of $y=f(x+1)$ is symmetric about the point $(-1,0)$, and $f(1)=2$, then $f(2019)=$\nA: $-2$\nB: $0$\nC: $1$\nD: $2$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to sol... |
438 | [{"role": "user", "content": "Rs. 595 is divided among A, B, and C. A gets 2/3 of what B gets, and B gets a certain fraction of what C gets. Their shares are respectively Rs. 420, Rs. 105, and Rs. 70. What is the ratio of B's share to C's share?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The probl... |
429 | [{"role": "user", "content": "Given a sphere with a radius of 13, there are three points A, B, and C on the surface of the sphere, with AB = 6, BC = 8, and AC = 10. The distance from the center of the sphere, O, to the plane ABC is \n\nA: 12\nB: 8\nC: 6\nD: 5"}, {"role": "assistant", "content": "<think>\n\nOkay, let's ... |
437 | [{"role": "user", "content": "A retailer buys a radio for some amount. His overhead expenses are Rs 15. He sells the radio for Rs 300. The profit percent of the retailer is 25%. What is the cost price of the radio?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem step by step. ... |
435 | [{"role": "user", "content": "Elena rolls two six-sided dice. What is the probability that she will roll a number greater than four on the first die and a number greater than two on the second die? Express your answer as a common fraction."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging... |
295 | [{"role": "user", "content": "Let $a, b, c$ be positive integers whose greatest common divisor is $1$ . Determine whether there always exists a positive integer $n$ such that, for every positive integer $k$ , the number $2^n$ is not a divisor of $a^k+b^k+c^k$ ."}, {"role": "assistant", "content": "<think>\n\nT... |
444 | [{"role": "user", "content": "Frank picked some apples. Susan picked 3 times as many apples as Frank. Susan gave out half of her apples, and Frank sold a third of his. They have 78 apples left in total. How many apples did Frank pick?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out how man... |
450 | [{"role": "user", "content": "Compare the sizes: $\\pi$ ____ $3.14$ (fill in the blank with $=$, $>$, or $<$)."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The question is asking to compare the size of π and 3.14, and fill in the blank with =, >, or <. Hmm, I need to remember what π is approximately... |
328 | [{"role": "user", "content": "(1) If the sum of the first $n$ terms of the sequence $\\{a_n\\}$ is $S_n=\\frac{2}{3}a_n+\\frac{1}{3}$, then the general formula for $\\{a_n\\}$ is $a_n=\\_\\_\\_\\_\\_\\_\\_\\_$.\n\n(2) In $\\triangle ABC$, the lengths of the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$,... |
399 | [{"role": "user", "content": "Find the product of all real values of $r$ for which $\\frac{1}{3x}=\\frac{r-x}{8}$ has exactly one real solution."}, {"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... |
407 | [{"role": "user", "content": "\\((\\cos x - \\sin x)^2 + \\cos^4 x - \\sin^4 x = 0.5 \\sin 4x\\)"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to solve this trigonometric equation: \\((\\cos x - \\sin x)^2 + \\cos^4 x - \\sin^4 x = 0.5 \\sin 4x\\). Hmm, first, I need to simplify both sides and see if ... |
338 | [{"role": "user", "content": "Given $f(x)=\\sin(2x+\\frac{π}{6})$. When $x\\in \\left[t,t+2\\right]$, $t\\in Z$, the range of $f\\left(x\\right)$ is $\\left[-1,1\\right]$. Find one possible value of $t$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem. The function given is \\... |
405 | [{"role": "user", "content": "The instruction manual for a certain medication includes the following statement: \"After taking the medication, the concentration of the drug in the blood reaches its highest level after (0.65±0.15) hours.\" Therefore, the possible time after taking the medication for the concentration of... |
442 | [{"role": "user", "content": "Determine the interval of decrease for the function $y=(x^2 - 3)e^x$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the interval where the function \\( y = (x^2 - 3)e^x \\) is decreasing. Hmm, right. To find where a function is decreasing, I remember that ... |
454 | [{"role": "user", "content": "Jitka hiked a trail. After hiking 60% of the length of the trail, she had 8 km left to go. What is the length of the trail?\n(A) 28 km\n(B) 12.8 km\n(C) 11.2 km\n(D) 13 \\(\\frac{1}{3}\\) km\n(E) 20 km"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says Jitka ... |
459 | [{"role": "user", "content": "Marguerite drove 150 miles in 3 hours. If Sam drove for 4.5 hours at the same average rate as Marguerite, how many miles did he drive?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about Marguerite driving 150 miles in 3 hours, and we need to find out how ... |
376 | [{"role": "user", "content": "Given real numbers $x \\gt 0$ and $y \\gt 0$, find the minimum value of $\\frac{3x}{3x+2y}+\\frac{y}{2x+y}$."}, {"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.\nWel... |
320 | [{"role": "user", "content": "The real numbers \\( x_{1}, x_{2}, \\ldots, x_{1996} \\) have the following property: for any polynomial \\( W \\) of degree 2, at least three of the numbers \\( W(x_{1}), W(x_{2}), \\ldots, W(x_{1996}) \\) are equal. Prove that at least three of the numbers \\( x_{1}, x_{2}, \\ldots, x_{1... |
325 | [{"role": "user", "content": "In the arithmetic sequence $\\{a_n\\}$, $a_2=5$, $a_6=21$. Let the sum of the first $n$ terms of the sequence $\\left\\{ \\frac{1}{a_n} \\right\\}$ be $S_n$. If $S_{2n+1}-S_n \\leqslant \\frac{m}{15}$ holds for all $n \\in \\mathbb{N}_+$, then the minimum value of the positive integer $m$ ... |
455 | [{"role": "user", "content": "In the expansion of \\((a+b)^n\\), there are \\(n+1\\) different terms. In the expansion of \\((a+b+c)^{10}\\), the number of different terms is:\n\n(A) 11 \n(B) 33 \n(C) 55 \n(D) 66 \n(E) 132 \n\n(Provided by the 9th American High School Mathematics Examination, 1958)"}, {"role": "as... |
391 | [{"role": "user", "content": "A person is practicing target shooting, starting at a distance of 100 meters from the target for the first shot. If the first shot misses, they move back 50 meters for the second shot and continue this pattern; each time they miss, they move back 50 meters and take another shot until they ... |
448 | [{"role": "user", "content": "The force exerted by the airflow on a sail can be calculated using the formula:\n\n\\[ F = \\frac{C S \\rho (v_0 - v)^2}{2}, \\]\n\nwhere \\(C\\) is the coefficient of aerodynamic force, \\(S\\) is the area of the sail (\\(S = 5 \\, \\text{m}^2\\)), \\(\\rho\\) is the air density, \\(v_0\\... |
375 | [{"role": "user", "content": "Show that for every positive integer \\( n \\), there exists a nonzero multiple of \\( n \\) that has at most \\( n \\) digits, all of which are either 0 or 1."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct... |
461 | [{"role": "user", "content": "In an election with two candidates, the winner received 70% of votes and won by a certain number of votes. The winning candidate received 490 votes. How many votes did the winner win by?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about an election with ... |
425 | [{"role": "user", "content": "If the real numbers $-1$, $a$, $b$, $c$, $-9$ form a geometric sequence, then $b=$ \\_\\_\\_\\_\\_\\_."}, {"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 ... |
378 | [{"role": "user", "content": "Let \\( F(x) \\) be the antiderivative of the function \\( f(x) \\) on the interval \\([a, b]\\), and let \\( \\varphi(y) \\) be a differentiable function on the interval \\([p, q]\\). Suppose \\( a \\leq \\varphi(y) \\leq b \\) for all \\( y \\) in the interval \\([p, q]\\), and for any p... |
452 | [{"role": "user", "content": "Among the following four functions, the one that is increasing on $\\left(0,+\\infty \\right)$ is:\n\nA: $f\\left(x\\right)=3-x$\n\nB: $f\\left(x\\right)=x^{2}+x$\n\nC: $f\\left(x\\right)=-|x|$\n\nD: $f(x)=-\\frac{3}{x-1}$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. Th... |
451 | [{"role": "user", "content": "Given the sets $A=\\left\\{ x\\mid (x+4)(x-2) > 0 \\right\\}$, $B=\\left\\{ y\\mid y=x^{2}-2x+2, x\\in \\mathbb{R} \\right\\}$, $C=\\left\\{ x\\mid -4 \\leqslant x \\leqslant a \\right\\}$. \n(Ⅰ) Find $A\\bigcap B$; \n\n(Ⅱ) If ${C}_{R}A \\subseteq C$, find the range of the real number $a... |
456 | [{"role": "user", "content": "At the presentation, students take turns giving presentations. Eunjung will be the 6th speaker from the back, and the seven students in front of Eunjung will make the presentation. How many students are giving presentations?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try t... |
415 | [{"role": "user", "content": "Determine the sum of all prime numbers $p$ for which there exists no integer solution in $x$ to the congruence $5(6x + 2) \\equiv 3 \\pmod{p}$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct ans... |
472 | [{"role": "user", "content": "Noa scored some points to win a bowl, and Phillip scores twice that number. The total number of points Noa and Phillip scored to win the bowl is 90. How many points did Noa score?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says Noa scored some points to wi... |
445 | [{"role": "user", "content": "One more than the reciprocal of a certain number is $\\frac{9}{4}$. What is this original number expressed as a common fraction?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to ... |
424 | [{"role": "user", "content": "A positive integer is a perfect number provided that the sum of all the positive factors of it, including 1 and itself, is equal to twice of it. The sum of the reciprocals of all the positive factors of the perfect number 28 is 2. What is this perfect number?"}, {"role": "assistant", "cont... |
389 | [{"role": "user", "content": "Compute the smallest base-10 positive integer greater than 15 that is a palindrome when written in both base 2 and base 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 ... |
409 | [{"role": "user", "content": "Find all values of $x$ that satisfy the inequalities:\n\\[ 3x - 2 < (x + 2)^2 < 9x - 8. \\]"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so I need to s... |
413 | [{"role": "user", "content": "Let $c$ and $d$ be positive real numbers such that each of the equations $x^2 + cx + 3d = 0$ and $x^2 + 3dx + c = 0$ has real roots. Find the smallest possible value of $c + 3d$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult ... |
349 | [{"role": "user", "content": "Let \\( f(m, n) \\) satisfy the condition\n$$\nf(m, n) \\leq f(m, n-1) + f(m-1, n),\n$$\nwhere \\( m \\) and \\( n \\) are positive integers, \\( m, n \\geq 2 \\), \nand \n$$\nf(1, n) = f(m, 1) = 1.\n$$\nProve that \\( f(m, n) \\leq C_{m+n} \\)."}, {"role": "assistant", "content": "<think>... |
464 | [{"role": "user", "content": "If the average (arithmetic mean) of 30 consecutive odd integers is 526, then the least of these integers is:"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that the average of 30 consecutive odd integers is 526, and we need to find the least of these inte... |
474 | [{"role": "user", "content": "when x is multiplied by 3 , the result is 26 more than the result of subtracting x from 26 . what is the value of x ?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to solve this problem step by step. The question says: \"When x is multiplied by 3, the result is 26 more th... |
446 | [{"role": "user", "content": "Calculate the value of $3.5 \\times 7.2 \\times (6.3 - 1.4)$.\n$\\text{(A)}\\ 100 \\qquad \\text{(B)}\\ 120 \\qquad \\text{(C)}\\ 122.5 \\qquad \\text{(D)}\\ 130 \\qquad \\text{(E)}\\ 140$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to calculate 3.5 times 7.2 ti... |
373 | [{"role": "user", "content": "Let $PQRS$ be a convex quadrilateral, and let $G_P,$ $G_Q,$ $G_R,$ $G_S$ denote the centroids of triangles $QRS,$ $PRS,$ $PQS,$ and $PQR,$ respectively. Prove that $\\frac{[G_P G_Q G_R G_S]}{[PQRS]} = \\frac{1}{9}$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or chall... |
477 | [{"role": "user", "content": "Which of the following algebraic expressions is written in standard form?\n\nA: $y\\times 9$\n\nB: $x\\div y$\n\nC: $9\\frac{1}{3}a$\n\nD: $-\\frac{1}{4}b$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The question is asking which of the given algebraic expressions is wr... |
481 | [{"role": "user", "content": "Simplify the expression \\(3x + 6x + 9x + 12x + 15x + 20 + 4y\\)."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to simplify the expression \\(3x + 6x + 9x + 12x + 15x + 20 + 4y\\). Hmm, simplifying usually means combining like terms. Like terms are terms that have... |
443 | [{"role": "user", "content": "The 900 students at Royal High School are divided into four groups of equal size for lunch. Each group dines at a different time. A computer randomly assigns each student to one of the four lunch groups. Calculate the probability that three friends, Alex, Bella, and Chris, will be assigned... |
457 | [{"role": "user", "content": "If \\( y = \\frac{1+i\\sqrt{3}}{2} \\) where \\( i = \\sqrt{-1} \\), then calculate \\( \\dfrac{1}{y^3-y} \\).\n(A) \\( -\\frac{1}{2} + \\frac{i\\sqrt{3}}{6} \\)\n(B) \\( -\\frac{1}{2} - \\frac{i\\sqrt{3}}{6} \\)\n(C) \\( -\\frac{3}{2} + \\frac{i\\sqrt{3}}{2} \\)\n(D) \\( -\\frac{3}{2} - \... |
473 | [{"role": "user", "content": "Given that the complex number $z$ satisfies the equation $\\frac{\\dot{z}}{1-i} = i^{2017}$, where $i$ is the imaginary unit, find the value of $z$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that the complex number \\( z \\) satisfies the equation \\... |
486 | [{"role": "user", "content": "The equation of the tangent line to the curve $y=2\\sin x$ at point $P(\\pi, 0)$ is ( )\nA: $y=-2x+2\\pi$\nB: $y=0$\nC: $y=-2x-2\\pi$\nD: $y=2x+2\\pi$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the equation of the tangent line to the curve y = 2 sin x a... |
485 | [{"role": "user", "content": "In a sample of associates at a law firm, some percent are second-year associates, and 60 percent are not first-year associates. 30 percent of the associates at the law firm have been there for more than two years. What percentage of the associates are second-year associates?"}, {"role": "a... |
357 | [{"role": "user", "content": "Given an isosceles triangle with a base \\(a\\), a leg \\(b\\), and a vertex angle equal to \\(12^{\\circ}\\). Prove that \\(b < 5a\\)."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I n... |
417 | [{"role": "user", "content": "Prove that for any positive integer \\( n \\), the following inequality holds:\n\\[ \\lg n \\geqslant k \\lg 2 \\]\nwhere \\( k \\) is the number of distinct prime factors of \\( n \\)."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is dif... |
475 | [{"role": "user", "content": "Let $l$, $m$, $n$ be three different lines, and $\\alpha$ be a plane. Among the following statements, the incorrect one is ( )\n\nA: If $l \\perp \\alpha$, then $l$ intersects $\\alpha$\n\nB: If $m \\subset \\alpha$, $n \\subset \\alpha$, $l \\perp m$, $l \\perp n$, then $l \\perp \\alpha$... |
478 | [{"role": "user", "content": "I'm going to a new restaurant that boasts a diverse menu including many healthy options. I am a vegan who needs to avoid gluten and prefers low-sugar dishes. The restaurant menu features six dishes that are vegan, which represent one-fourth of the entire menu. Out of these vegan dishes, fo... |
492 | [{"role": "user", "content": "3 years ago, James turned 27. In a certain number of years, Matt will be twice James' age. Matt is now 65 years old. How many years from now will Matt be twice James' age?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem step by step. First, let's ... |
505 | [{"role": "user", "content": "Given that the diameter of circle $\\odot O$ is $10cm$, point $P$ is outside of circle $\\odot O$. The length of $OP$ could be $\\left(\\ \\ \\right)cm$.\n\nA: $3$\n\nB: $4$\n\nC: $5$\n\nD: $6$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that the diame... |
494 | [{"role": "user", "content": "Calculate: $\\sqrt{12}+|1-\\sqrt{3}|+(\\pi -2023)^{0}$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to calculate the expression: √12 + |1 - √3| + (π - 2023)^0. Hmm, let's break this down step by step. First, I should handle each part separately and then add them... |
493 | [{"role": "user", "content": "Suppose that $a * b$ means $4a - 2b$. What is the value of $x$ if\n\\[3 * (6 * x) = -2\\]\n$\\textbf{(A) }\\frac{17}{2} \\qquad\\textbf{(B) }\\frac{12}{5} \\qquad\\textbf{(C) }\\frac{19}{4} \\qquad\\textbf{(D) }8 \\qquad \\textbf{(E) }-\\frac{1}{2}$"}, {"role": "assistant", "content": "<th... |
500 | [{"role": "user", "content": "Suppose you invest $ 10,410 in equipment to manufacture a new board game . Each game costs $ 2.65 to manufacture and sells for $ 20 . How many games must you make and sell before your buisness breaks even ?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to figure o... |
502 | [{"role": "user", "content": "The seventh term of an arithmetic sequence is $20$. If the difference between two consecutive terms is $2$, what is the product of the first two terms?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about an arithmetic sequence. The seventh term is 20, and ... |
499 | [{"role": "user", "content": "Given $a > b > 0$, which of the following systems of inequalities has no solution?\n\nA: $\\begin{cases} x < a \\\\ x > -b \\end{cases}$\n\nB: $\\begin{cases} x > -a \\\\ x > -b \\end{cases}$\n\nC: $\\begin{cases} x > a \\\\ x < -b \\end{cases}$\n\nD: $\\begin{cases} x > -a \\\\ x < b \\en... |
377 | [{"role": "user", "content": "A rhombus with a side length of 6 cm is inscribed in a right triangle with a $60^{\\circ}$ angle, such that the $60^{\\circ}$ angle is common to both shapes and all vertices of the rhombus lie on the sides of the triangle. Find the sides of the triangle."}, {"role": "assistant", "content":... |
382 | [{"role": "user", "content": "\nKing Arthur wants to order a new knight's shield from the blacksmith according to his sketch. The king used a compass and drew three arcs with a radius of 1 yard, as shown in the figure. What is the area of the shield? Round your answer to two decimal places. Recall that the area of a ci... |
496 | [{"role": "user", "content": "The complex number $\\dfrac{1+3i}{i-1}$ equals to?\n\nA: $1 - 2i$\n\nB: $1 + 2i$\n\nC: $-1 + 2i$\n\nD: $-1 - 2i$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the value of the complex number (1 + 3i)/(i - 1). Hmm, complex numbers in the denominator can be ... |
458 | [{"role": "user", "content": "A right circular cylinder with radius 3 is inscribed in a hemisphere with radius 7 so that its bases are parallel to the base of the hemisphere. What is the height of this cylinder?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficu... |
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