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[
{
"content": "Classify if the following are hollywood or bollywood movies: Zanjeer; The Shawshank redemption; Sholay; Pride & prejudice",
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"content": "Zanjeer and Sholay are bollywood moves. The Shawshank redemption and Pride & Prejudice are hollywood movies.",
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"content": "A function $g$ is defined by $g(z) = (3 - 2i) z^2 + \\beta z + \\delta$ for all complex numbers $z$, where $\\beta$ and $\\delta$ are complex numbers and $i^2 = -1$. Suppose that $g(1)$ and $g(-i)$ are both real. What is the smallest possible value of $|\\beta| + |\\delta|$?",
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"content": "Points $P$, $Q$, and $R$ lie on the surface of a sphere with center $O$ and radius $25$. It is given that $PQ=15$, $QR=20$, $RP=25$, and that the distance from $O$ to $\\triangle PQR$ is $\\frac{x\\sqrt{y}}{z}$, where $x$, $y$, and $z$ are positive integers, $x$ and $z$ are relatively prime, and $... |
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{
"content": "Why is Brazilian jiu jitsu an excellent martial art?",
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"content": "Brazilian jiu jitsu (BJJ) is an excellent martial art for a number of reasons. BJJ is, first and foremost, a generally safe martial art. BJJ does not emphasize or focus on striking techniques like ... |
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{
"content": "Given the function $f(x)=\\cos (2x+\\varphi)$, where $(-\\pi\\leqslant \\varphi < \\pi)$, its graph is shifted to the right by $\\frac{\\pi}{2}$ units and overlaps with the graph of the function $y=\\sin x\\cos x + \\frac{\\sqrt{3}}{2}\\cos x$. What could be the value(s) of $|\\varphi|$?\n\nA: $\\... |
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{
"content": "A certain stock yields 8%. The market value of the stock is $150. What is the percentage of the stock's original value?",
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"content": "To determine the percentage of the stock's original value, we need to know the original value of the stock. Without this information... |
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"content": "In a class of 94 students, 41 are taking French, 22 are taking German. Of the students taking French or German, some are taking both courses. There are 40 students not enrolled in either course. How many students are taking both French and German?",
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"content": "Let'... |
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{
"content": "What sport did Troy Stradford play in college?",
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"content": "Troy Stradford played football at Boston College in the 1980s and went on to play professionally for the Miami Dolphins in the NFL.",
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[
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"content": "There are 11 square formations, each consisting of the same number of soldiers. If 1 general is added, a larger square formation can be formed. What is the minimum number of soldiers in one of the original square formations?",
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"content": "\n1. **Define the variables... |
[
{
"content": "Suggest some brass instruments I can learn if I want to play in an orchestra?",
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"content": "French Horn, Trombone, Trumpet and Tuba are common brass instruments in orchestras.",
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] |
[
{
"content": "Sony and Johnny caught 40 fishes. Sony caught some times as many as Johnny. Johnny caught 8 fishes. How many times more fishes did Sony catch than Johnny?",
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"content": "If Johnny caught 8 fishes and Sony caught some times as many as Johnny, we can find out how many ... |
[
{
"content": "In the plane, the triangles $ABD$ and $BCE$ are outside the triangle $ABC$ and are also isosceles triangles right at $D$ and $C$ respectively. The point $H$ is the intersection of $CD$ and $AE$ . Show that $BH$ and $AE$ are perpendicular.",
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"conte... |
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{
"content": "What are a couple date night ideas?",
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"content": "Date nights are a great way to connect with your significant other. You could go to dinner and a movie. This option may sound cliché but try to be creative by choosing a restaurant you haven't been to and see a mov... |
[
{
"content": "What are the four primary states of matter? Answer in bullet point list, and capitalize each words",
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"content": "- Solid\n- Liquid\n- Gas\n- Plasma",
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] |
[
{
"content": "Name five NFL teams in the NFC.",
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"content": "Five NFL teams in the NFC are the Carolina Panthers, New Orleans Saints, Philadelphia Eagles, New York Giants, and Detroit Lions.",
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"content": "In the Cartesian coordinate system, if the line $ax-y+1=0$ passes through the focus of the parabola $y^2=4x$, then the real number $a=$ ____.",
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"content": "Firstly, the focus of the parabola $y^2=4x$ has the coordinates $(1,0)$, following the standard form of the pa... |
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"content": "The opposite of $2023$ is\n\nA: $-\\frac{1}{{2023}}$\n\nB: $\\frac{1}{{2023}}$\n\nC: $-2023$\n\nD: $2023$",
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"content": "To find the opposite of a number, we simply change its sign. If the number is positive, its opposite is negative, and vice versa. For the number $... |
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{
"content": "In town A, there are \\( n \\) girls and \\( n \\) boys, and each girl knows each boy. In town B, there are \\( n \\) girls \\( g_{1}, g_{2}, \\ldots, g_{n} \\) and \\( 2n-1 \\) boys \\( b_{1}, b_{2}, \\ldots, b_{2n-1} \\). The girl \\( g_{i}, i=1,2, \\ldots, n \\), knows the boys \\( b_{1}, b_{2}... |
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{
"content": "There are many CDs in the store. The rock and roll CDs are $5 each, the pop CDs are $10 each, the dance CDs are a certain price each, and the country CDs are $7 each. Julia wants to buy 4 of each, but she only has 75 dollars and is short by $25. How much does each dance CD cost?",
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"content": "Which TV show features a team of teenagers that power up with powers given to them by Zordon to save the world from monsters?",
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{
"content": "The Mighty Morphin Power Rangers.",
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] |
[
{
"content": "In the series A Song of Ice and Fire, who is the founder of House Clegane?",
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"content": "The name of House Clegane's founder is unknown. He was a kennelmaster of Casterly Rock and saved Lord Tytos Lannister from a lionness. As a reward, Lord Lannister granted the un... |
[
{
"content": "in the rectangular coordinate system , points ( 4 , 0 ) and ( – 4 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c",
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},
{
"content": "The points (4, 0) and (-4, 0) are both on the x-axis and are 8 units apart. Since they both lie on circ... |
[
{
"content": "The area of the smallest square that will contain a circle of radius 4 is what?",
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"content": "The smallest square has side 8 and area $8^2=\\boxed{64}$. [asy]\ndraw(Circle((12,12), 12));\ndraw((0,0)--(0,24)--(24,24)--(24,0)--cycle);\ndraw((0,12)--(24,12));\ndot((12,... |
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{
"content": "The number $N$ is between $7$ and $15$. The average of $4$, $8$, and $N$ could be\n$\\text{(A)}\\ 6 \\qquad \\text{(B)}\\ 7 \\qquad \\text{(C)}\\ 9 \\qquad \\text{(D)}\\ 11 \\qquad \\text{(E)}\\ 13$\n$\\text{(A)}\\ 6 \\qquad \\text{(B)}\\ 7 \\qquad \\text{(C)}\\ 9 \\qquad \\text{(D)}\\ 11 \\qquad ... |
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{
"content": "How do you plan a trip?",
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"content": "There are many different ways to plan a trip. In addition, there are many different factors to include in order to plan a trip. First of all, it is important to know the type of travel. Is this a business trip? Is this family tr... |
[
{
"content": "For any real numbers $x$ and $y$, find the minimum value of $|x-1|+|x|+|y-1|+|y+1|$.",
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"content": "To find the minimum value of the given expression, we will consider the properties of absolute values and the triangle inequality.\n\nWe have\n\\[\n|x-1|+|x|+|y-1|+|y+... |
[
{
"content": "The base six number $125_{6}$ is equal to the base $b$ number $221_{b}$. What is the positive value of $b$?",
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{
"content": "First, convert the base six number $125_6$ to base ten:\n$$ 125_{6} = 1 \\cdot 6^2 + 2 \\cdot 6^1 + 5 \\cdot 6^0 = 1 \\cdot 36 + 2 \\cdot 6 + 5 ... |
[
{
"content": "Tell me whether these numbers are odd or even",
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{
"content": "10, 2, 7, 17, 777, 1284, 28, 57, 298, 102",
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"content": "What is the smallest positive four-digit integer equivalent to 6 mod 7?",
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"content": "An integer that is equivalent to 6 mod 7 can be written in the form $7k+6$.\n\n$1000$ is the smallest four-digit integer, so we want to solve the inequality $7k+6 \\ge 1000$. This ... |
[
{
"content": "Two circles touch each other externally. Find the length of their common external tangent (between the points of tangency), given that the radii are 16 and 25.",
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"content": ": \n1. Let's name the centers of the given circles $O$ and $O_2$, having radii 16 and 25, re... |
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{
"content": "Given the function $f(x)=x^{2}+\\\\ln x$, if the equation of the tangent line to the curve $y=f(x)$ at the point $(1,f(1))$ is $y=ax+b$, then $a+b=$ _____ .",
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"content": "Since $f(x)=x^{2}+\\\\ln x$,\n\nThen $f(1)=1^{2}+\\\\ln 1=1$, so the point of tangency is $(1,1... |
[
{
"content": "What are good native plants for a garden in Ohio?",
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"content": "Native plants that will grow well in Ohio include Purple Coneflower, Thin Leaf Mountain Mint, Sawtooth Sunflower, and Little Bluestem Grass. There's quite a few plants that grow well in Ohio and are nat... |
[
{
"content": "What is the Fallout game?\n\nContext: Fallout: A Post Nuclear Role Playing Game is a 1997 role-playing video game developed and published by Interplay Productions. In a mid-22nd century post-apocalyptic and retro-futuristic world, decades after a global nuclear war between the United States and Ch... |
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{
"content": "Let $F(0) = 0,$ $F(1) = \\frac{3}{2},$ and\n\\[F(n) = \\frac{5}{2} F(n - 1) - F(n - 2)\\]for $n \\ge 2.$ Find\n\\[\\sum_{n = 0}^\\infty \\frac{1}{F(2^n)}.\\]",
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"content": "We claim that $F(n) = 2^n - \\frac{1}{2^n}$ for all nonnegative integers $n.$ We prove this ... |
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{
"content": "Each subsequent number is chosen independently of the previous ones. If it matches one of the already chosen numbers, you should move clockwise to the first unchosen number.\n\nIn the end, $k$ different numbers are obtained.\n\na) Is it true that the appearance of each specific number in such a se... |
[
{
"content": "What is the greatest product obtainable from two integers whose sum is 2024?",
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"content": "Let the two integers be $x$ and $2024-x$. The product we want to maximize is $2024x - x^2$. To find the maximum, we can complete the square:\n\n1. Rewrite the expression: $202... |
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{
"content": "Let $A = (-4, 0),$ $B = (-3, 2),$ $C = (3, 2),$ and $D = (4, 0).$ Suppose that point $P$ satisfies \\[PA + PD = 10,\\] and \\[PB + PC = 8.\\] Find the $y-$coordinate of $P$, which can be expressed in the form $\\frac{-a + b \\sqrt{c}}{d},$ where $a, b, c, d$ are positive integers. Find $a + b + c ... |
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{
"content": "Solve the system of differential equations\n\n$$\n\\left\\{\\begin{array}{l}\nx^{\\prime}=2 x-4 y \\\\\ny^{\\prime}=x-3 y\n\\end{array}\\right.\n$$",
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"content": "\nTo solve the system of differential equations\n\n\\[ \n\\left\\{\n\\begin{array}{l}\nx' = 2x - 4y \\\\... |
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{
"content": "In a modified walking game, I stand still on move 1, and for each subsequent move $n$ where $2 \\le n \\le 30$, I take two steps forward if $n$ is prime and three steps backward if $n$ is composite. After completing move 30, I walk directly back to my original starting point. How many steps long i... |
[
{
"content": "Each square in the grid shown is 1 cm by 1 cm. What is the area of the shaded figure, in cm²?",
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"content": "\n1. **Determine the total area of the grid:**\n\n The grid is composed of squares measuring \\(1 \\, \\text{cm} \\times 1 \\, \\text{cm}\\). There are \\(3... |
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{
"content": "Construct a parallelogram given its perimeter, one diagonal, and the angle between the given diagonal and one side of the parallelogram.",
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"content": "\n1. **Given Data and Definitions:**\n - Let \\( P \\) be the perimeter of the parallelogram.\n - Let \\( d \\)... |
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{
"content": "Add $4_6 + 14_6.$ Express your answer in base $6.$",
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"content": "When adding the numbers, we notice that $4+4$ leaves a residue of $2$ when divided by $6.$ Thus, the sum will have a rightmost digit of $2,$ and we must carry-over. This yields that $$\\begin{array}{c@... |
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{
"content": "Five rays $\\overrightarrow{OA}$ , $\\overrightarrow{OB}$ , $\\overrightarrow{OC}$ , $\\overrightarrow{OD}$ , and $\\overrightarrow{OE}$ radiate in a clockwise order from $O$ forming four non-overlapping angles such that $\\angle EOD = 2\\angle COB$ , $\\angle COB = 2\\angle BOA$ , while... |
[
{
"content": "A truncated cone has horizontal bases with radii 24 and 5. A sphere is tangent to the top, bottom, and lateral surface of the truncated cone. What is the radius of the sphere?",
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{
"content": "Let's denote the radii of the bottom and top bases of the truncated cone as ... |
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{
"content": "Evaluate $\\log_464$.",
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{
"content": "We have $4^3=64$, so $\\log_4 64 = \\boxed{3}$.",
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] |
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"content": "Consider a problem where hexagonal tiles are arranged such that each subsequent hexagon has an additional band of dots, with each side of a layer containing one more dot than its previous layer. The first hexagon in the sequence has 2 dots, and the pattern extends outwards uniformly. How many dots... |
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{
"content": "\nConsider an arithmetic sequence $\\left\\{a_{n}\\right\\}$ with the sum of the first $n$ terms denoted as $S_{n}$. Given that $S_{2}=10$ and $S_{5}=55$, the coordinates of a direction vector for the line passing through the points $P\\left(n, a_{n}\\right)$ and $Q\\left(n+2, a_{n+2}\\right)$ cou... |
[
{
"content": "What is the least common multiple of 18 and 30?",
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{
"content": "Firstly, we factorize each number:\n- \\(18 = 2 \\cdot 3^2\\)\n- \\(30 = 2 \\cdot 3 \\cdot 5\\)\n\nTo find the LCM, we take the highest power of all prime factors present:\n- The highest power of 2 presen... |
[
{
"content": "A number 12 is multiplied by 3 and then by a certain number. The result is subtracted from 7899665 to get 7899593. What is the number that the product is multiplied by after the first multiplication?",
"role": "user"
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{
"content": "Let's call the certain number by which the product i... |
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{
"content": "Given a function $f(x)$, if there exists a real number $x$ in its domain such that $f(-x) = -f(x)$, then $f(x)$ is called a \"restricted odd function\".\n(1) Determine whether $f(x) = x^2 + 2x - 4$ is a \"restricted odd function\" and explain why.\n(2) If $f(x) = 2^x + m$ is a \"restricted odd fun... |
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{
"content": "Let $S$ be the set of all rational numbers $r$, $0<r<1$, that have a repeating decimal expansion in the form $0.abcabcabc\\ldots=0.\\overline{abc}$, where the digits $a$, $b$, and $c$ are not necessarily distinct. To write the elements of $S$ as fractions in lowest terms, how many different numera... |
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{
"content": "Let $A_1A_2,B_1B_2, C_1C_2$ be three equal segments on the three sides of an equilateral triangle. Prove that in the triangle formed by the lines $B_2C_1, C_2A_1,A_2B_1$ , the segments $B_2C_1, C_2A_1,A_2B_1$ are proportional to the sides in which they are contained.",
"role": "user"
},... |
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"content": "Triangle $ABC$ has $BC=20.$ The incircle of the triangle evenly trisects the median $AD.$ If the area of the triangle is $m \\sqrt{n}$ where $m$ and $n$ are integers and $n$ is not divisible by the square of a prime, find $m+n.$\n",
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"content": "[asy] size(300); poin... |
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{
"content": "The length of 3 ropes are in a certain ratio. The sum of the weights of the longest and the shortest rope is 100 meters more than the length of the third rope. The length of the shortest rope is 80 meters. What is the ratio of the lengths of the ropes?",
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{
"content": ... |
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{
"content": "Given the following expressions: \n$$1 > \\frac{1}{2}$$ \n$$1+ \\frac{1}{2}+ \\frac{1}{3} > 1$$ \n$$1+ \\frac{1}{2}+ \\frac{1}{3}+ \\frac{1}{4}+ \\frac{1}{5}+ \\frac{1}{6}+ \\frac{1}{7} > \\frac{3}{2}$$ \n$$1+ \\frac{1}{2}+ \\frac{1}{3}+…+ \\frac{1}{15} > 2$$ \n... \nConjecture the expressio... |
[
{
"content": "A box with a volume of 24 $\\text{cm}^3$ can hold 75 paperclips. How many paperclips could a box with a volume of 60 $\\text{cm}^3$ hold, assuming the number of paperclips scales directly with the volume?",
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{
"content": "1. Let $x$ be the number of paperclips that the... |
[
{
"content": "What is the sum of the number of faces, edges and vertices of a triangular prism?\n\n[asy]\ndraw((0,0)--(10,0)--(5,8.7)--cycle);\ndraw((0,0)--(20,20),dashed);\ndraw((10,0)--(30,20));\ndraw((5,8.7)--(25,28.7));\ndraw((25,28.7)--(30,20)--(20,20)--cycle,dashed);\ndraw((25,28.7)--(30,20));\n[/asy]",
... |
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{
"content": "Corn costs 99 cents per pound, and beans cost 45 cents per pound. If Shea buys 24 total pounds of corn and beans, and it costs $\\$18.09$, how many pounds of corn did Shea buy? Express your answer as a decimal to the nearest tenth.",
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{
"content": "Let $c$ and $b$ be t... |
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{
"content": "Let $ABC$ be a triangle in which $\\angle BAC = 60^{\\circ}$ . Let $P$ (similarly $Q$ ) be the point of intersection of the bisector of $\\angle ABC$ (similarly of $\\angle ACB$ ) and the side $AC$ (similarly $AB$ ). Let $r_1$ and $r_2$ be the in-radii of the triangles $ABC$ and ... |
[
{
"content": "What are the characteristics of chihuahuas?",
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},
{
"content": "Chihuahuas are among the smallest of the dog breeds. Small in size but confident and big-dog natured. They originated from Mexico with lineage going back to ancient kingdoms of pre-Columbian times. Chihuahuas... |
[
{
"content": "Based on the paragraph below, how much did Beyonce earn in 2013 - 2014\n\nContext: MTV estimated that by the end of 2014, Beyoncé would become the highest-paid Black musician in history; this became the case in April 2014. In June 2014, Beyoncé ranked at number one on the Forbes Celebrity 100 list... |
[
{
"content": "What is functional genomics?",
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},
{
"content": "Functional genomics is a field of molecular biology that attempts to describe gene (and protein) functions and interactions. Functional genomics make use of the vast data generated by genomic and transcriptomic projects (su... |
[
{
"content": "Rationalize the denominator of $\\frac{7}{2\\sqrt{50}}$.",
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},
{
"content": "Start by simplifying the denominator:\n$$\n\\frac{7}{2\\sqrt{50}} = \\frac{7}{2 \\times 5\\sqrt{2}} = \\frac{7}{10\\sqrt{2}}\n$$\nNow, rationalize the denominator by multiplying the numerator and... |
[
{
"content": "Let $a$ and $b$ be positive integers such that $(2a+b)(2b+a)=4752$ . Find the value of $ab$ .\n\n*Proposed by James Lin*",
"role": "user"
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{
"content": "1. **Expand the given equation:**\n \\[\n (2a + b)(2b + a) = 4752\n \\]\n Expanding the left-hand side, we get:\n \... |
[
{
"content": "In what part of the world could you find wild bonobos?\n\nContext: The bonobo, also historically called the pygmy chimpanzee and less often the dwarf chimpanzee or gracile chimpanzee, is an endangered great ape and one of the two species making up the genus Pan, the other being the common chimpanz... |
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{
"content": "The equation of the tangent line to the circle \\\\(x^{2}+y^{2}-4x+2y=0\\\\) at the point \\\\(P(1,1)\\\\) is: __________.",
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"content": "The center of the circle \\\\(x^{2}+y^{2}-4x+2y=0\\\\) is \\\\((2,-1)\\\\). The slope of the line passing through \\\\((1,1)\\\\)... |
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{
"content": "Inside the triangle $ABC$, a point $P$ is chosen such that $\\angle BPC = \\angle A + 60^\\circ$, $\\angle APC = \\angle B + 60^\\circ$, and $\\angle APB = \\angle C + 60^\\circ$. The lines $AP$, $BP$, and $CP$ intersect the circumcircle of triangle $ABC$ at points $A'$, $B'$, and $C'$ respectivel... |
[
{
"content": "Simplify $5\\cdot\\frac{13}{3}\\cdot \\frac{21}{-65}$.",
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{
"content": "Note that 65 and 13 have a common factor of 13. Also, 3 and 21 have a common factor of 3. Since there is one negative sign among all the factors, our result will be negative. We get:\n\\[\n5\\cdot\... |
[
{
"content": "Kelvin the Frog is hopping on a number line that extends infinitely in both directions. Kelvin starts at 0. Every minute, he has a $\\frac{1}{3}$ chance of moving 1 unit left, a $\\frac{1}{3}$ chance of moving 1 unit right, and a $\\frac{1}{3}$ chance of getting eaten. Find the expected number of ... |
[
{
"content": "Why do people foster dogs?",
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"content": "Fostering animals of any kind can be a great way to reduce the stress and suffering of an animal that has not adjusted to life in a shelter. Fostering can also reduce the number of animals that a shelter is forced to put down... |
[
{
"content": "Where was buddha born?\n\nContext: Lumbinī (Nepali: लुम्बिनी pronounced [ˈlumbini] (listen), \"the lovely\") is a Buddhist pilgrimage site in the Rupandehi District of Lumbini Province in Nepal. It is the place where, according to Buddhist tradition, Queen Mahamayadevi gave birth to Siddhartha Gau... |
[
{
"content": "Given this paragraph about National Beer Day in the United States, which president signed National Beer Day into law?\n\nContext: National Beer Day is celebrated in the United States every year on April 7, marking the day that the Cullen–Harrison Act came into force after having been signed into l... |
[
{
"content": "How much has the population of Puerto Rico been growing?\n\nContext: The population of Puerto Rico according to the 2020 census was 3,285,874, an 11.8% decrease since the 2010 United States Census. The commonwealth's population peaked in 2000, when it was 3,808,610, before declining (for the first... |
[
{
"content": "Find the value of $c$ such that $x+5$ is a factor of $cx^3 + 17x^2 - 4cx + 45$.",
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{
"content": "Let $f(x) = cx^3 + 17x^2 - 4cx + 45$. According to the Factor Theorem, if $x+5$ is a factor of $f(x)$, then $f(-5) = 0$.\nHence, substituting $x = -5$ into $f(x)$:\n\\[ f(-... |
[
{
"content": "Name some famous 1990 music",
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},
{
"content": "Oasis - Wonderwall, The Offspring - Self Esteem, Nirvana - Smells Like Teen Spirit, Daft Punk - Around the World.",
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] |
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{
"content": "From the integers \\\\(1, 2, 3, \\ldots, 9\\\\), any three different numbers are taken as the coefficients of the quadratic function \\\\(f(x) = ax^2 + bx + c\\\\). The total number of functions \\\\(f(x)\\\\) that satisfy \\\\(\\dfrac{f(1)}{2} \\in \\mathbf{Z}\\\\) is\nA: \\\\(44\\\\)\nB: \\\\(20... |
[
{
"content": "Seven of the nine numbers 1871, 1997, 2020, 2028, 2113, 2125, 2140, 2222, and 2300 have a mean (average) of 2100. What is the mean (average) of the other two numbers?",
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{
"content": "1. Calculate the sum of the nine numbers: $1871 + 1997 + 2020 + 2028 + 2113 + 2125 + ... |
[
{
"content": "Calculate $\\frac{1}{4} \\cdot \\frac{2}{5} \\cdot \\frac{3}{6} \\cdot \\frac{4}{7} \\cdots \\frac{52}{55} \\cdot \\frac{53}{56} \\cdot \\frac{54}{57} \\cdot \\frac{55}{58}$. Express your answer as a common fraction.",
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{
"content": "- **Observation**: From $\\frac{4}{... |
[
{
"content": "What rock icon was the founder of The Society for the Prevention of Cruelty to Long-haired Men?",
"role": "user"
},
{
"content": "David Bowie.",
"role": "assistant"
}
] |
[
{
"content": "Given events $A$ and $B$ with $P(A) = 0.3$ and $P(B) = 0.6$, then ()\n\nA: If $A \\subseteq B$, then $P(AB) = 0.18$\n\nB: If $A$ and $B$ are mutually exclusive, then $P(A+B) = 0.9$\n\nC: If $P(A|B) = 0.1$, then $A$ and $B$ are independent\n\nD: If $A$ and $B$ are independent, then $P(A\\overline{B... |
[
{
"content": "The numbers 1 through 30 are written on 30 cards with one number on each card. Tom picks one of the 30 cards at random. What is the probability that the number on his card will be a multiple of 3 or 4?",
"role": "user"
},
{
"content": "1. Count multiples of 3 in the range from 1 to 30:... |
[
{
"content": "What is the value of the expression $(25 + 8)^2 - (8^2 +25^2)$?",
"role": "user"
},
{
"content": "To solve the given expression $(25 + 8)^2 - (8^2 +25^2)$, we follow these steps:\n\n1. First, we expand the square of the sum $(25 + 8)^2$:\n\\[ (25 + 8)^2 = 25^2 + 2\\cdot25\\cdot8 + 8^2 ... |
[
{
"content": "Two trains of equal lengths take 9 sec and 15 sec respectively to cross a telegraph post. The length of each train is 120 m. In what time will they cross each other travelling in opposite direction?",
"role": "user"
},
{
"content": "First, let's find the speed of each train.\n\nSpeed i... |
[
{
"content": "classify these as kitchen or bathroom items: toothpaste, pan, pots, spoons, shampoo, dish soap, bath soap, bath bombs, plates, oven mitts, cups, toilet paper",
"role": "user"
},
{
"content": "Kitchen items: pan, pots, spoons, dish soap, plates, oven mitts, cups\nBathroom items: toothpa... |
[
{
"content": "Chuck the llama is tied to the corner of a $2\\text{ m}$ by $3\\text{ m}$ shed on a $3\\text{ m}$ leash. How much area (in square meters) does Chuck have in which to play if he can go only around the outside of the shed? [asy]\ndraw((0,0)--(15,0)--(15,10)--(0,10)--cycle,black+linewidth(1));\ndraw(... |
[
{
"content": "Triangle $PQR$ has side lengths $PQ=150, QR=270$, and $PR=210$. Lines $m_P, m_Q$, and $m_R$ are drawn parallel to $\\overline{QR}, \\overline{PR}$, and $\\overline{PQ}$, respectively, such that the intersections of $m_P, m_Q$, and $m_R$ with the interior of $\\triangle PQR$ are segments of lengths... |
[
{
"content": "Find the smallest positive integer $b$ such that $x^4 + x^3 + b^2 + 5$ is not prime for any integer $x.$",
"role": "user"
},
{
"content": "To solve for $b$, we first need to test if $x^4 + x^3 + b^2 + 5$ can be prime by checking for smaller values of $b$ and decomposing the polynomial ... |
[
{
"content": "List all the school districts in the following paragraph in a bullet list.\n\nContext: The City of Drew is served by the Sunflower County Consolidated School District. Elementary school students attend A. W. James Elementary School in Drew and middle school students attend Drew Hunter Middle Schoo... |
[
{
"content": "Given that $x+\\cos y=1004$ and $x+1004 \\sin y=1003$, where $0 \\leq y \\leq \\frac{\\pi}{2}$, find the value of $x+y$.",
"role": "user"
},
{
"content": "Starting from the given equations:\n1. $x+\\cos y=1004$\n2. $x+1004 \\sin y=1003$\n\nSubtract equation 1 from equation 2:\n\\[\nx +... |
[
{
"content": "The sides of a triangle have lengths of $24$, $24$, and $24\\sqrt{2}$. Find the length of the shortest altitude.",
"role": "user"
},
{
"content": "First, we identify that this triangle is a right triangle since $24^2 + 24^2 = (24\\sqrt{2})^2$. This conforms to the Pythagorean theorem (... |
[
{
"content": "James is observing a large tree with 100 branches, with each branch having 150 twigs. During spring, 20% of the twigs sprout 3 leaves, 30% of the twigs sprout 4 leaves, and the remaining percentage sprout 5 leaves. However, as summer progresses, the number of leaves per twig increases by 2 for eac... |
[
{
"content": "How many cubic feet are in the volume of a round swimming pool which is 16 feet in diameter and 4 feet deep throughout? Express your answer in terms of $\\pi$.",
"role": "user"
},
{
"content": "The radius of this pool is $16/2=8$ feet; the volume of this pool is thus $\\pi(8^2)(4)=\\bo... |
[
{
"content": "What is the experience of Microsoft Office users moving to Google Docs?",
"role": "user"
},
{
"content": "Microsoft Office has been an enterprise software of choice for over 2 decades. Long term users have seen Office evolve from its early days when it was installed on Windows machine... |
[
{
"content": "What is the distance, in units, between the points $(-3, -4)$ and $(4, -5)$? Express your answer in simplest radical form.",
"role": "user"
},
{
"content": "We use the distance formula: \\begin{align*}\n\\sqrt{(4 - (-3))^2 + ((-5) - (-4))^2} &= \\sqrt{7^2 + (-1)^2} \\\\\n&= \\sqrt{49 ... |
[
{
"content": "Let $T$ be the set of integers between $1$ and $2^{30}$ whose binary expansions have exactly two $1$s. If a number is chosen at random from $T$, the probability that it is divisible by 15 is $p/q$, where $p$ and $q$ are relatively prime positive integers. Find $p+q.$",
"role": "user"
},
{
... |
[
{
"content": "What is a PFD?\n\nContext: Process engineering involves the utilization of multiple tools and methods. Depending on the exact nature of the system, processes need to be simulated and modeled using mathematics and computer science. Processes where phase change and phase equilibria are relevant requ... |
[
{
"content": "What is the area enclosed by the graph of $|x| + |2y|$ = 10 shown here?\n\n[asy]\ndraw((0,-10)--(0,10),Arrows);\ndraw((-15,0)--(15,0),Arrows);\nlabel(\"$y$\",(0,10),NE);\nlabel(\"$x$\",(15,0),SE);\ndraw((10,0)--(0,5)--(-10,0)--(0,-5)--cycle);\n[/asy]",
"role": "user"
},
{
"content": "T... |
[
{
"content": "Let $f(z) = a_3z^3 + a_2z^2 + a_1z + a_0$ and $g(z) = b_2z^2 + b_1z + b_0$, with $a_3 \\neq 0$ and $b_2 \\neq 0$. What is the degree of the polynomial $f(z) + g(z)$?",
"role": "user"
},
{
"content": "Given:\n$$f(z) = a_3z^3 + a_2z^2 + a_1z + a_0$$ \n$$g(z) = b_2z^2 + b_1z + b_0$$\n\nTh... |
[
{
"content": "Given a reference text about Joseph Charlton, what college football team did he play for?\n\nContext: Joseph Charlton (born April 7, 1997) is an American football punter who is a free agent. He played college football at South Carolina.\n\nCollege career\nCharlton was a member of the South Carolin... |
[
{
"content": "Given a circle with center $C$ that passes through points $A(-1, 1)$ and $B(-2, -2)$, and the center $C$ lies on the line $L: x+y-1=0$, find the standard equation of the circle with center $C$.",
"role": "user"
},
{
"content": "Let the standard equation of the circle be $(x-a)^2 + (y-b... |
End of preview. Expand in Data Studio
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