messages listlengths 2 2 |
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[
{
"role": "user",
"content": "Coach Grunt is preparing the 5-person starting lineup for his basketball team, the Grunters. There are 12 players on the team. Two of them, Ace and Zeppo, are league All-Stars, so they'll definitely be in the starting lineup. How many different starting lineups are possible?... |
[
{
"role": "user",
"content": "Mark has $\\frac{3}{4}$ of a dollar and Carolyn has $\\frac{3}{10}$ of a dollar. How many dollars do they have altogether? (Give your answer as a decimal.)"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. Mark has 3/4 of a dollar, and Carolyn has 3/1... |
[
{
"role": "user",
"content": "If $c$ is a constant such that $x^2 + 100x + c$ is the perfect square of a binomial, what is the value of $c$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to find the value of $ c $ such that the quadratic expression $ x^2 + 100x + c $ is a perfe... |
[
{
"role": "user",
"content": "Given the four digits 2, 4, 6, and 7, how many different positive two-digit integers can be formed using these digits if a digit may not be repeated in an integer?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem again. The question is... |
[
{
"role": "user",
"content": "If $(x+2)(x-3)=14$, find the product of the possible values of $x$."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is to find the product of the possible values of x given the equation (x + 2)(x - 3) = 14. Hmm, first step, I need to sol... |
[
{
"role": "user",
"content": "The quadratic $x^2-3x+9=x+41$ has two solutions. What is the positive difference between these solutions?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to figure out how to solve this problem. The original equation is x² - 3x + 9 = x + 41. The qu... |
[
{
"role": "user",
"content": "If X! \\cdot 3! = n!$, The value of $n$ is 6. What is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem says that X! multiplied by 3! equals n!, and we're told that n is 6. We need to find the value of X.\n... |
[
{
"role": "user",
"content": "Let $\\mathbf{v}$ and $\\mathbf{w}$ be vectors such that\n\\[\\operatorname{proj}_{\\mathbf{w}} \\mathbf{v} = \\begin{pmatrix} 1 \\\\ X \\\\ -3 \\end{pmatrix}.\\]Compute $\\operatorname{proj}_{\\mathbf{w}} (-2 \\mathbf{v}).$\nIf we know the answer to the above question is \\beg... |
[
{
"role": "user",
"content": "For the nonzero numbers $a$, $b$, and $c$, define $$\n\\text{{J}}(a,b,c) = \\frac{a}{b} + \\frac{b}{c} + \\frac{c}{a}.\n$$Find $\\text{{J}}(2,12, 9)$."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. I need to find J(2, 12, 9) where J(a,b,c) is defin... |
[
{
"role": "user",
"content": "Rounded to 2 decimal places, what is $\\frac{7}{9}$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is asking me to round 7 divided by 9 to two decimal places. Alright, first, I need to figure out what 7 divided by 9 is exactly. Let me ... |
[
{
"role": "user",
"content": "A prism has 15 edges. How many faces does the prism have?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to figure out how many faces a prism has when it has 15 edges. \n\nFirst, I remember that prisms have two congruent bases connected by rectangle... |
[
{
"role": "user",
"content": "If $\\begin{vmatrix} a & b \\\\ c & d \\end{vmatrix} = 5,$ then find\n\\[\\begin{vmatrix} a - c & b - d \\\\ c & d \\end{vmatrix}.\\]"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem step by step. The original matrix is:\n\n$$\n\\begin... |
[
{
"role": "user",
"content": "Evaluate: $64^2-36^2$"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is to evaluate 64 squared minus 36 squared. Hmm. I remember there's a formula for the difference of squares. Let me recall. Oh right! The difference of squares formula... |
[
{
"role": "user",
"content": "The area of the smallest square that will contain a circle of radius X is what? The answer is 64. What is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem step by step. The question is asking for the va... |
[
{
"role": "user",
"content": "What is the sum of the potential values of $x$ if $(x + 2)(x - 3) = 14$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to figure this out again. So the problem is asking for the sum of the potential values of x in the equation (x + 2)(x - 3) = 14.... |
[
{
"role": "user",
"content": "Seven distinct points are identified on the circumference of a circle. There can be 35 different triangles formed if each vertex must be one of these X points. What is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try t... |
[
{
"role": "user",
"content": "How many ways are there to put 4 distinguishable balls into 2 distinguishable boxes?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so the problem is asking how many ways there are to put 4 distinguishable balls into 2 distinguishable boxes. Let me think abou... |
[
{
"role": "user",
"content": "In base 4, what is the result of dividing $1023_4$ by $11_4$?"
},
{
"role": "assistant",
"content": "<think>\n\n</think>\n\n<think>\nOkay, let's tackle this problem step by step. The question is asking for the result of dividing 1023 base 4 by 11 base 4. \n\nFirst, ... |
[
{
"role": "user",
"content": "Bao received $\\$1,000$ for his birthday and chose to invest it in a bank account that earns $10\\%$ interest, compounded annually. How much interest, in dollars, will Bao have earned after 3 years?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so Bao invest... |
[
{
"role": "user",
"content": "A rectangle with dimensions 6 cm by 8 cm is enclosed within a circle. What is the circumference of the circle, expressed in terms of $\\pi$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem says a rectangle with dimensions 6 cm by 8 cm is... |
[
{
"role": "user",
"content": "How many units long is a segment whose endpoints are (2,3) and (7,15)?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is asking for the length of a segment between the points (2,3) and (7,15). I remember there's a formula for the distan... |
[
{
"role": "user",
"content": "Let $2^x$ be the greatest power of $2$ that is a factor of $144$, and let $3^y$ be the greatest power of $3$ that is a factor of $144$. Evaluate the following expression: $$\\left(\\frac15\\right)^{y - x}$$"
},
{
"role": "assistant",
"content": "<think>\nOkay, let m... |
[
{
"role": "user",
"content": "What was Karen's average speed in miles per hour if she drove continuously from 9:40 a.m. to 1:20 p.m. and covered a distance of 165 miles?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. Karen drove from 9:40 a.m. to 1:20 p.m. and covered 165 miles... |
[
{
"role": "user",
"content": "How many $x$-intercepts does the graph of the parabola $x = -2y^2 + y + 1$ have?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to figure out how many x-intercepts the graph of the parabola $ x = -2y^2 + y + 1 $ has.\n\nFirst, I remember that an x-i... |
[
{
"role": "user",
"content": "Determine the greatest common factor of 84, 112, and 210."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem step by step. The question is asking for the greatest common factor (GCF) of 84, 112, and 210. Hmm, GCF... right, that's the lar... |
[
{
"role": "user",
"content": "Find $0.4 \\cdot X$.\nIf we know the answer to the above question is 0.24, what is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is to find 0.4 multiplied by X, and we're told that the result is 0.24. S... |
[
{
"role": "user",
"content": "Given that the sums of any two of three numbers are 29, 46, and 53, what is the sum of all three numbers?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem says that the sums of any two of three numbers are 29, 46, and 53. I need to find t... |
[
{
"role": "user",
"content": "Let $p$ and $q$ satisfy $pq=9$ and $p+q=6$. What is the value of $p^2 + q^2$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem step by step. The question is asking for the value of $ p^2 + q^2 $ given that $ pq = 9 $ and $ p + q = 6 $.... |
[
{
"role": "user",
"content": "A slant asymptote of the rational expression $y = \\frac{2x^2 + 3x - 7}{x-3}$ is the line approached by the equation as $x$ approaches $\\infty$ or $-\\infty$. If this line is of the form $y = mx + b$, find $m+b$."
},
{
"role": "assistant",
"content": "<think>\nOkay... |
[
{
"role": "user",
"content": "Determine the distance between the points (-2,4) and (3,-8)."
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to find the distance between the two points (-2, 4) and (3, -8). Let me start by recalling the formula for the distance between two points in... |
[
{
"role": "user",
"content": "Find the inverse of the matrix\n\\[\\begin{pmatrix} 6 & -4 \\\\ -3 & X \\end{pmatrix}.\\]If the inverse does not exist, then enter the zero matrix. The answer is 0. What is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's ... |
[
{
"role": "user",
"content": "What is the greatest integer $n$ such that $n^2 - 11n +24 \\leq 0$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem again step by step to make sure I don't miss anything. The question is asking for the greatest integer $ n $ such that... |
[
{
"role": "user",
"content": "Calculate: $(243)^{\\frac35}$"
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to calculate (243) raised to the power of 3/5. Let me think about how to approach this. \n\nFirst, I remember that when dealing with exponents, especially fractions, you ca... |
[
{
"role": "user",
"content": "Let $x$ be a real number, $x > X Compute\n\\[\\sum_{n = 0}^\\infty \\frac{1}{x^{2^n} - x^{-2^n}}.\\]\nIf we know the answer to the above question is \\frac{1}{x-1}, what is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's... |
[
{
"role": "user",
"content": "If a rectangular prism has a length of $l$, a width of $w$, and a height of $h$, then the length of its diagonal is equal to $\\sqrt{l^2 + w^2 + h^2}$. Suppose $l = 3$ and $h = 12$; if the length of the diagonal is $13$, what is the width?"
},
{
"role": "assistant",
... |
[
{
"role": "user",
"content": "What is the second number in the row of Pascal's triangle that has 43 numbers?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to figure this out step by step. So, the problem is asking for the second number in the row of Pascal's triangle that has ... |
[
{
"role": "user",
"content": "Let $C = (3, 5)$ be the midpoint of $AB,$ where $A = (1, 8)$ and $B = (x, y).$ What is the value of $xy$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to solve this problem step by step. The problem says that point C is the midpoint of AB, where A... |
[
{
"role": "user",
"content": "Daniel has exactly $20$ pieces of candy. He has to divide them equally among his $3$ sisters. What is the least number of pieces he should take away so that he could distribute the candy equally?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. Danie... |
[
{
"role": "user",
"content": "Let $f(x)=2x+1$. Find the sum of all $x$ that satisfy the equation $f^{-1}(x)=f(x^{-1})$."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's go through this problem step by step to make sure I understand and solve it correctly.\n\nFirst, the problem is to f... |
[
{
"role": "user",
"content": "How many values of $x$, where $0^\\circ \\le x < 360^\\circ$, satisfy the equation $\\sin x = -0.73$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem step by step. The question is asking how many values of $ x $ between $ 0^\\circ $ a... |
[
{
"role": "user",
"content": "An 18-slice pizza was made with only pepperoni and mushroom toppings, and every slice has at least one topping. Exactly ten slices have pepperoni, and exactly ten slices have mushrooms. How many slices have both pepperoni and mushrooms?"
},
{
"role": "assistant",
"c... |
[
{
"role": "user",
"content": "If $200\\%$ of $x$ is equal to $50\\%$ of $y$, and $x = 16$, what is the value of $y$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to figure out this problem again. So, the question is: If 200% of x is equal to 50% of y, and x is 16, what is the... |
[
{
"role": "user",
"content": "In a kennel with 60 dogs, 9 dogs like watermelon, 48 dogs like salmon, and 5 like both salmon and watermelon. How many dogs in the kennel will not eat either?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. There's a problem about dogs in a kennel.... |
[
{
"role": "user",
"content": "The coin used in the experiment has a higher chance of landing on heads, with a probability of 3/4, compared to landing on tails, with a probability of 1/4. If heads come up, the experiment gains $3, while if tails come up, the experiment loses $8. What is the expected value of... |
[
{
"role": "user",
"content": "What is the modular inverse of $11$, modulo $1000$?\n\nExpress your answer as an integer from $0$ to $999$, inclusive."
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to find the modular inverse of 11 modulo 1000. Let me recall what a modular inverse... |
[
{
"role": "user",
"content": "Determine the product of the largest two one-digit primes and the largest two-digit prime."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem step by step. First, I need to determine the product of the largest two one-digit primes and th... |
[
{
"role": "user",
"content": "How many even perfect square factors does $2^4 \\cdot 7^9$ have?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so the problem is asking how many even perfect square factors the number $2^4 \\cdot 7^9$ has. Let me think through this step by step.\n\nFirst, I ... |
[
{
"role": "user",
"content": "Calculate $6 \\cdot 8\\frac{1}{3}$."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. I need to calculate 6 multiplied by 8 and 1/3. Hmm, mixed numbers can sometimes be tricky, but I remember that converting them to improper fractions helps with multi... |
[
{
"role": "user",
"content": "The U.S. produces about 5.5 million tons of apples each year. Of the total, $20\\%$ is mixed with other products, with $50\\%$ of the remainder used for apple juice and the other $50\\%$ sold fresh. How many million tons of apples are used for apple juice? Express your answer a... |
[
{
"role": "user",
"content": "Given that $O$ and $H$ are the circumcenter and orthocenter of triangle $ABC$ respectively, and $a$, $b$, and $c$ are the side lengths, and $R$ is the circumradius, find $OH^2$ if $R = 7$ and $a^2 + b^2 + c^2 = 29$."
},
{
"role": "assistant",
"content": "<think>\nOk... |
[
{
"role": "user",
"content": "The product of a number $M$ and six less than $M$ is $-5$. What is the sum of all possible values of $M$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to solve this problem step by step. The problem says that the product of a number M and six less... |
[
{
"role": "user",
"content": "What is the absolute value of the difference between the solutions of the equation $x^2 - 5x + 5 = 0$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem step by step. The question is asking for the absolute value of the difference betwe... |
[
{
"role": "user",
"content": "A regular polygon has perimeter 108 cm and each side has length X cm. This polygon has 9 sides. What is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is about finding the length of each side of a regula... |
[
{
"role": "user",
"content": "My three friends and I have dinner together every weekend. Each weekend, two of us cook and the other two clean up afterwards. How many different ways are there for us to choose who cooks and who cleans?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so the p... |
[
{
"role": "user",
"content": "Out of the 60 dogs in the kennel, 9 like watermelon, 48 like salmon, and 5 like both salmon and watermelon. How many dogs in the kennel do not like either watermelon or salmon?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is about dog... |
[
{
"role": "user",
"content": "Calculate $\\sqrt{30p} \\cdot \\sqrt{5p} \\cdot \\sqrt{6p}$ . Express your answer in simplest radical form in terms of $p$."
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to figure out how to solve this problem step by step. The original expression... |
[
{
"role": "user",
"content": "Simplify: $(\\sqrt{5})^4$."
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to simplify the expression $(\\sqrt{5})^4$. Let me start by recalling some basic exponent rules. I remember that when you have a square root, which is the same as raising to t... |
[
{
"role": "user",
"content": "Margaret started a stamp collection. She collected 8 stamps the first day. Each subsequent day she collected 8 more stamps than she had collected the previous day. If she collected stamps for 5 consecutive days, what was the average number of stamps collected per day?"
},
{... |
[
{
"role": "user",
"content": "If the area of an equilateral triangle is $64\\sqrt{3}$ $\\text{cm}^2$, and each side of the triangle is decreased by 4 cm, by how many square centimeters is the area decreased?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem step by ... |
[
{
"role": "user",
"content": "What is the sum of the prime numbers less than 10?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to find the sum of all prime numbers less than 10. Let me start by recalling what a prime number is. A prime number is a number greater than 1 that has... |
[
{
"role": "user",
"content": "Let $x_1,$ $x_2,$ $\\dots,$ $x_n$ be nonnegative real numbers such that $x_1 + x_2 + \\dots + x_n = 1$ and\n\\[x_1^2 + x_2^2 + \\dots + x_n^2 \\le \\frac{1}{100}.\\]Find the smallest possible value of $n.$"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's ... |
[
{
"role": "user",
"content": "Ivan rents a car for $\\$$25 a day and $\\$$0.20 a mile. If he rents it for 4 days and drives it X miles, how many dollars does he pay?\nIf we know the answer to the above question is 180, what is the value of unknown variable X?"
},
{
"role": "assistant",
"content"... |
[
{
"role": "user",
"content": "Among all possible arithmetic sequences formed by four positive integers whose sum is 46, what is the largest possible value for the third term?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is about finding the largest possible third ... |
[
{
"role": "user",
"content": "Convert $427_8$ to base 5."
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to convert the octal number 427 into base 5. Let me start by recalling how to convert numbers between different bases. \n\nFirst, I remember that converting from base 8 to bas... |
[
{
"role": "user",
"content": "Three friends have a total of 6 identical pencils, and each one has at least one pencil. In how many ways can this happen?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem again. So, three friends have a total of 6 identical pencils, a... |
[
{
"role": "user",
"content": "The first three terms of an arithmetic sequence are X, 10 and 19, respectively. The value of the 21st term is 181. What is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. So the problem says that the first three term... |
[
{
"role": "user",
"content": "Let\n\\[f(x) = \\left\\{\n\\begin{array}{cl}\nx + 3 & \\text{if $x < 20$}, \\\\\n2x - X & \\text{if $x \\ge 20$}.\n\\end{array}\n\\right.\\]Find $f^{-1}(7) + f^{-1}(46).$\nIf we know the answer to the above question is 28, what is the value of unknown variable X?"
},
{
... |
[
{
"role": "user",
"content": "Out of the 100 people surveyed, 87 people liked Mozart and 70 people liked Bach. What is the smallest possible number of people who could have said they liked both Mozart and Bach?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is about... |
[
{
"role": "user",
"content": "Find $1-0.\\overline{9}.$"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem step by step. The question is to find $1 - 0.\\overline{9}$. First, I need to make sure I understand what exactly is being asked here. The notation $0.\\overlin... |
[
{
"role": "user",
"content": "What is the total of all the values of $y$ for which the expression $\\frac{y+6}{y^2-5y+4}$ is not defined?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to figure this out again. The problem is asking for the total of all values of $ y $ where th... |
[
{
"role": "user",
"content": "A teacher wants to arrange 3 copies of Introduction to Geometry and 4 copies of Introduction to Number Theory on a bookshelf. In how many ways can he do that?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to figure out how to solve this problem st... |
[
{
"role": "user",
"content": "Rationalize the denominator of $\\frac{1+\\sqrt{3}}{1-\\sqrt{3}}$. When you write your answer in the form $A+B\\sqrt{C}$, where $A$, $B$, and $C$ are integers, what is $ABC$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to solve this problem agai... |
[
{
"role": "user",
"content": "The marble statue of Abraham Lincoln in the Lincoln Memorial has a height of 60 feet. A scale model of the statue has a height of X inches. One inch of the model represents 15 feet of the statue. What is the value of unknown variable X?"
},
{
"role": "assistant",
"c... |
[
{
"role": "user",
"content": "For what positive value of $t$ is $|6+ti| = 10$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to figure this out again. The problem is asking for the positive value of $ t $ such that the modulus of the complex number $ 6 + ti $ equals 10. Alrigh... |
[
{
"role": "user",
"content": "If Andrew's grandfather's age is twelve times Andrew's age and Andrew's grandfather was 55 years old when Andrew was born, what is Andrew's current age?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to figure out Andrew's current age again. The pro... |
[
{
"role": "user",
"content": "How many odd digits are there in the base-4 representation of the number 233 in base-10?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to figure out how many odd digits are in the base-4 representation of the number 233 in base-10. Let me start by ... |
[
{
"role": "user",
"content": "Evaluate the polynomial \\[ x^3 - 2 x^2 - 8 x + X, \\]where $x$ is the positive number such that $x^2 - 2x - 8 = 0$. The answer is 4. What is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is to evaluate... |
[
{
"role": "user",
"content": "Determine the smallest integer greater than the square root of 300."
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to find the smallest integer that's greater than the square root of 300. Let me start by recalling that the square root of a number is... |
[
{
"role": "user",
"content": "Compute: $55\\times1212-15\\times1212$ ."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is to compute 55 times 1212 minus 15 times 1212. Hmm, so I need to figure out how to approach this. Let me start by breaking it down. \n\nFirst, I n... |
[
{
"role": "user",
"content": "Evaluate: $(2^2)^3$."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem step by step. The question is to evaluate (2 squared) cubed. Hmm, so first, I need to make sure I understand the expression correctly. It's (2^2)^3, right? Let me br... |
[
{
"role": "user",
"content": "$24$ lemons are required to make $32$ gallons of lemonade. How many lemons are needed to make $4$ gallons of lemonade?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem says that 24 lemons are needed to make 32 gallons of lemonade. We need... |
[
{
"role": "user",
"content": "For a positive integer $x$ that is less than 100, how many solutions does the congruence $x + 13 \\equiv 55 \\pmod{34}$ have?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem step by step. The question is asking for how many positive i... |
[
{
"role": "user",
"content": "Sarah is trying to fence a rectangular area containing at least 100 sq. ft while using the least amount of material to build the fence. The length of the rectangular area should be 15 ft longer than the width. What should the width, in ft, be?"
},
{
"role": "assistant",... |
[
{
"role": "user",
"content": "The graph of $y = 4x^2 + x - 1$ intersects the line $y = 3$ at two points, labeled as points A and B. The distance between point A and point B can be expressed as $\\frac{\\sqrt{m}}{n}$, where $m$ and $n$ are positive integers that are relatively prime. What is the value of $m ... |
[
{
"role": "user",
"content": "What is the count of positive two-digit integers that, when divided by 8, leave a remainder of 2?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to figure out this problem again. The question is asking for the number of positive two-digit integers ... |
[
{
"role": "user",
"content": "What is the sum of the proper divisors of 256?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to find the sum of the proper divisors of 256. Let me start by recalling what a proper divisor is. A proper divisor is a divisor of a number other than the... |
[
{
"role": "user",
"content": "Determine the value of the expression $5^3 - 3 \\times 5^2 + 3 \\times 5 - 1$."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is to evaluate the expression 5³ - 3×5² + 3×5 - 1. Alright, first, I need to remember the order of operations ... |
[
{
"role": "user",
"content": "What is the sum of the sequence 1, 3, 5, ..., 15, 17?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem again. The question is asking for the sum of the sequence 1, 3, 5, ..., 15, 17. Hmm, first, I need to confirm how many terms there a... |
[
{
"role": "user",
"content": "What is the smallest positive integer that satisfies the conditions of having a remainder of 0 when divided by 2, a remainder of 1 when divided by 3, and a remainder of 2 when divided by 4?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to figure t... |
[
{
"role": "user",
"content": "Determine the value of $\\dfrac{3 \\times 4}{6}$."
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to figure out this problem again. The question is to determine the value of (3 × 4) divided by 6. Hmm, so first, I need to remember the order of operat... |
[
{
"role": "user",
"content": "In a class of 30 students, all students take math and history. Seven students received an A in history, and 13 received an A in math, with four of them receiving an A in both courses. How many students did not receive an A in either math or history?"
},
{
"role": "assis... |
[
{
"role": "user",
"content": "Evaluate $\\left\\lceil\\sqrt{140}\\right\\rceil$."
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to evaluate the ceiling of the square root of 140. Let me start by recalling what the ceiling function does. The ceiling of a number is the smallest in... |
[
{
"role": "user",
"content": "Determine the smallest positive integer that is divisible by three different prime numbers."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to figure out the smallest positive integer divisible by three different prime numbers. \n\nFirst, I remember ... |
[
{
"role": "user",
"content": "Determine the length, in units, of the hypotenuse of a right triangle with leg lengths of 75 and 100 units."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is to find the hypotenuse of a right triangle with legs 75 and 100 units. Alright... |
[
{
"role": "user",
"content": "How many distinct $x$-intercepts does the graph of $y = (x-5)(x^2+5x+6)$ have?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is asking how many distinct x-intercepts the graph of y = (x - 5)(x² + 5x + 6) has. \n\nFirst, I remember that... |
[
{
"role": "user",
"content": "Kim earned scores of 87, 83 and 88 on her first three mathematics examinations. If Kim receives a score of X on the fourth exam, Her average will increase by 1. What is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so Kim has... |
[
{
"role": "user",
"content": "The value of $\\log_{10}{579}$ is between the consecutive integers $a$ and $b$. Find $a+b$."
},
{
"role": "assistant",
"content": "<think>\nOkay, so the problem is asking for the value of log base 10 of 579, and it says that this value lies between two consecutive ... |
[
{
"role": "user",
"content": "One and one-half of what number is 30?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to figure out this problem again. The question is: \"One and one-half of what number is 30?\" So, first, I need to understand what \"one and one-half\" means here.... |
[
{
"role": "user",
"content": "What is the value of $\\dbinom{15}{3}$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to find the value of the combination $\\dbinom{15}{3}$. Let me start by recalling what combinations are. Combinations are used when the order doesn't matter, just... |
[
{
"role": "user",
"content": "What is the base X representation of $84_{10}$?\nIf we know the answer to the above question is 1010100_2, what is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem step by step. The question is asking f... |
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