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[
{
"content": "Tony loved to solve difficult pen and paper puzzles. He did a warm-up puzzle that only took 10 minutes and after that he did 2 puzzles that each took 3 times as long. How long did he spend solving puzzles?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\... |
[
{
"content": "If Amelia does one load at a time, how many minutes will it take her to wash and dry all three loads, considering that the load of whites takes 72 minutes in the washing machine and 50 minutes in the dryer, the load of darks takes 58 minutes in the washing machine and 65 minutes in the dryer, and ... |
[
{
"content": "If $6543_{10}$ is converted to base 8, then each digit of the result is squared, and finally, the squared digits are summed, what is the final result?",
"role": "user"
},
{
"content": "Let's first convert $6543_{10}$ to base 8 using Python's standard library.\n```python\nimport math\n\... |
[
{
"content": "The sum of three numbers is $66$. The first number is $3$ times the third number, and the second number is $24$. What is the third number?",
"role": "user"
},
{
"content": "Let's call the three numbers $a$, $b$, and $c$.\nFrom the first sentence we get:\n$a + b + c = 66$\nFrom the seco... |
[
{
"content": "$f (x) = x + X and $g(x) = x^2 -6$, The value of $f(g(2))$ is 1. What is the value of unknown variable X?",
"role": "user"
},
{
"content": "The function $f(x) = x + X$ and $g(x) = x^2 -6$.\n$f(g(2))$ means that we need to plug $g(2)$ in for $x$ in $f(x)$.\n```python\nfrom sympy import ... |
[
{
"content": "The line segment connecting $(-2,7)$ and $(3,11)$ can be parameterized by the equations\n\\begin{align*}\nx &= at + b, \\\\\ny &= ct + d,\n\\end{align*}where $0 \\le t \\le X and $t = 0$ corresponds to the point $(-2,7).$ Find $a^2 + b^2 + c^2 + d^2. 94. What is the value of unknown variable X?",... |
[
{
"content": "I have X marbles numbered 1 through 5 in a bag. Suppose I take out two different marbles at random. What is the expected value of the sum of the numbers on the marbles?\nIf we know the answer to the above question is 6, what is the value of unknown variable X?",
"role": "user"
},
{
"... |
[
{
"content": "Sasha made x chocolate muffins for her school bake sale fundraiser. Melissa made 4 times as many muffins as Sasha, and Tiffany made half of Sasha and Melissa's total number of muffins. If one muffin sold for $4, how much money did Sasha, Melissa, and Tiffany contribute to the fundraiser?\nIf we kn... |
[
{
"content": "Given the functions $f(x) = 3x^2 - 7$, $g(t) = 4t + c$, $h(x) = g(f(x))$ and $j(y) = y^3 + h(y)$, if $h(2) = 5$ and $j(2) = 13$, what is the value of $c$?",
"role": "user"
},
{
"content": "We can find the desired value of $c$ by making use of Python's sympy library.\n```python\nfrom sy... |
[
{
"content": "What is the sum of the least common multiple and the greatest common divisor of the numbers 1332 and 888?",
"role": "user"
},
{
"content": "First, let's find the prime factorization of the two numbers using sympy.\n```python\nfrom sympy import primefactors, Mul\n\n# we want to know the... |
[
{
"content": "If a 40-foot tree is casting a 10-foot shadow, and Andrea is casting a 15-inch shadow at the same time, how tall is Andrea in inches?",
"role": "user"
},
{
"content": "Let's write down the ratio of the shadow to the height of the tree and Andrea, and then use this ratio to express Andr... |
[
{
"content": "What is the value of the expression $\\left\\lceil\\left(-\\frac{5}{3}\\right)^2\\right\\rceil$ when evaluated?",
"role": "user"
},
{
"content": "The built-in function ceil() is perfect to compute the ceiling of fractional numbers.\n```python\nfrom math import ceil\n\nexpression = (-5/... |
[
{
"content": "If one were to begin counting from the start of 2001 to the end of 2004, how many days would have passed?",
"role": "user"
},
{
"content": "Let's solve this problem using Python's datetime library.\n```python\nimport datetime\n\n# the start of 2001\nstart_date = datetime.date(2001, 1, ... |
[
{
"content": "If Molly and her parents spent most of the day at the beach and were joined by 100 people, but then 40 people left at 5:00, what is the total number of people at the beach if everyone stayed until evening?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n`... |
[
{
"content": "What is $\\frac{1}{4}\\%$ of X? Express your answer as a decimal. The answer is 0.3. What is the value of unknown variable X?",
"role": "user"
},
{
"content": "We know that the answer is $0.3 = \\frac{3}{10}$, so $\\frac{1}{4}\\%$ of X is $\\frac{3}{10}$.\nLet's compute the value of X ... |
[
{
"content": "A fan can create an airflow of x liters per second. If the fan works for 10 minutes each day, calculate the amount of airflow it will create in one week.\nIf we know the answer to the above question is 42000, what is the value of unknown variable x?",
"role": "user"
},
{
"content": "Le... |
[
{
"content": "For $x=-3$, $y=5$, and $z=-4$, find the outcome of the algebraic expression $x^2+y^2-z^2+2xy$.",
"role": "user"
},
{
"content": "To solve this expression, we first substitute the values of $x$, $y$, and $z$.\n```python\nimport sympy\n\nx, y, z = -3, 5, -4\n\nexpression = x**2 + y**2 - ... |
[
{
"content": "Find the value of $x + y + z + w$ if $x$, $y$, $z$, and $w$ are positive integers, $x + y + xy = 76$, $z$ is the greatest prime number less than $20$, and $w$ is the smallest prime number greater than $20$.",
"role": "user"
},
{
"content": "To solve this problem, we need to find the sm... |
[
{
"content": "How many prime numbers with two digits have a ones digit of 1?",
"role": "user"
},
{
"content": "Let's write a function in python to generate prime numbers with two digits and with a ones digit of 1.\n```python\n# create function that checks if a number is prime\ndef is_prime(n):\n ... |
[
{
"content": "Let $a$, $b$, $c$, $m$, $n$, and $p$ be integers with $m$ and $n$ odd, $n < m$, $c$ even, and $p$ a prime number such that $a^2 + b^2 + c^2 + p = m^2 - n^2 + c^2 + p$. Find the largest integer that divides $a^2 + b^2 + c^2 + p$ for any such $m$, $n$, $c$, and $p$.\n$\\textbf{(A)}\\ 2\\qquad \\text... |
[
{
"content": "Three faucets fill a 100-gallon tub in 6 minutes. How long, in seconds, does it take six faucets to fill a 25-gallon tub? Assume that all faucets dispense water at the same rate.",
"role": "user"
},
{
"content": "Let's denote the flow rate of each faucet by $x$ gallons/minute.\nThen ... |
[
{
"content": "The average age of the three Wilson children is 7 years. If the two younger children are 4 years old and 7 years old, how many years old is the oldest child?",
"role": "user"
},
{
"content": "We can create a Python function that calculates the age of the oldest child using sympy.\n```p... |
[
{
"content": "If $a \\triangle b = 2a^2 + 4b^2$ for all $a$ and $b$, then what is the value of $3 \\triangle 2$?",
"role": "user"
},
{
"content": "Let's substitute $a$ and $b$ with given values:\n```python\na = 3\nb = 2\n# calculate a ^ 2 and b ^ 2\na_squared = a ** 2\nb_squared = b ** 2\n# calculat... |
[
{
"content": "When Jo calculates the sum of all whole numbers from 1 through 100, and Kate also tallies up the first 100 whole numbers, but rounds each number to the closest ten before summing (with 5 rounding up), what is the difference in their totals?",
"role": "user"
},
{
"content": "I can find ... |
[
{
"content": "Find the number that when added to the numerator and denominator of the fraction $\\frac{3}{5}$ will make it equal to $\\frac{5}{6}$. What is this number?",
"role": "user"
},
{
"content": "Let's name the number we need to find x.\nAnd we have: $\\frac{3 + x}{5 + x} = \\frac{5}{6}$.\nSo... |
[
{
"content": "The average of three positive integers is 26, with the central number being 27. Knowing that the largest of these numbers is 5 greater than the median, determine the smallest integer in the sequence.",
"role": "user"
},
{
"content": "Let's define our variables and write down the equati... |
[
{
"content": "What is the value of $\\sin 6^\\circ \\sin 42^\\circ \\sin 66^\\circ \\sin 78^\\circ$?",
"role": "user"
},
{
"content": "To compute this product, we can simplify it using the identities for $\\sin(A + B)$ and $\\sin 2A$.\n```python\nfrom sympy import sin, pi, simplify\nfrom sympy.abc i... |
[
{
"content": "Stan drove 300 miles in 5 hours, 20 minutes. Next, he drove X miles in 6 hours, 40 minutes. What was Stan's average speed in miles per hour for the total trip?\nIf we know the answer to the above question is 55, what is the value of unknown variable X?",
"role": "user"
},
{
"content": ... |
[
{
"content": "Calculate the volume of a cube that has a surface area of 294 square inches.",
"role": "user"
},
{
"content": "A cube has six sides of equal length. \nWe can take the square root of the surface area of the cube to get a side length of $x$.\n```python\nimport math\n\n# area of a cube = ... |
[
{
"content": "Adam and Tom are brothers. Adam is 8 years old and Tom is x years old. Their combined age will be 44 years old in 12 years. What is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's solve this problem using Python's sympy library.\n```python\nimport sympy as sp\n... |
[
{
"content": "Determine the maximum value possible for the expression $x+\\frac{1}{x}$ provided that $7=x^2+\\frac{1}{x^2}$.",
"role": "user"
},
{
"content": "I can find the answer by solving a quadratic equation.\n```python\nfrom sympy import symbols, solve\n\n# define the variables\nx = symbols('x... |
[
{
"content": "Given that $f(x) = 3x^2-2$ and we have another function $g(f(x))$ which equals $x^2 + x +1$, evaluate and sum up all the possible values for $g(25)$.",
"role": "user"
},
{
"content": "We can use sympy to evaluate $f(25)$ as follows.\n```python\nfrom sympy import Symbol, simplify, Eq, s... |
[
{
"content": "If there exists an integer $p$ in the range $0 < 4p < 30$, can you determine the sum of all the distinct integer values that $p$ could take?",
"role": "user"
},
{
"content": "Since we have a range of $0 < 4p < 30$, this means that $0 < p < 30/4$.\nWe can easily enumerate values for $p$... |
[
{
"content": "Mary is going on a business trip. It takes 10 minutes for her Uber to get to her house and 5 times longer to get to the airport. It takes 15 minutes to check her bag and three times as long to get through security. Then she has to wait for x minutes for her flight to start boarding and twice as lo... |
[
{
"content": "In a school garden, there are flowers in different colors. In total there are 96 flowers of four colors: green, red, blue, and yellow. There are 9 green flowers and x times more red flowers. Blue flowers make up to 50% of the total flower count. There are 12 yellow flowers. What is the value of un... |
[
{
"content": "Cary is x inches tall. Her younger brother Bill is half her height, and her younger sister Jan is 6 inches taller than Bill. Jan is 42 tall. What is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's use Python code to solve this problem.\n```python\nCary_height =... |
[
{
"content": "At the zoo, there are 5 different types of animals. Seeing each animal type takes around 6 minutes. How much time would it take to see each animal type if the zoo decided to import x new species?\nIf we know the answer to the above question is 54, what is the value of unknown variable x?",
"ro... |
[
{
"content": "When you take the square root of $\\frac{y}{50}$ you get $\\frac{3}{5}$. What does $y$ equal?",
"role": "user"
},
{
"content": "Let $y$ equal $k$\n```python\nfrom sympy import Eq, sympify, Symbol, solve\n\nk = Symbol('k')\n\neq = Eq(sympify('sqrt(k/50)'), sympify('3/5'))\n\nsolve(eq, k... |
[
{
"content": "Mr. and Mrs. Lopez have two children. When they get into their family car, two people sit in the front, and the other two sit in the back. Either Mr. Lopez or Mrs. Lopez must sit in the driver's seat. How many seating arrangements are possible?",
"role": "user"
},
{
"content": "To f... |
[
{
"content": "Determine the independent term of $x$ when expanding the binomial $\\left(\\sqrt{x} + \\frac{5}{x}\\right)^9$.",
"role": "user"
},
{
"content": "To calculate the independent term of $x$ when expanding $\\left(\\sqrt{x} + \\frac{5}{x}\\right)^9$, we will use Python's sympy library.\n```... |
[
{
"content": "Determine $\\arctan (0).$ Give your answer in radians.",
"role": "user"
},
{
"content": "In Python, we can use numpy to calculate $\\arctan(0)$ as follows:\n```python\nimport numpy as np\n\nvalue = np.arctan(0)\nprint(value)\n```",
"role": "assistant"
},
{
"content": "```o... |
[
{
"content": "Janice has been working part-time at a convenience store 5 days a week. She can earn $x per day and can earn $15 more when she works a 2 hour overtime shift. If she works three overtime shifts this week, She will earn 195 this week. What is the value of unknown variable x?",
"role": "user"
}... |
[
{
"content": "Frank went to a shop to buy some food for his breakfast. He bought 10 buns for $0.1 each, two bottles of milk, for $2 each, and a carton of eggs, which was x times more expensive than one bottle of milk. How much did Frank pay for his breakfast shopping?\nIf we know the answer to the above questio... |
[
{
"content": "If $g(x) = f(x) + \\cos(x)$ and $f(x) = 2\\arcsin(\\sin(x))$, find the value of $g(7\\pi)$. Express your answer in radians.",
"role": "user"
},
{
"content": "We can compute $f(7\\pi)$ and $\\cos(7\\pi)$ and calculate $f(7\\pi) + \\cos(7\\pi)$:\n```python\nimport math\n\n# Define f and ... |
[
{
"content": "A toy car factory made 60 cars yesterday. Today, they made twice the number of cars than yesterday. How many toy cars did the factory make?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\ncars_yesterday = 60\ncars_today = cars_yesterday * 2\nto... |
[
{
"content": "Mary chose an even $4$-digit number $n$. She wrote down all the divisors of $n$ in increasing order from left to right: $1,2,...,\\dfrac{n}{2},n$. At some moment Mary wrote $323$ as a divisor of $n$. What is the smallest possible value of the next divisor written to the right of $323$?\n$\\textbf{... |
[
{
"content": "What is the sum of all distinct prime factors of 5463?",
"role": "user"
},
{
"content": "Let's list out the prime factors of 5463 using sympy.\n```python\nimport sympy as sp\n\ndef find_prime_factors(num):\n return [p for p in sp.ntheory.factorint(num).keys() if sp.isprime(p)]\n\npr... |
[
{
"content": "A koala's diet consists of 75\\% fiber. Koalas absorb only $25\\%$ of the fiber they eat. If a koala absorbed 10.5 ounces of fiber in one day, how many ounces of koala's total food did he eat that day?",
"role": "user"
},
{
"content": "Let's find the number of ounces of fiber in the to... |
[
{
"content": "June's house and Julia's residence are separated by a distance of 1 mile. June can cycle to Julia's place in 4 minutes. How long will it take her to bike 3.5 miles to visit Bernard's house if she maintains the same cycling speed?",
"role": "user"
},
{
"content": "The question is asking... |
[
{
"content": "Given the equation $(a + b)^2 = 45$ and the product $ab = 10$, calculate the value of $(a - b)^2$.",
"role": "user"
},
{
"content": "In order to compute the value of $(a-b)^2$, we'll have to manipulate the provided expressions to form the required quadratic equation.\n```python\nfrom s... |
[
{
"content": "Jimmy is going to sell pizzas at the carnival to make some money. The carnival only gave him x hours to do so. He bought a 22kg sack of flour to make his pizzas and he takes 10 min to make each pizza for the customers. At the end of the 7 hours, he saw some flour was left. Knowing that each pizza ... |
[
{
"content": "If Jack goes hunting 6 times a month during the hunting season, which lasts for 1 quarter of the year, and he catches 2 deer each time weighing 600 pounds each, how many pounds of deer does he keep in a year, keeping half the weight?",
"role": "user"
},
{
"content": "Let's solve this p... |
[
{
"content": "For every 4 apple trees in Ben's orchard, he can collect 36 baskets of apples. If he exchanges 9 baskets for 1 pumpkin, how many apple trees are needed to collect enough apples for 6 pumpkins?",
"role": "user"
},
{
"content": "The number of trees we need is a certain amount times 4 and... |
[
{
"content": "If Stu has 9 books and Albert has 4 times the number of books as Stu, what is the total number of books that Stu and Albert have together?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\nnumber_of_books_stu_has = 9\nnumber_of_books_albert_has =... |
[
{
"content": "A farmer planted 30 rows of tomatoes with 10 plants in each row. Each tomato plant yields x pieces of tomatoes. How many pieces of tomatoes can the farmer get from all his planted tomatoes?\nIf we know the answer to the above question is 6000, what is the value of unknown variable x?",
"role":... |
[
{
"content": "Let $f(x) = ax^7 + bx^3 + cx - 5.$ If $f(-7) = 7,$ then find $f(7).$",
"role": "user"
},
{
"content": "To solve this problem we should substitute $x$ in the given polynomial by $-7$ and $7$ and find the relation between the resulting values.\n```python\nfrom sympy import symbols, Eq, ... |
[
{
"content": "If the ratio of goats to sheep on Mr. Mathews' farm is 5:7 and there is a total of 360 goats and sheep combined, he decides to sell half of the goats at $40 each and 2/3 of the sheep at $30 each. What is the total amount of money he makes from the sale of the animals?",
"role": "user"
},
{... |
[
{
"content": "If Susan is making jewelry with a repeating pattern consisting of 3 green beads, 5 purple beads, and twice as many red beads as green beads, and the pattern repeats three times per bracelet and five times per necklace, how many beads does she need to make 1 bracelet and 10 necklaces in total?",
... |
[
{
"content": "Hallie is an artist. She wins an art contest, and she receives a $150 prize. She sells 3 of her paintings for $x each. She makes 300 money in total from her art. What is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's solve this problem using Python's sympy lib... |
[
{
"content": "Mimi has decided to start going to the gym again. Over the weekend, she spent $8,000 on athletic sneakers and clothes. She spent thrice as much on Nike sneakers as she did on Adidas. What she spent on Adidas was 1/5 the cost of Skechers. If Mimi's Adidas sneakers purchase was $600, what amount did... |
[
{
"content": "If Grandma wants to order 5 personalized backpacks for each of her grandchildren's first days of school, and the backpacks are currently 20% off the original price of $20.00, with an additional cost of $12.00 each for monogramming, what will be the total cost of the backpacks?",
"role": "user"... |
[
{
"content": "In a stem-and-leaf plot detailing the ride times in minutes and seconds for the 17 most popular roller coasters, the entry $2 \\ 20$ corresponds to a duration of 2 minutes and 20 seconds, or 140 seconds. Which number represents the median value of the times listed in the dataset? Your answer shoul... |
[
{
"content": "What is the greatest number that divides both the least common multiples of 8 and 14 and the least common multiples of 7 and 12 without any remainder (find GCF(LCM(8, 14), LCM(7, 12)))?",
"role": "user"
},
{
"content": "Let's first compute LCM(8, 14) and LCM(7, 12) using Python's sympy... |
[
{
"content": "Consider a single roll of an unbiased six-sided die with faces numbered 1 to 6. For the outcome $n$, my prize will be the square of $n$ in dollars. What is the expected value of the prize I will receive? Round off your answer to the nearest two decimal points.",
"role": "user"
},
{
"co... |
[
{
"content": "In Zeoland the fine for speeding is $16 for each mile per hour the driver is traveling over the posted speed limit. In Zeoland, Jed was fined $256 for speeding on a road with a posted speed limit of x mph. Jed was fined for traveling at what speed in miles per hour?\nIf we know the answer to the a... |
[
{
"content": "Determine the positive real number $t$ for which the equation $|t + 2i\\sqrt{3}| \\times |6 - 4i| = 26$ holds true.",
"role": "user"
},
{
"content": "We're dealing with complex numbers. Let's find the value of $|t + 2i\\sqrt{3}| \\times |6 - 4i|$ using sympy.\n```python\nimport sympy a... |
[
{
"content": "Find the minimum value of\n\\[4x + \\frac{1}{x^4}\\]for $x > X The answer is 5. What is the value of unknown variable X?",
"role": "user"
},
{
"content": "To solve this problem, we first need to use Python's sympy library to solve for x to find out the minumum value.\n\n```python\nfrom... |
[
{
"content": "Let $f$ be a function with domain and codomain as the set of real numbers. It follows that for all $x, y \\in \\mathbb{R}$:\n\\[f(f(x) + y) = f(x + y) + xf(y) - xy - x + 1\\]\n\nLet the number of conceivable values of $f(1)$ be denoted by $n$, and the sum of these values is $s$. Determine the valu... |
[
{
"content": "Let $r$ and $s$ be the solutions to $2x^2 - 3x = 11.$ Compute the value of $(4r^3 - 4s^3)(r - s)^{-1}.$",
"role": "user"
},
{
"content": "To solve this problem, we first solve the quadratic equation $2x^2 - 3x = 11.$\n\n```python\nfrom sympy import Symbol, Eq, solve\n\n# Symbol x\nx =... |
[
{
"content": "Denny, an Instagram influencer, has x followers and gets 1000 new followers every day. How many followers will he have if 20000 people unfollowed him in a year?\nIf we know the answer to the above question is 445000, what is the value of unknown variable x?",
"role": "user"
},
{
"conte... |
[
{
"content": "In the diagram, what is the perimeter of polygon $PQRST$? [asy]\n\nimport olympiad;\n\nsize(6cm); // ADJUST\n\npair p = (0, 6);\npair q = (3, 6);\n\npair r = (3, 3);\npair t = (0, 0);\npair s = (7, 0);\n\ndraw(p--q--r--s--t--cycle);\nlabel(\"$P$\", p, NW);\nlabel(\"$Q$\", q, NE);\nlabel(\"$R$\", r... |
[
{
"content": "Calculate the expense in dollars for purchasing 1000 peppermint gums, each priced at 1 cent.",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\ngum_price = 0.01\nnumber_of_gums = 1000\ncost_in_cents = gum_price * number_of_gums\ncost_in_cents\n```... |
[
{
"content": "If $y = 8x + 2$ and $y = (2c)x - 4$ represent two parallel lines, what is $c$?",
"role": "user"
},
{
"content": "We know that the two lines $y = 8x + 2$ and $y = (2c)x - 4$ are parallel.\nThe slope of the first line is 8.\nWe can calculate the slope of the second line by dividing the c... |
[
{
"content": "Laura wants to bake a cake for her mother. She checks the recipe and the pantry and sees that she needs to buy 2 cups of flour, 2 cups of sugar, a cup of butter, and two eggs. The flour costs $4. The sugar costs $2. The eggs cost $.5, and the butter costs $2.5. When she is done baking it, she cuts... |
[
{
"content": "The function $f(x)$ satisfies\n\\[f(x + y) = f(x) + f(y)\\]for all real numbers $x$ and $y,$ and $f(4) = 5.$ Find $f(5).$",
"role": "user"
},
{
"content": "The function $f(x)$ has a property of linearity. This means that it can be represented in the form\n```python\ndef linear_f(x):\n... |
[
{
"content": "Expand the product ${(x-2)(x+6)}$.",
"role": "user"
},
{
"content": "We can use sympy to expand the product and get the answer.\n```python\nimport sympy as sp\n\nx = sp.Symbol('x')\n\nprod = (x - 2) * (x + 6)\n\nexpanded_prod = prod.expand()\nprint(expanded_prod)\n```",
"role": "as... |
[
{
"content": "What is the units digit of $6^{1999}$?",
"role": "user"
},
{
"content": "Let's first figure out the units digit of $6^4$ which is $16$. So the units digit of $6^n$ repeats in a cycle of 4.\nThen we need to find the remainder of $1999$ divided by $4$, which is $3$.\nSo we have $6^{1999}... |
[
{
"content": "The volume of a rectangular box is 108 cubic feet. How many cubic yards are in the volume of this box?",
"role": "user"
},
{
"content": "Volume is measured in cubic units.\nTo convert from cubic feet to cubic yards, we need to divide by $N$ (number of cubic feet in a cubic yard).\n$1 \... |
[
{
"content": "If you want to split 40 apples and 48 oranges into groups of equal quantity without any leftovers, how many fruits will be in each group?",
"role": "user"
},
{
"content": "We have 40 apples and 48 oranges.\nWe want to split them into groups of equal quantity.\nLet X be the number of fr... |
[
{
"content": "If Paige bought new stickers and wants to divide a sheet of 100 space stickers and a sheet of 50 cat stickers equally among her 3 friends, how many stickers will she have remaining?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\nnumber_of_spac... |
[
{
"content": "If 52 cards are dealt to 8 people as evenly as possible, how many people will end up with fewer than 7 cards?",
"role": "user"
},
{
"content": "First we can calculate the number of cards each person will get:\n```python\npeople = 8\ncards = 52\nnumber_of_cards_per_person = cards // peo... |
[
{
"content": "Let $f(x)=x+3$, $g(x)=3x+5$, and $h(x)=2x-1$. If $k(x) = f(g(h(x)))$, calculate $k(2) + h(f(g(2))) + g(h(f(2))) + f(g(h(2)))$.",
"role": "user"
},
{
"content": "We will simply apply the functions in the given order to compute the answer.\n```python\nfrom sympy import symbols, simplify\... |
[
{
"content": "Convert the point $(3,-3)$ in rectangular coordinates to polar coordinates. Enter your answer in the form $(r,\\theta),$ where $r > 0$ and $0 \\le \\theta < 2 \\pi.$",
"role": "user"
},
{
"content": "I will find the answer by calculating the distance and the angle with respect to the ... |
[
{
"content": "If we divide $5^{2010}$ evenly into 7 parts, what will be the leftover?",
"role": "user"
},
{
"content": "To solve this problem we should calculate $5^{2010}$ modulo 7. We can do it using python:\n```python\nimport math\ndef modulo(num, mod):\n return num % mod\n\n# Calculate 5^2010... |
[
{
"content": "A group of 5 children are taken to an amusement park. Only 3 of them were daring enough to get on the Ferris wheel which cost $5 per child. Everyone had a go at the merry-go-round (at $3 per child). On their way home, they bought 2 cones of ice cream each (each cone cost $8). How much did they spe... |
[
{
"content": "Find the sum of the products of the coefficients $b_1 c_1 + b_2 c_2 + b_3 c_3$, knowing that for every real $x$, the polymonial expression $x^6 - x^5 + x^4 - x^3 + x^2 - x + 1$ can be factored as\n\\[\n (x^2 + b_1 x + c_1)(x^2 + b_2 x + c_2)(x^2 + b_3 x + c_3). \n\\]",
"role": "user"
},
{... |
[
{
"content": "Oliver needs to create a wire frame for a cube with a minimum volume of 64 cubic centimeters. What should the edge of the cube be to use the least amount of wire?",
"role": "user"
},
{
"content": "The volume of the cube is given by the following formula.\n\\[V = s^3\\]\nWhere $V$ is th... |
[
{
"content": "If $f(x) = x(3x^2-2)-5(x^2-2x+7)$ and $g(x) = 2x^2 - 4$, find $f(x) - g(x)$. Express your answer in the form $Ax^3+Bx^2+Cx+D.$",
"role": "user"
},
{
"content": "Let $f(x) = x(3x^2-2)-5(x^2-2x+7)$ and $g(x) = 2x^2 - 4$.\n```python\nfrom sympy import symbols, simplify, pprint\n\n# define... |
[
{
"content": "The sum of the squares of the roots of the quadratic equation $3x^2 + 4x - 9 = 0$ is known to be $\\frac{70}{9}$. What is the product of the roots of this quadratic equation?",
"role": "user"
},
{
"content": "We can use sympy to get the polynomial's roots.\n```python\nfrom sympy import... |
[
{
"content": "Jake agrees to work part of his debt off. He owed someone $100 but paid them $x before agreeing to work off the rest. He worked for $15 an hour. How many hours did he have to work?\nIf we know the answer to the above question is 4, what is the value of unknown variable x?",
"role": "user"
... |
[
{
"content": "The probability of snow for each of the next three days is $\\frac{3}{4}$. What is the probability that it will not snow at all during the next three days? Express your answer as a common fraction.",
"role": "user"
},
{
"content": "The probability of snowing is 3/4.\nThe probability of... |
[
{
"content": "What do you get when you subtract the second complex number (1 + 4i) from the first one (-3 - 2i)?",
"role": "user"
},
{
"content": "We're subtracting a number with a negative real part and a positive imaginary part from a number with a negative real part and a negative imaginary part.... |
[
{
"content": "Last night, Jim bought a $7 lamp and a bulb which cost $4 less. If he bought x lamps and 6 bulbs, Jim paid 32 in all. What is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's solve this problem using Python's sympy library.\n```python\nimport sympy as sp\n\n# Le... |
[
{
"content": "Given vectors $\\mathbf{v}$ and $\\mathbf{w}$ with $\\|\\mathbf{v}\\| = 4$, $\\|\\mathbf{w}\\| = 3$, $\\mathbf{v} \\perp \\mathbf{w}$, and $\\mathbf{u} = 2\\mathbf{v} - \\mathbf{w}$, find $\\mathbf{u} \\cdot \\mathbf{u}$.",
"role": "user"
},
{
"content": "We have $\\mathbf{v} \\perp \\... |
[
{
"content": "Using the digits 2, 4, and 7, how many unique two-digit positive integers can be formed without repeating any digits?",
"role": "user"
},
{
"content": "Let's write a python code to enumerate all the possible ways to construct a two-digit positive integer using the digits 2, 4, and 7 wi... |
[
{
"content": "What is the combined sum of the roots of the cubic polynomials \\(2x^3 + x^2 - 8x + 20\\) and \\(5x^3 - 25x^2 + 19\\) if they are set to equal zero?",
"role": "user"
},
{
"content": "To compute the total roots of the cubic polinomials, we can first solve each of the polynomials for the... |
[
{
"content": "Suppose there are four distinct positive integers, $P$, $Q$, $R$, and $S$, which when added together give a total of 64. Moreover, these integers satisfy $P + 3 = Q - 3 = R \\times 3 = S \\div 3$. Can you determine the product $P \\times Q \\times R \\times S$?",
"role": "user"
},
{
"c... |
[
{
"content": "Hannah is making banana bread. She needs to use 3 cups of flour for every cup of banana mush. It takes 4 bananas to make one cup of mush. If Hannah uses x bananas, how many cups of flour should she use?\nIf we know the answer to the above question is 15, what is the value of unknown variable x?",
... |
[
{
"content": "Marcus has two numbers, $a$ and $b$. When he divides $a$ by 45 he gets a remainder of 37. When he divides $b$ by 30 he gets a remainder of X$. What remainder does he get when he divides $a+b$ by 15?\nIf we know the answer to the above question is 1, what is the value of unknown variable X?",
... |
[
{
"content": "If $h(x) = g(x) + x^3$ where $g(x) = 2f(x) + 3$ and $f(x) = x^2 - x$, what is $h(4)$?",
"role": "user"
},
{
"content": "To solve this problem we should calculate $g(4)$ and $f(4)$ and then plug it into the original formula:\n```python\nfrom sympy import symbols, Function\n\n# Define th... |
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