gt stringlengths 1 43 | rej sequencelengths 1 1 | chosen listlengths 4 12 | rejected listlengths 4 12 |
|---|---|---|---|
70 | [
"130"
] | [
{
"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": "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": "The time spent on the third puzzle depends o... |
103 | [
"11636149"
] | [
{
"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.\n```python\n# Convert 6543 to base 8\nimport math\n\nbase ... | [
{
"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 write a function that converts numbers from base 10 to base 8 in python.\n```python\ndef decima... |
10.5 | [
"7"
] | [
{
"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 use sympy to write out the equations and solve for the third number.\n```python\nfrom sympy import symbols,... | [
{
"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": "The second number is 24, let's call the third number $x$.\n```python\nfrom sympy import symbols, solve\n\n# Let's... |
3 | [
"1"
] | [
{
"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": "Let's use sympy to solve for $X$.\n```python\nimport sympy as sp\n\n# define the symbols\nx, y, X = sp.symbols('x y X')\n\n# define the functions\... | [
{
"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": "It is very easy to find the value of $X$, by just using the definition of $f$ and $g$:\n```python\ndef f(x):\n return x + X\n\ndef g(x):\n r... |
1 | [
"94"
] | [
{
"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": "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?",... |
5 | [
"30"
] | [
{
"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": "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"
},
{
"... |
30 | [
"40"
] | [
{
"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": "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... |
-15 | [
"-1323"
] | [
{
"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": "Let's substitute the known values into the equations.\n$g(f(2)) = 5$ and $j(2) = 13$.\n$g(f(2)) =... | [
{
"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": "To solve this problem we need to express $c$ in terms of $M$ and $N$.\nWe will use sympy to expre... |
3108 | [
"2708"
] | [
{
"content": "What is the sum of the least common multiple and the greatest common divisor of the numbers 1332 and 888?",
"role": "user"
},
{
"content": "We have two numbers $1332$ and $888$.\nTo compute the gcd and lcm of two numbers, we will use Python's sympy library.\n```python\nfrom sympy impor... | [
{
"content": "What is the sum of the least common multiple and the greatest common divisor of the numbers 1332 and 888?",
"role": "user"
},
{
"content": "The least common multiple of $1332$ and $888$ is $1332888$ which we can get using sympy.\n```python\nfrom sympy import lcm\n\n# calculate the LCM ... |
60 | [
"720"
] | [
{
"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 solve this problem using Python code.\n```python\n# length of tree and length of its shadow\nlength_of_tree = 40... | [
{
"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 solve this problem using Python code.\n```python\nheight_of_tree = 40\nlength_of_tree_shadow = 10\nlength_of_and... |
1461 | [
"1096"
] | [
{
"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 code.\n```python\n# each year has 365 days\nyear_length = 365\n# but 2004 is a leap year so it has 366 days\... | [
{
"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 code.\n```python\nstart_year = 2001\nend_year = 2004\nnumber_of_years = end_year - start_year\ntotal_days = ... |
63 | [
"61"
] | [
{
"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": "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`... |
120 | [
"1.2"
] | [
{
"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": "To compute the value of X when $\\frac{1}{4}\\%$ of X is 0.3, we can set up and solve an equation.\nLet $x$ be the unknown var... | [
{
"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": "Let's first solve the equation by converting the percent to a decimal number using sympy:\n```python\nfrom sympy import symbol... |
10 | [
"600"
] | [
{
"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": "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... |
-12 | [
"34"
] | [
{
"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": "Let's use sympy to substitute in the values of $x$, $y$, and $z$ into the expression and simplify.\n```python\nfrom sympy import symbols, Eq, simplify\n\n# d... | [
{
"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": "Let's use sympy to solve this.\n```python\nimport sympy as sp\n\nx, y, z = sp.symbols('x y z')\n\nequation = sp.Eq(x**2 + y**2 - z**2 + 2*x*y, -49)\n\nsoluti... |
58 | [
"63"
] | [
{
"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": "Let's use sympy to list out the possible valu... | [
{
"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 reduce the number of possible cases to che... |
5 | [
"9"
] | [
{
"content": "How many prime numbers with two digits have a ones digit of 1?",
"role": "user"
},
{
"content": "To reduce the computation time, let's first determine which numbers are prime and then filter through them to find those that end in 1.\n```python\nfrom sympy import isprime\n\nprimes = [n ... | [
{
"content": "How many prime numbers with two digits have a ones digit of 1?",
"role": "user"
},
{
"content": "Counting primes with 2 digits with a ones digit of 1 is not a great use of time. Let's use sympy to find all primes up to 100.\n```python\nfrom sympy import prime\nprimes = [x for x in ran... |
8 | [
"16"
] | [
{
"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": "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... |
45 | [
"15"
] | [
{
"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": "The question is asking to calculate the time taken to fill a 25-gallon ... | [
{
"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": "The rate of each faucet is $100 / 6$ gallons per minute, and we have si... |
34 | [
"24"
] | [
{
"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": "To solve this problem, we need to use sympy's symbolic mathematics capabilities.\n```python\nfrom sympy import symbols, Eq, solve\n\n# Define symbols for... | [
{
"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": "We can use sympy to solve this:\n```python\nfrom sympy import Symbol, Eq\nfrom sympy.solvers import solve\n\n# Define symbols for a and b\na = Symbol('a'... |
50 | [
"4995"
] | [
{
"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": "We will wri... | [
{
"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": "The sum of ... |
7 | [
"1.4"
] | [
{
"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 call this number $x$.\nWe have $\\frac{3 + x}{5 + x} = \\frac{5}{6}$.\n\nLet's simplify thi... | [
{
"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 find this number using sympy.\n```python\nimport sympy as sp\n\nx = sp.symbols('x')\n\n# Gi... |
19 | [
"17"
] | [
{
"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 call the numbers $x$, $y$, and $z$ where $x$ i... | [
{
"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 call the three numbers $a$, $b$, and $c$, with... |
\frac{1}{16} | [
"0.062"
] | [
{
"content": "What is the value of $\\sin 6^\\circ \\sin 42^\\circ \\sin 66^\\circ \\sin 78^\\circ$?",
"role": "user"
},
{
"content": "It's a good idea to use sympy to simplify this expression.\n```python\nfrom sympy import sin, pi\n\nproduct = sin(6*pi/180)*sin(42*pi/180)*sin(66*pi/180)*sin(78*pi/1... | [
{
"content": "What is the value of $\\sin 6^\\circ \\sin 42^\\circ \\sin 66^\\circ \\sin 78^\\circ$?",
"role": "user"
},
{
"content": "To solve this, we can use Python's sympy library.\n```python\nfrom sympy import sin, pi, solve\n\n# Convert angles from degrees to radians\nangle1 = 6 * pi / 180\nan... |
360 | [
"34\\frac{1}{3}"
] | [
{
"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": "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": ... |
343 | [
"46656"
] | [
{
"content": "Calculate the volume of a cube that has a surface area of 294 square inches.",
"role": "user"
},
{
"content": "The formula for the surface area of a cube with side length $s$ is $6s^2$.\nLet's write down this formula as a sympy expression and solve for $s$.\n```python\nfrom sympy impor... | [
{
"content": "Calculate the volume of a cube that has a surface area of 294 square inches.",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\narea = 294\nside_length = 6\narea_of_a_face = area / 6\nside_length_sqrt = side_length * side_length\nvolume = side_len... |
12 | [
"24"
] | [
{
"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": "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... |
3 | [
"-3"
] | [
{
"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": "Let's use sympy to solve for $x$.\n```python\nimport sympy as sp\n\n# define the symbols\nx = sp.symbols('x')\n\n# define the equation\neq = ... | [
{
"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": "We can use sympy to solve such problems:\n```python\nfrom sympy import symbols, solve, Symbol, Eq, simplify\n\nx = Symbol(\"x\")\nequation = ... |
20 | [
"1302"
] | [
{
"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": "To find the possible values of $g(25)$ we need to find where $f(x)=25$ and plug these $x$ values into ... | [
{
"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": "To solve this problem, we can use Python's sympy library.\n```python\nfrom sympy import Symbol, solve\... |
28 | [
"112"
] | [
{
"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": "Let's first check if $4p$ is between 1 and 30:\n```python\nfrom sympy import symbols, solve\n\np = symbols('p')... | [
{
"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": "Let's use sympy to loop through all the integers in the range $0 < 4p < 30$ and take the sum of all the values ... |
20 | [
"23"
] | [
{
"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": "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... |
3 | [
"4"
] | [
{
"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": "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... |
4 | [
"8"
] | [
{
"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": "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... |
18 | [
"4.242640687119271"
] | [
{
"content": "When you take the square root of $\\frac{y}{50}$ you get $\\frac{3}{5}$. What does $y$ equal?",
"role": "user"
},
{
"content": "The question is asking to solve the equation $\\sqrt{\\frac{y}{50}} = \\frac{3}{5}$.\nLet's square both sides and simplify.\n```python\nimport sympy as sp\n\n... | [
{
"content": "When you take the square root of $\\frac{y}{50}$ you get $\\frac{3}{5}$. What does $y$ equal?",
"role": "user"
},
{
"content": "To solve this, we can use Python's sympy library.\n```python\nfrom sympy import symbols, Eq, solve\n\ny = symbols('y')\n# Define the equation\nequation = Eq(y... |
12 | [
"8"
] | [
{
"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": "The ... | [
{
"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": "The ... |
10500 | [
"5^63!/6^3"
] | [
{
"content": "Determine the independent term of $x$ when expanding the binomial $\\left(\\sqrt{x} + \\frac{5}{x}\\right)^9$.",
"role": "user"
},
{
"content": "To determine the independent term of $x$ when expanding the binomial $\\left(\\sqrt{x} + \\frac{5}{x}\\right)^9$, we need to focus on the ter... | [
{
"content": "Determine the independent term of $x$ when expanding the binomial $\\left(\\sqrt{x} + \\frac{5}{x}\\right)^9$.",
"role": "user"
},
{
"content": "The independent term is the term that does not have $x$ in it, i.e., constant term.\n```python\nimport sympy as sp\n\n# define the symbols\nx... |
18 | [
"12"
] | [
{
"content": "If a kilogram of pork costs $6 and a kilogram of chicken costs $2 less, what will be the total cost of 3 kilograms of chicken and 1 kilogram of pork?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\nkg_of_pork_price = 6\nkg_of_chicken_price = 6 ... | [
{
"content": "If a kilogram of pork costs $6 and a kilogram of chicken costs $2 less, what will be the total cost of 3 kilograms of chicken and 1 kilogram of pork?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\nprice_per_kilo_pork = 6\nprice_per_kilo_chicke... |
30 | [
"75"
] | [
{
"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": "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"
}... |
3 | [
"5"
] | [
{
"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": "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... |
-1 | [
"-\\frac{180}{\\pi}"
] | [
{
"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": "Let's plug in 7$\\pi$ in the expressions for $f(x)$ and $g(x)$ and simplify the expressions using sympy.\n```python\nimport symp... | [
{
"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": "To reduce the computation complexity, let's simplify $f(x)$.\n```python\nfrom sympy import atan, pi, sin, asin\n\n# Simplify the... |
340 | [
"361"
] | [
{
"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": "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{... |
610 | [
"39"
] | [
{
"content": "What is the sum of all distinct prime factors of 5463?",
"role": "user"
},
{
"content": "To find the sum of all distinct prime factors of 5463, we need to first identify the prime factors of 5463.\n\nLet's use sympy library:\n```python\nfrom sympy import factorint\n\nnumber = 5463\npri... | [
{
"content": "What is the sum of all distinct prime factors of 5463?",
"role": "user"
},
{
"content": "The prime factorization of 5463 is done by first taking its square root, and then finding the prime factors of the number under the square root of 5463.\n```python\nimport numpy as np\n\n# Finding ... |
14 | [
"12"
] | [
{
"content": "If the standard poodle is 8 inches taller than the miniature poodle, and the miniature poodle is 6 inches taller than the toy poodle, what is the height of the toy poodle in inches if the standard poodle is 28 inches tall?",
"role": "user"
},
{
"content": "Let's solve this problem usin... | [
{
"content": "If the standard poodle is 8 inches taller than the miniature poodle, and the miniature poodle is 6 inches taller than the toy poodle, what is the height of the toy poodle in inches if the standard poodle is 28 inches tall?",
"role": "user"
},
{
"content": "Let's solve this problem usin... |
56 | [
"42"
] | [
{
"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 first determine the amount of fiber that a k... | [
{
"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": "It is very important to realize that half of the f... |
14 | [
"3.5/15"
] | [
{
"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": "Let's solve this probl... | [
{
"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": "Let's solve this probl... |
5 | [
"1985"
] | [
{
"content": "Given the equation $(a + b)^2 = 45$ and the product $ab = 10$, calculate the value of $(a - b)^2$.",
"role": "user"
},
{
"content": "It is very easy to get the answer. So, let's just use math for that:\n```python\n# Given $(a + b)^2 = 45$ and the product $ab = 10$, calculate the value ... | [
{
"content": "Given the equation $(a + b)^2 = 45$ and the product $ab = 10$, calculate the value of $(a - b)^2$.",
"role": "user"
},
{
"content": "Let's use sympy to solve for $a$ and $b$ given the equations $(a + b)^2 = 45$ and $ab = 10$.\n```python\nfrom sympy import Symbol, Eq, solve\n\n# Define ... |
7 | [
"7.333333333333333"
] | [
{
"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": "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 ... |
10800 | [
"64800"
] | [
{
"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": "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... |
0 | [
"4"
] | [
{
"content": "Let $r$ be the positive real solution to $x^3 + \\frac{2}{5} x - 1 = X Find the exact numerical value of\n\\[r^2 + 2r^5 + 3r^8 + 4r^{11} + \\dotsb. The answer is 4. What is the value of unknown variable X?",
"role": "user"
},
{
"content": "The value of X is 0.\n```python\nfrom sympy i... | [
{
"content": "Let $r$ be the positive real solution to $x^3 + \\frac{2}{5} x - 1 = X Find the exact numerical value of\n\\[r^2 + 2r^5 + 3r^8 + 4r^{11} + \\dotsb. The answer is 4. What is the value of unknown variable X?",
"role": "user"
},
{
"content": "To solve this problem we need to express $r$ ... |
6 | [
"2"
] | [
{
"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": "Let's solve this problem using Python code.\n```python\nnum... | [
{
"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": "Let's solve this problem using Python code.\n```python\napp... |
-17 | [
"0"
] | [
{
"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 can use Python's sympy library.\n```python\nfrom sympy import symbols, simplify, solve\n\nx, a, b, c = symbols('x, a, b, c')\nf_x = a*x**7 + b*x**3 + c*x - ... | [
{
"content": "Let $f(x) = ax^7 + bx^3 + cx - 5.$ If $f(-7) = 7,$ then find $f(7).$",
"role": "user"
},
{
"content": "We can use sympy to solve this question.\n```python\nfrom sympy import symbols, Eq, solve, simplify\n\n# define the variables\na, b, c, x = symbols('a b c x')\n\n# define the equatio... |
7200 | [
"20360"
] | [
{
"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 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"
},
{... |
742 | [
"714"
] | [
{
"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": "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?",
... |
163 | [
"143"
] | [
{
"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": "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... |
28 | [
"1"
] | [
{
"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 calculate the LCMs.\n```python\nfrom sympy import lcm\... | [
{
"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 calculate the lcm of 8 and 14 and the lcm of 7 and 12:\n```p... |
15.17 | [
"73.50"
] | [
{
"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": "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... |
50 | [
"82"
] | [
{
"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": "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... |
1 | [
"2.16666666666667"
] | [
{
"content": "Determine the positive real number $t$ for which the equation $|t + 2i\\sqrt{3}| \\times |6 - 4i| = 26$ holds true.",
"role": "user"
},
{
"content": "To solve the problem, we will use Python's sympy library.\n```python\nfrom sympy import symbols, sqrt, solve\n\n# Introduce a symbol for... | [
{
"content": "Determine the positive real number $t$ for which the equation $|t + 2i\\sqrt{3}| \\times |6 - 4i| = 26$ holds true.",
"role": "user"
},
{
"content": "It's a good idea to rewrite it in the form $(t + 2i\\sqrt{3}) \\times (6 - 4i) = 26$.\nLet's solve it using sympy.\n```python\nfrom symp... |
2 | [
"0"
] | [
{
"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 $f$ 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... |
2 | [
"4"
] | [
{
"content": "How many prime numbers are between 80 and 90?",
"role": "user"
},
{
"content": "The range of numbers between 80 and 90 is [81, 89]. \nLet's find all the primes in this range using sympy.\n```python\nimport sympy as sp\n\n# list of numbers between 80 and 90\nnumber_range = list(range(81... | [
{
"content": "How many prime numbers are between 80 and 90?",
"role": "user"
},
{
"content": "Let's use sympy to find the prime numbers between 80 and 90.\n```python\nfrom sympy import sieve\n\n# find the prime numbers between 80 and 90\nprint(sieve.primerange(80, 90))\n``````",
"role": "assista... |
100000 | [
"345000"
] | [
{
"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": "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... |
2 | [
"3"
] | [
{
"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": "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... |
10 | [
"1000"
] | [
{
"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\nnumber_of_gums = 1000\nprice_of_one_gum = 0.01\nexpense = number_of_gums * price_of_one_gum\nexpense\n`... | [
{
"content": "Calculate the expense in dollars for purchasing 1000 peppermint gums, each priced at 1 cent.",
"role": "user"
},
{
"content": "The cost of 1 gum is 1 cent, so the cost of 1000 gums will be 1000 times 1 cent.\nLet's solve this problem using Python code.\n```python\ncost_per_gum = 1\nnum... |
4 | [
"(y+4)/(2x)"
] | [
{
"content": "If $y = 8x + 2$ and $y = (2c)x - 4$ represent two parallel lines, what is $c$?",
"role": "user"
},
{
"content": "For two lines with equations $y=ax+b$ and $y=cx+d$ to be parallel, their slopes have to be equal.\nThe slope of the first line is $a = 8$ and the slope of the second line is... | [
{
"content": "If $y = 8x + 2$ and $y = (2c)x - 4$ represent two parallel lines, what is $c$?",
"role": "user"
},
{
"content": "Let's write down an equation for the parallel lines and solve for $c$ using sympy.\n```python\nimport sympy as sp\n\n# define the symbols\nx, y, c = sp.symbols('x y c')\n\n#... |
6 | [
"12"
] | [
{
"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": "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... |
\frac{25}{4} | [
"5"
] | [
{
"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": "Let's define our function $f(x)$ in python and compute $f(5)$.\n```python\ndef f(x):\n return 5*x/4\n\nprint(f(5))\n``````",
... | [
{
"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": "Since $f(x+y) = f(x) + f(y)$, applying this with $x = 4$ and $y = 1$, we have $f(4 + 1) = f(4) + f(1)$ so $f(5) = f(4) + f(1)$.\n... |
6 | [
"4"
] | [
{
"content": "What is the units digit of $6^{1999}$?",
"role": "user"
},
{
"content": "The units digit of 6 raised to any power $n$ is equal to the units digit of $6^{k}$ where $k$ is the remainder of $n$ when divided by 4.\n```python\nimport math\n\nn = 1999\n\nremainder = n % 4\n\nif remainder == ... | [
{
"content": "What is the units digit of $6^{1999}$?",
"role": "user"
},
{
"content": "First, let's recall the pattern of units digits of $6^n$:\n1, 6, 4, 6, 6, 4, ...\n1999 is an odd number, so $6^{1999}$ will end with 6.\nLet's use sympy to calculate 6^1999.\n```python\nfrom sympy import symbols, ... |
4 | [
"108"
] | [
{
"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": "Let $l,w,h$ be the length, width, and height of the box.\nThe volume of the box is $108 = l \\times w \\times h$.\nWe are asked to find the volume in... | [
{
"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": "Each cubic foot is 1 yard. Hence, the number of cubic yards in the volume of the box is the same as the volume in cubic feet.\n```python\n108\n``````... |
8 | [
"44"
] | [
{
"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": "The number of fruits in each group must be a factor of 40 and 48. We will compute the greatest common divisor of 4... | [
{
"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": "Let's solve this problem using Python code.\n```python\nfruits = 40 + 48\nresult = fruits / 2\nresult\n```",
"... |
3 | [
"0"
] | [
{
"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\nspace_stickers... | [
{
"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\ntotal_sticky_c... |
4 | [
"7"
] | [
{
"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": "Let's use sympy to find the number of people that will end up with fewer than 7 cards.\n```python\nimport sympy as sp\n\n# 52 cards are dealt ... | [
{
"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": "The best way to solve this problem is to calculate using Python\n```python\nnumber_of_players = 8\nnumber_of_cards = 52\n\ndef find_number_of_... |
93 | [
"100"
] | [
{
"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": "Let's implement the following functions in python and use them to calculate $k(2) + h(f(g(2))) + g(h(f(2))) + f(g(h(2)))$.\n`... | [
{
"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": "It's a good idea to write down what $f(g(h(x)))$ means. It means that we first compute $h(x)$, then we compute $g(h(x))$, an... |
(3\sqrt{2},\frac{7\pi}{4}) | [
"(3\\sqrt{2},-\\pi/4)"
] | [
{
"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": "Let's use sympy to compute the polar coordinates.\n```python\nfrom sympy import sqrt,... | [
{
"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": "To find the polar coordinates of $(3, -3)$ we can use the following formula:\n\\[r = ... |
1 | [
"5"
] | [
{
"content": "If we divide $5^{2010}$ evenly into 7 parts, what will be the leftover?",
"role": "user"
},
{
"content": "We will use modular arithmetic to solve this.\n```python\nmodulus = 7\n\nfactors = 2**2010\n\nremainder = factors % modulus\nprint(remainder)\n``````",
"role": "assistant"
},... | [
{
"content": "If we divide $5^{2010}$ evenly into 7 parts, what will be the leftover?",
"role": "user"
},
{
"content": "Let's use Python's sympy library to compute the remainder.\n```python\nfrom sympy import symbols, Mod\n\nn = symbols('n')\n\n# n is the number we want to divide 5^2010 by\n# we wan... |
-1 | [
"3"
] | [
{
"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": "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"
},
{... |
4 | [
"48"
] | [
{
"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": "We know that the formula for the volume of a cube is $v = s^3$\nTherefore, $s = \\sqrt[3]... | [
{
"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 a cube is $s^3$.\nGiven a minimum volume of $64$, we find that $s = 4$.\nNo... |
3x^3-7x^2+8x-31 | [
"-7x^3+3x^2+10x-31"
] | [
{
"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": "We are given two functions $f$ and $g$. We are required to find $f(x) - g(x)$.\n```python\nfrom sympy import Symbol, simplify... | [
{
"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's use sympy to write out $f(x) - g(x)$ and simplify.\n```python\nfrom sympy import symbols, expand\n\nx = symbols('x')\nf... |
-3 | [
"-9"
] | [
{
"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": "The product of the roots can be obtained from the quadratic formula:\n```pyth... | [
{
"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": "The sum of the squares of the roots is equal to $70/9$.\nLet's find the roots... |
40 | [
"25"
] | [
{
"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": "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"
... |
\frac{1}{64} | [
"\\frac{63}{64}"
] | [
{
"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": "We will use Python's sympy library to calculate the pr... | [
{
"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 that it doesn't snow on any given day ... |
2 | [
"7"
] | [
{
"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 code.\n```python\ncost_of_a_lamp = 7\ncost_of_a_bulb = ... | [
{
"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... |
73 | [
"25"
] | [
{
"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": "Let $u = 2v - w$. Then,\n```py... | [
{
"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": "Let's use sympy to find $\\mat... |
6 | [
"4"
] | [
{
"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": "We can enumerate all possible numbers that satisfy the constraints using sympy.\n```python\nimport sympy as sp\n\n# define the digits ... | [
{
"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 try to encode a number in a 2-dimensional vector:\n- 1st dimension - 1 or 2 digits from 2 and 4\n- 2nd dimension - 1 or 2 digits... |
\frac{9}{2} | [
"0"
] | [
{
"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": "We will use sympy's solve function to find the roots of the given cubic polynomials and then compute th... | [
{
"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 solve this problem, we can set up a system of equations based on the fact that the roots of the cubi... |
120 | [
"1024"
] | [
{
"content": "In how many different ways can five students stand in a line for a photograph?",
"role": "user"
},
{
"content": "Let $N$ denote the number of ways to arrange five students in a line.\nOne way to compute $N$ is to imagine counting the ways to arrange the students by starting with a fixe... | [
{
"content": "In how many different ways can five students stand in a line for a photograph?",
"role": "user"
},
{
"content": "Each student has 4 possible options to stand: left, right, or in the middle, so there are $4^5$ possibilities.\n```python\nprint(4**5)\n``````",
"role": "assistant"
},... |
19440 | [
"3185"
] | [
{
"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": "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... |
20 | [
"12"
] | [
{
"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": "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?",
... |
2 | [
"\\frac{2}{6}"
] | [
{
"content": "Find the slope of a line that is parallel to the line represented by the equation $3y - 6x = 9$. Give your answer as a fraction.",
"role": "user"
},
{
"content": "Let's first find the equation of the line i.e. $y = mx + c$.\n```python\nfrom sympy import symbols, Eq, solve\n\n# define t... | [
{
"content": "Find the slope of a line that is parallel to the line represented by the equation $3y - 6x = 9$. Give your answer as a fraction.",
"role": "user"
},
{
"content": "The equation of a line is $3y - 6x = 9$.\nWe need to find the slope of a line parallel to this line.\nLet's rearrange the e... |
3 | [
"6"
] | [
{
"content": "How many unordered pairs of prime numbers have a sum of 40?",
"role": "user"
},
{
"content": "To solve this problem we need to generate all primes smaller than 40 and check which pairs sum to 40.\nHere is the python code to do that.\n```python\nfrom sympy import isprime\n\n# Initialize... | [
{
"content": "How many unordered pairs of prime numbers have a sum of 40?",
"role": "user"
},
{
"content": "We can enumerate all pairs of prime numbers that add up to 40 using a simple Python code as follows.\n```python\nfrom sympy import isprime\n\ncount = 0\n\nfor p in range(2, 41):\n q = 40 - ... |
15 | [
"150"
] | [
{
"content": "There are x tables in the school's cafeteria. Each table can seat 10 people. Usually, only 1/10 of the seats are left unseated. Usually, 135 seats are taken. What is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's solve this problem using Python's sympy library... | [
{
"content": "There are x tables in the school's cafeteria. Each table can seat 10 people. Usually, only 1/10 of the seats are left unseated. Usually, 135 seats are taken. What is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```pytho... |
19 | [
"3"
] | [
{
"content": "What is the positive integer \\(b\\) that satisfies the equation \\(0.76 = \\frac{4b+19}{6b+11}\\)?",
"role": "user"
},
{
"content": "Let's solve this equation.\n```python\nfrom sympy import symbols, Eq, solve\n\nb = symbols('b')\n\neq = Eq(0.76, (4*b + 19) / (6*b + 11))\nsolve(eq, b)\... | [
{
"content": "What is the positive integer \\(b\\) that satisfies the equation \\(0.76 = \\frac{4b+19}{6b+11}\\)?",
"role": "user"
},
{
"content": "To solve this problem, we can use Python's sympy library.\n```python\nfrom sympy import Symbol, Eq, solve\n\nb = Symbol('b')\nequation = Eq(0.76, (4*b+1... |
5 | [
"6"
] | [
{
"content": "What is the highest integer $n$ that can be used in $n^2 - 9n + 18 < 0$ to still have a negative result?",
"role": "user"
},
{
"content": "To find the highest integer $n$ that satisfies the inequality $n^2 - 9n + 18 < 0$, we can use sympy library to solve the inequality:\n```python\nfr... | [
{
"content": "What is the highest integer $n$ that can be used in $n^2 - 9n + 18 < 0$ to still have a negative result?",
"role": "user"
},
{
"content": "Let's try some values for $n$ from $1$ to $9$ to see if the equation is true or false.\n```python\nfor i in range(1,10):\n equation = i**2 - 9*i... |
4 | [
"5"
] | [
{
"content": "If there are 32 students in a class and each student needs 5 minutes to present their project, with each period being 40 minutes long, how many periods will it take for every student to present their project?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.... | [
{
"content": "If there are 32 students in a class and each student needs 5 minutes to present their project, with each period being 40 minutes long, how many periods will it take for every student to present their project?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.... |
8 | [
"4t+8"
] | [
{
"content": "On the first day of the week, David is able to assemble $w$ units every hour, working for a total of $t$ hours. Feeling worn out, he decides to shorten his workday on the following day by $2$ hours, although his productivity increases by $4$ units per hour. Given that $w = 2t$, what is the differe... | [
{
"content": "On the first day of the week, David is able to assemble $w$ units every hour, working for a total of $t$ hours. Feeling worn out, he decides to shorten his workday on the following day by $2$ hours, although his productivity increases by $4$ units per hour. Given that $w = 2t$, what is the differe... |
50 | [
"5000"
] | [
{
"content": "Kyle bikes for 2 hours to work every day. Ten times the time he takes to travel to work and back is the same as the cost of buying a pack of snacks (in dollars). How much will Ryan pay, in dollars, to buy x packs of snacks?\nIf we know the answer to the above question is 2000, what is the value of... | [
{
"content": "Kyle bikes for 2 hours to work every day. Ten times the time he takes to travel to work and back is the same as the cost of buying a pack of snacks (in dollars). How much will Ryan pay, in dollars, to buy x packs of snacks?\nIf we know the answer to the above question is 2000, what is the value of... |
\frac{-1}{4} | [
"0.25"
] | [
{
"content": "If $\\det \\mathbf{B} = -4,$ then evaluate $ \\det (\\mathbf{B}^{-1}).$",
"role": "user"
},
{
"content": "We know that the determinant of a matrix is the same as the determinant of its inverse, up to a factor of $-1$.\nThus we have\n```python\nprint(f\"-4 = {1/-4} = {1/(-4)}\")\n``````... | [
{
"content": "If $\\det \\mathbf{B} = -4,$ then evaluate $ \\det (\\mathbf{B}^{-1}).$",
"role": "user"
},
{
"content": "First, let's recall the formula for the determinant of a matrix product:\n\\begin{equation*}\n\\det(\\mathbf{AB}) = \\det(\\mathbf{A})\\det(\\mathbf{B})\n\\end{equation*}\nIf we ta... |
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