messages listlengths 4 12 |
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[
{
"content": "If $y = x-a+3$ and the value of $x$ is $a+7$, find the value of $y$.",
"role": "user"
},
{
"content": "We can substitute $x = a + 7$ into $y = x - a + 3$ to get\n$y = x - a + 3 = (a + 7) - a + 3 = 10$.\nLet's verify this using sympy.\n```python\nimport sympy as sp\n\n# define the symbo... |
[
{
"content": "Seven identical bowling balls weigh the same as four identical canoes. If three of the canoes weigh a total of X pounds, One of the bowling balls weighs 16 pounds. What is the value of unknown variable X?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n``... |
[
{
"content": "For each positive integer $n$, let $n!$ denote the product $1\\cdot 2\\cdot 3\\cdot\\,\\cdots\\,\\cdot (n-1)\\cdot n$.\n\nWhat is the remainder when $9! + 11$ is divided by $11$?",
"role": "user"
},
{
"content": "We can compute this directly using Python.\n```python\nimport math\n\nx =... |
[
{
"content": "Kim drives 30 miles to her friend's house. On the way back she has to take a detour that is x% longer. She spends 30 minutes at her friend's house. She drives at a speed of 44 mph. How long did she spend away from home?\nIf we know the answer to the above question is 2, what is the value of un... |
[
{
"content": "Jack is on the phone with a scammer who says the IRS will arrest Jack if he doesn't send them the codes from 6 $500 Best Buy gift cards and 9 $200 Walmart gift cards. After sending the codes for 1 Best Buy gift card and 2 Walmart gift cards, Jack wises up and hangs up. How many dollars' worth of g... |
[
{
"content": "If a container has a volume of 12 cubic yards and another container has a volume of 8 cubic yards, what is the total volume of the two containers in cubic feet?",
"role": "user"
},
{
"content": "Let's use sympy and numpy to solve this problem.\n```python\nimport sympy as sp\nimport num... |
[
{
"content": "How many diagonals can be drawn from a single vertex of a regular pentagon (a 5-sided polygon)?",
"role": "user"
},
{
"content": "Let's use sympy to find the number of diagonals from a vertex in a regular pentagon.\nA diagonal is a line that connects two non-adjacent vertices.\nLet $n$... |
[
{
"content": "What is the result of evaluating the expression $(5^2-4^2)^3$?",
"role": "user"
},
{
"content": "Let's use sympy to evaluate the expression.\n```python\nfrom sympy import Symbol, simplify\n\n# define the variable\nx = Symbol('x')\n\n# the expression to evaluate\nexpr = (x**2-4**2)**3\n... |
[
{
"content": "Liam wants to go to Paris, but first, he has to pay his bills. His trip costs $7,000, and his bills cost x. Knowing that Liam has saved $500/month for 2 years, how much money will he have left after paying his bills?\nIf we know the answer to the above question is 8500, what is the value of unknow... |
[
{
"content": "If the greatest common divisor (GCD) of $400$ and $450$ is added to the sum of all distinct prime factors of their least common multiple (LCM), what is the result?",
"role": "user"
},
{
"content": "Let's list the prime factors of 400 and 450 and then find their LCM and GCD.\nWe will th... |
[
{
"content": "Theo and Tia are purchasing food for their picnic basket, including individual sandwiches and fruit salads for themselves and their two friends. They are also buying two sodas per person and 3 bags of snacks to share. The cost of each sandwich is $5, each fruit salad is $3, each soda is $2, and ea... |
[
{
"content": "Ruth prepared sandwiches. She ate 1 sandwich and gave 2 sandwiches to her brother. Her first cousin arrived and ate 2 sandwiches. Then her two other cousins arrived and ate 1 sandwich each. There were x sandwiches left. Ruth prepared 10 sandwiches. What is the value of unknown variable x? What is ... |
[
{
"content": "A solid triangular prism has a right triangular base with legs of lengths 5 units and 12 units, and the height of the prism is 7 units. What is the volume, in cubic units, of the prism?",
"role": "user"
},
{
"content": "The volume of a triangular prism can be computed as base times hei... |
[
{
"content": "A rectangular garden has the same area as a right triangle with sides of $6$ units, $8$ units, and $10$ units. If the width of the garden is $4$ units, and a path of width $1$ unit runs along the inside of the entire perimeter of the garden, what is the area covered by the path in square units?",
... |
[
{
"content": "There are 30 pieces of popcorn in a serving. Jared can eat 90 pieces of popcorn and his three other friends can each eat 60 pieces of popcorn. How many servings of popcorn should Jared order for all of them?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\... |
[
{
"content": "Given $\\mathbf{a} = \\begin{pmatrix} -7 \\\\ 0 \\\\ X \\end{pmatrix}$ and $\\mathbf{b} = \\begin{pmatrix} 4 \\\\ 2 \\\\ -1 \\end{pmatrix},$ find $\\mathbf{a} - 3 \\mathbf{b}.$\nIf we know the answer to the above question is \\begin{pmatrix}-19\\-6\\4\\end{pmatrix}, what is the value of unknown va... |
[
{
"content": "Let the operation $\\#$ be defined as $\\#(a, b, c) = b^2 - 4ac$, for all real numbers $a, b$ and $c$. What is the value of $\\#(1, X, The value of 3) is -8. What is the value of unknown variable X?",
"role": "user"
},
{
"content": "We can define a function based on the given rule and ... |
[
{
"content": "Tom is cutting a piece of wood to make a shelf. He cut the wood to 143 cm, but it is too long to fit in the bookshelf he is making. He decides to cut 25 cm off the board. But it turned out longer than the other boards. He had to cut off 7 cm from each to make them the same size. How long were the ... |
[
{
"content": "Tommy goes for a run around his neighborhood and decides to calculate how many wheels he saw. All the trucks in his neighborhood have 4 wheels and all the cars in his neighborhood also have 4 wheels. If he saw x trucks and 13 cars, He saw 100 wheels. What is the value of unknown variable x? What i... |
[
{
"content": "If $x^2+3x-7=0$ has roots $a$ and $b$, find the value of $10(2a-3)(4b-6) + 16$.",
"role": "user"
},
{
"content": "We can solve quadratic equation to get $a$ and $b$. Then we can put these values to expression and calculate the result.\n```python\ndef solve_quadratic(a, b, c):\n # D... |
[
{
"content": "Consider a right-angled triangle with $\\angle B$ being the right angle. There's a circle whose diameter is side $BC$ and it intersects side $AC$ at point $D$. The area of this triangle is $150$ square units and the length of $AC$ is $25$ units. Find the length of $BD$.",
"role": "user"
},
... |
[
{
"content": "Alissa used discarded paper to make notepads for her friends. She would fold 5 pieces of letter-size paper 3 times then cut along the edges to form smaller note papers. She would then stack these smaller note papers and staple them together. How long would 1 notepad last if someone wrote 10 notes ... |
[
{
"content": "What is the sum of the smallest positive multiple of $32$, the smallest positive multiple of $8$, and the smallest positive multiple of $5$?",
"role": "user"
},
{
"content": "The smallest positive multiple of $32$ is $32$, the smallest positive multiple of $8$ is $8$, and the smallest ... |
[
{
"content": "Calculate the value of $f(g(5))$ for the functions $f(x) = x^2 + 1$ and $g(x) = 2x - 1$.",
"role": "user"
},
{
"content": "Let's plug $g(5)$ directly in $f(x)$.\n```python\nx = 5\nf = lambda x: x**2 + 1\ng = lambda x: 2*x - 1\n\nprint(f(g(x)))\n```",
"role": "assistant"
},
{
... |
[
{
"content": "What is the smallest odd abundant number?",
"role": "user"
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{
"content": "We can solve this problem by checking all the odd numbers for which they are abundant.\n```python\n# An abundant number is a number that is less than the sum of its proper divisors\ndef is_abundant(n):\n div... |
[
{
"content": "If Emily uses the same method to calculate $45^2$ by squaring 50 and subtracting a number, and calculates $40^2$ by squaring 30 and adding a different number, what are the two numbers she subtracts and adds?",
"role": "user"
},
{
"content": "Let's use sympy to solve this:\n```python\nf... |
[
{
"content": "Koalas absorb only X of the fiber they eat. A koala absorbed 10.5 ounces of fiber in one day. He ate 42 ounces of fiber that day. What is the value of unknown variable X?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\n# let's solve for X\neq =... |
[
{
"content": "UF got into the national championship. For them to get into the championship, they scored a total of 720 points during their previous 24 games. In the championship game, however, their opponent was much stronger than any other team they had previously gone against and they scored 2 points less th... |
[
{
"content": "Square $WXYZ$ has an area of $2500.$ A circle has a circumference of $50\\pi$ and passes through $W$ and $Y$ with its center at point $X.$ What is the side length of the square?",
"role": "user"
},
{
"content": "The correct answer is 50. Here's the Python code to solve the problem and ... |
[
{
"content": "Starting from 100 and ending at 900, how many numbers will you encounter that are exact cubes of natural numbers?",
"role": "user"
},
{
"content": "Since we're looking at cubes, we need to look for numbers of the form $x^3$ between $100$ and $900$.\nRather than enumerating, we can iter... |
[
{
"content": "If the side lengths of a triangle are $\\sqrt{2u-1}$, $\\sqrt{2u+1}$, and $2\\sqrt{u}$, what is the measure of the largest angle in degrees?",
"role": "user"
},
{
"content": "Since $\\sqrt{2u - 1} < \\sqrt{2u + 1}$, a maximum angle means the side $\\sqrt{2u - 1}$ is the longest, follow... |
[
{
"content": "Assuming an algebra test at the Education Emporium requires a pass mark of $80\\%$ and consists of 35 items, what is the largest count of questions one can fail to answer correctly and still meet the passing criterion?",
"role": "user"
},
{
"content": "Let $n$ be the number of question... |
[
{
"content": "Which of the following statements are true?\n\nA. 4 is a factor of 64.\n\nB. 17 is a divisor of 289.\n\nC. 12 is a divisor of 144.\n\nD. 13 is a divisor of 78.\n\nE. 9 is a factor of 81.\n\nWrite your answer with the letters in alphabetical order, separated by commas. For example, if you thi... |
[
{
"content": "To calculate $41^2$, David mentally figures the value $40^2$ and adds X. David subtracts a number from $40^2$ to calculate $39^2$. What number does he subtract?\nIf we know the answer to the above question is 79, what is the value of unknown variable X?",
"role": "user"
},
{
"content":... |
[
{
"content": "If I divide a four-digit number by 7 and get a remainder of 6, what is the smallest such number I could have?",
"role": "user"
},
{
"content": "Let's use sympy to check each digit of the 4 digit number.\n```python\nimport sympy\n\nfor i in range(1000, 10000):\n if i % 7 == 6:\n ... |
[
{
"content": "Rationalize the denominator of $\\displaystyle\\frac{5}{\\sqrt{5}}$.",
"role": "user"
},
{
"content": "We can use Python's sympy library to rationalize the denominator of $\\frac{5}{\\sqrt{5}}$.\n```python\nfrom sympy import sqrt, ratsimp, simplify\nfrom sympy.abc import M\n\nM = sqrt(... |
[
{
"content": "For which highest value of $x$ does the fraction \\[\\frac{x+1}{8x^2-65x+8}\\] fail to have a valid value?",
"role": "user"
},
{
"content": "The fraction fails to have a valid value when the denominator is 0.\n```python\nfrom sympy import symbols, solve\n\n# let's define the variables ... |
[
{
"content": "Three vertices of a cube are $P=(7,12,10)$, $Q=(8,8,1)$, and $R=(11,3,9)$. What is the surface area of the cube?",
"role": "user"
},
{
"content": "Let's calculate all the distances $QP$, $QR$, $PR$.\n```python\nfrom sympy import Point3D, pi, sqrt\n\npoint_p = Point3D((7, 12, 10))\npoin... |
[
{
"content": "If $(x^2-9)(x^2-16)=0$, what is the sum of the squares of all the integer solutions of the equation?",
"role": "user"
},
{
"content": "Let's write down the equation and solve it using sympy.\n```python\nfrom sympy import symbols, Eq, solve\n\n# define the variables\nx = symbols('x')\n\... |
[
{
"content": "Clare's mother gave her $47 to go to the store. Clare bought 4 loaves of bread and 2 cartons of milk. Each loaf of bread cost $2 and each carton of milk cost x. Clare has 35 money left. What is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's solve this problem ... |
[
{
"content": "If $m$ is an integer and $0 < 5m < 35$, what is the sum of all possible integer values of $m$?",
"role": "user"
},
{
"content": "In Python, we can use a for loop to iterate over all the possible values of $m$ satisfying the given conditions, and then sum up the values.\n```python\nposs... |
[
{
"content": "Find the sum that is closest to 1, and express it as a mixed number in simplest form:\n$$\\frac{3}{5} + \\frac{1}{2}, \\ \\ \\frac{3}{5} + \\frac{1}{4}, \\ \\ \\frac{3}{5} + \\frac{1}{3}, \\ \\ \\frac{3}{5} + \\frac{2}{5}, \\ \\ \\frac{3}{5} + \\frac{1}{6}$$",
"role": "user"
},
{
"cont... |
[
{
"content": "Consider an integer such that it can be divided evenly by $4$, and the total of its last two digits equals $13$. What would be the multiplication result of those two digits?",
"role": "user"
},
{
"content": "We can iterate through all numbers from 1 to 99 which are exactly divisible by... |
[
{
"content": "Find the value of $x$ between 0 and 180 such that\n\\[\\tan (120^\\circ - x^\\circ) = \\frac{\\sin 120^\\circ - \\sin x^\\circ}{\\cos 120^\\circ - \\cos x^\\circ}.\\]",
"role": "user"
},
{
"content": "Let's solve it using python:\n```python\nimport math\n\ndef f(x):\n return math.ta... |
[
{
"content": "Janet has 24 dresses. Half of them have pockets. Of those, a third have 2 pockets and the rest have 3 pockets. How many total pockets do her dresses have?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\n# number of dresses in total\nnum_dres... |
[
{
"content": "A fair 6-sided die is rolled. What is the probability that the number rolled is a divisor of X?\nIf we know the answer to the above question is \\frac{2}{3}, what is the value of unknown variable X?",
"role": "user"
},
{
"content": "The probability of a number to be divisible by 3 is ... |
[
{
"content": "Brennan was researching his school project and had to download files from the internet to his computer to use for reference. After downloading 800 files, he deleted 70% of them because they were not helpful. He downloaded 400 more files but again realized that 3/5 of them were irrelevant. How many... |
[
{
"content": "Compute the real part of $(1 + i)^8.$",
"role": "user"
},
{
"content": "We can compute this directly using complex numbers:\n```python\nfrom cmath import exp\n\nnum = 1 + 1j\n\n# Take the 8th power and extract only the real part\nreal_part = num**8.0\nreal_part.real\n```",
"role": ... |
[
{
"content": "What is the greatest common factor of $132$ and $198$?",
"role": "user"
},
{
"content": "We can use the following Mathematica script to do the factorization:\n\n```python\nfrom sympy import gcd\nprint(gcd(132,198))\n```",
"role": "assistant"
},
{
"content": "```output\n66\n... |
[
{
"content": "Suppose you have 12 containers of different sizes with a positive amount of water in each. Together, these containers hold exactly 1 liter of water. What is the minimum sum of the reciprocals of the volumes of these containers in liters?",
"role": "user"
},
{
"content": "We can formula... |
[
{
"content": "Find the greater of two numbers if their sum is 31 and they are 3 units apart.",
"role": "user"
},
{
"content": "Let's define two variables a and b, denoting the two numbers.\nTheir sum is $31$ and the difference is $3$.\nSo we can write the following equations: $a + b = 31$ and $a - b... |
[
{
"content": "Calculate the result of the quadratic expression $x^2 + 5x - 6$ given that $x$ equals $-1$.",
"role": "user"
},
{
"content": "We can use the following Mathematica script to do the calculation.\n```python\nfrom sympy import symbols, Eq\n\n# Define x, and the equation to be evaluated\nx ... |
[
{
"content": "If I want to organize my five different keys on a circular key holder and ensure my house key is always adjacent to my car key, how many unique configurations are possible? Remember, arrangements that can rotate or reflect into another are indistinguishable.",
"role": "user"
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{
"cont... |
[
{
"content": "Calculate the number of positive factors for the integer $P = 2^2 \\cdot 3^5 \\cdot 7^1 \\cdot 11^1$.",
"role": "user"
},
{
"content": "To calculate the total number of positive factors for the integer, we will use Python's sympy library.\n```python\nfrom sympy import divisor_count\n\n... |
[
{
"content": "A square has an area of X A rectangle has the same width as the square. The length of the rectangle is double its width. The area of the rectangle is 50. What is the value of unknown variable X?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\n#... |
[
{
"content": "Caleb picked a handful of dandelion puffs. He gave 3 to his mom, another 3 to his sister, 5 to his grandmother, and 2 to his dog. Then, he divided the remaining dandelion puffs equally among his 3 friends. Each friend received 9 dandelion puffs if he originally picked x dandelion puffs. What is th... |
[
{
"content": "Brenda has two stops to make, starting from $(-4,5)$ to $(0,0)$ and then from $(0,0)$ to $(5,-4)$. What is the sum of the distances for both legs of her journey?",
"role": "user"
},
{
"content": "Distance formula: $d = \\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$. We have:\n\n$d_1 = \\sqrt{(... |
[
{
"content": "If $(a + b)^2 = 64$ and $ab = 12$, what is $(a - b)^2$?",
"role": "user"
},
{
"content": "Using the difference of two squares expansion, we have\n```python\nfrom sympy import symbols, expand, solve\n\n# let a and b be positive\na, b = symbols('a b', positive=True)\n\neq1 = (a + b)**2 -... |
[
{
"content": "James needs to get a new pair of glasses. His frames cost $200 and the lenses cost $500. Insurance will cover 80% of the cost of lenses and he has a $50 off coupon for frames. How much does everything cost?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code... |
[
{
"content": "What is the base seven equivalent of $250_{10}$?",
"role": "user"
},
{
"content": "Let's convert $250_{10}$ to base seven by repeatedly dividing by 7 and keeping track of the remainders.\n```python\nnum = 250\nbase = 7\nprint('base 10 = ', num)\nrems = []\nwhile num > 0:\n rem = num... |
[
{
"content": "Determine the fractional representation of the repeating decimal $0.\\overline{73}$.",
"role": "user"
},
{
"content": "We can use Python's fractions library to represent and solve repeating decimals.\n```python\nfrom fractions import Fraction\n\nrepeating_decimal = Fraction(73, 99)\nre... |
[
{
"content": "A cookie recipe calls for 2 cups of flour for every 30 cookies. How much flour is necessary if one needs to produce a batch of 60 cookies instead?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\ncookies_required = 60\nflour_per_30_cookies = 2\n... |
[
{
"content": "Given that the points $(2,m,n),$ $(m,3,n),$ and $(m,n,4)$ are on the same straight line, what is $m + n$?",
"role": "user"
},
{
"content": "A straight line contains the equation\n$Ax + By + Cz - D = 0$, where $D$ is a constant.\nFor example, the line $y = x$ has the equation $Ax = x$.\... |
[
{
"content": "At a gathering, it was reported that 26 people took wine, 22 people took soda, and 17 people took both drinks. If each person could have taken one or more drinks regardless of what was reported, how many people altogether were at the gathering?",
"role": "user"
},
{
"content": "Let's s... |
[
{
"content": "If $f(x) = 3x^2 - 7$ and $g(f(4)) = 9$, what is the value of $g(f(-4))$?",
"role": "user"
},
{
"content": "```python\nf = lambda x: 3*x**2 - 7\ng = lambda y: 9\n\nresult = g(f(-4))\nprint(result)\n```",
"role": "assistant"
},
{
"content": "```output\n9\n```",
"role": "u... |
[
{
"content": "You have x to spend on groceries. You buy a loaf of bread for 3$, a candy bar for 2$, and 1/3 of whats left on a Turkey. You have 18 money left. What is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's solve this problem using Python's sympy library.\n```python... |
[
{
"content": "How many positive perfect square integers are factors of the product $\\left(2^{8}\\right)\\left(3^{10}\\right)\\left(7^{14}\\right)$?",
"role": "user"
},
{
"content": "A positive perfect square integer is one that can be written as $x^2$ for some positive integer $x$.\nWe can iterate ... |
[
{
"content": "Calculate the value of $(-5)^5\\div5^3+3^{4}-6^{1}\\times2^2$.",
"role": "user"
},
{
"content": "Let's write this out as a Python expression using the power operator `**` and the multiplication operator `*`:\n```python\n(-5)**5//5**3 + 3**4 - 6**1 * 2**2\n```",
"role": "assistant"
... |
[
{
"content": "Maurice had only been horseback riding a handful of times in his life. His best friend, Matt, goes horseback riding regularly. When Maurice went to visit Matt for two weeks, he rode another x times. Each time, Matt went with him. Meanwhile, besides the times that Matt accompanied Maurice, he rode ... |
[
{
"content": "If $95^2$ is increased by $5^2$ and then decreased by $25$, what is the result?",
"role": "user"
},
{
"content": "Let's solve it using python:\n```python\nproduct_of_95_squared = 95 * 95\nincreased_by_square_of_5 = product_of_95_squared + 5 * 5\ndecreased_by_minus_25 = increased_by_squ... |
[
{
"content": "If each boat in a boat race is 3 feet across and there needs to be at least 2 feet of space between the boats or the riverbank, what is the maximum number of boats that can race in a river that is 42 feet across?",
"role": "user"
},
{
"content": "Let's solve this problem using Python's... |
[
{
"content": "Regions I, II and III are bounded by squares. The perimeter of region I is 12 units and the perimeter of region II is 24 units. What is the ratio of the area of region I to the area of region III? Express your answer as a common fraction.\n\n[asy]\ndraw((0,0)--(9,0)--(9,9)--(0,9)--(0,0)--cycle,lin... |
[
{
"content": "What is the outcome of raising negative twenty-seven to the five-thirds power?",
"role": "user"
},
{
"content": "Raising a number, $x$, to the power of $y$ is the same as multiplying $x$ by itself, $y$ times. In sympy we can write this as $x^y$.\nIn our case we need to raise $-27$ to t... |
[
{
"content": "There are 480 grains of rice in one cup. If x% a cup is 8 tablespoons and one tablespoon is 3 teaspoons, There are 10 grains of rice in a teaspoon. What is the value of unknown variable x? What is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's solve this probl... |
[
{
"content": "Abigail, Beatrice, Carson, and David combine their eggs to sell them at the market. If Abigail has 37 eggs, Beatrice has 49 eggs, Carson has 14 eggs, and David has 31 eggs, and if eggs can only be sold in cartons of 12, how many eggs will be left over if all cartons are sold?",
"role": "user"
... |
[
{
"content": "Simplify $(5 \\times 10^7) \\div (2 \\times 10^2)$. (Your answer should be a single number, with no products or quotients.)",
"role": "user"
},
{
"content": "Let's use sympy.\n```python\nimport sympy as sp\n\nN, M, P, Q, O = sp.symbols('N M P Q O')\n\nsolution = sp.simplify((5 * 10**7)... |
[
{
"content": "What is the positive difference between the two solutions of $|3x - 4| = 18$?",
"role": "user"
},
{
"content": "We can easily solve the equation.\n```python\nimport sympy\n\n# Because |3x - 4| = 18, we can write 3x - 4 = 18 or 3x - 4 = -18.\n# Solving 3x - 4 = 18 for x\nx_1 = sympy.sym... |
[
{
"content": "If a woodworker has crafted a total of 40 furniture legs, which is the exact amount needed for their projects, and they have built 6 chairs using these legs, how many tables have they made?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\nchairs... |
[
{
"content": "In a quadrilateral, three angles measure 42 degrees, 78 degrees, and 90 degrees. What is the degree measure of the fourth angle?",
"role": "user"
},
{
"content": "Since the sum of all the angles of a quadrilateral is 360, and we know three angles, the unknown one is $x$ so its value is... |
[
{
"content": "If $f(x) = x^k$ and $k < 0$, what is the range of $f(x)$ for values of $x$ in the interval $[1, \\infty)$?",
"role": "user"
},
{
"content": "If $x \\in [1, \\infty)$, then $f(x) = x^k \\in (0, 1)$.\nHence, the answer is:\n```python\n'Range: (0, 1)'\n```",
"role": "assistant"
},
... |
[
{
"content": "A right triangle has a 24-inch leg and a 25-inch hypotenuse. A square is inscribed in this triangle so that one of its sides lies on the hypotenuse. What is the combined area, in square inches, of the right triangle and the square?",
"role": "user"
},
{
"content": "We can use the Pytha... |
[
{
"content": "If there are 3 convenience stores along Jason's route to work, with a distance of 6 miles between the first and second store and a distance that is 2/3rds longer between the second and third store compared to the first two stores, and if the distance from Jason's house to the first store and from ... |
[
{
"content": "Haily wants to go to the salon and do her nails, cut her hair and do a facial cleaning. She doesn't want to spend much, so she called 3 salons to get their prices: Gustran Salon, Barbara's Shop, and The Fancy Salon. At Gustran Salon, the haircut is $45, the facial cleaning is $22 and the nails are... |
[
{
"content": "Find $\\dbinom{200}{200}$.",
"role": "user"
},
{
"content": "Let's use sympy:\n```python\nfrom sympy import binomial\nprint(binomial(200, 200))\n```",
"role": "assistant"
},
{
"content": "```output\n1\n```",
"role": "user"
},
{
"content": "So $\\dbinom{200}{200}... |
[
{
"content": "Matthew, the baker, arrives at work early every morning to make his famous caramel-apple coffee cakes for the day. It usually takes Matthew 1 hour to assemble ingredients, 1.5 hours to bake the cakes, and another 1 hour to decorate each cake with cinnamon sprinkles. One day, Matthew's oven faile... |
[
{
"content": "If $a=2$ and $b=\\frac{2^2 \\cdot 2^{-3}}{2^3 \\cdot 2^{-2}}$, what is the value of $a^2b$?",
"role": "user"
},
{
"content": "We can compute $a^2b$ as follows:\n\n```python\na = 2\nb = (2**2 * 2**(-3)) / (2**3 * 2**(-2))\n\n# a^2 cpu * b\na**2 * b\n```",
"role": "assistant"
},
... |
[
{
"content": "How much is $\\frac{7}{12}$ minus $\\frac{1}{3}$?",
"role": "user"
},
{
"content": "Let's write this out as a sympy expression and simplify.\n```python\nfrom sympy import Rational, simplify\n\nleft_term = Rational(7, 12)\nright_term = Rational(1, 3)\n\nprint(f\"{left_term - right_term}... |
[
{
"content": "John scores 2 shots worth x points and 1 shot worth 3 points every 4 minutes. He plays for 2 periods. Each period is 12 minutes. He scores 42 points. What is the value of unknown variable x?",
"role": "user"
},
{
"content": "Let's solve this problem using Python code.\n```python\npoi... |
[
{
"content": "Find the least common multiple of 18 and 32.",
"role": "user"
},
{
"content": "Let's use sympy to solve this problem.\n```python\nfrom sympy import lcm\n\na = 18\nb = 32\n\nprint(lcm(a, b))\n```",
"role": "assistant"
},
{
"content": "```output\n288\n```",
"role": "user"... |
[
{
"content": "In the set of two-digit natural numbers, find the total count of numbers where at least one of the digits is a 7.",
"role": "user"
},
{
"content": "We can iterate through all numbers from 10 to 99 and check if one of the digits is 7:\n```python\ncount = 0\n\nfor num in range(10, 100):\... |
[
{
"content": "Determine the slope of the line represented by the equation $2y = -3x + 6$.",
"role": "user"
},
{
"content": "Let's first try the sympy solution.\n```python\nimport sympy as sp\n\n# define a symbol x\nx = sp.symbols('x')\n\n# define a symbol y\ny = sp.symbols('y')\n\n# write the equati... |
[
{
"content": "Determine the slope of the straight line that intersects the middle points of the segments joining (0, 0) to (2, 3) and (5, 0) to (6, 3). Provide your response in the simplest form possible.",
"role": "user"
},
{
"content": "Let A = (0, 0), B = (2, 3), C = (5, 0), and D = (6, 3).\nThe ... |
[
{
"content": "At his craftwork store, Howard has a collection of 70 wooden bowls where he rewards two to his customers for every 10 they buy. If he had 20 customers that day, half of whom bought 20 bowls each, calculate the number of bowls remaining in the rewards collection.",
"role": "user"
},
{
"... |
[
{
"content": "A point $P$ is located on the vertical line represented by the equation $x= -3$. If this point is 10 units distant from another point with coordinates $(5,2)$, what is the product of all potential $y$-coordinates of point $P$?",
"role": "user"
},
{
"content": "Let's write down the equa... |
[
{
"content": "A rectangle $R$ in the plane has area 40. We apply three successive linear transformations to $R$ using matrices $\\begin{pmatrix} 2 & 1 \\\\ 7 & -3 \\end{pmatrix}$, $\\begin{pmatrix} 1 & 3 \\\\ -2 & 4 \\end{pmatrix}$, and $\\begin{pmatrix} 1 & 0 \\\\ 0 & 2 \\end{pmatrix}$, resulting in a new para... |
[
{
"content": "How many different positive, five-digit integers can be formed using the digits 2, 2, 2, 9 and 9?",
"role": "user"
},
{
"content": "Let's list out all possible 5 digit numbers using the digits 2 and 9.\nThis is a bit tricky to do using sympy.\nWe need to create a string of characters c... |
[
{
"content": "If a man initially had 39 cows and 25 of them died last year, and he sold 6 more, then this year the number of cows increased by 24 and he bought an additional 43 cows. In addition, his friend gave him 8 cows as a gift. What is the current total number of cows the man has?",
"role": "user"
}... |
[
{
"content": "If you have $0.1$ kg of a substance and you distribute it equally into containers each weighing $0.004$ kg, how many containers can you fill?",
"role": "user"
},
{
"content": "We can use sympy to calculate the number of containers.\n```python\nfrom sympy import Rational\n\n# Define the... |
[
{
"content": "If $x = X$, The value of $2x + 3$ is 9. What is the value of unknown variable X?",
"role": "user"
},
{
"content": "We can use Python's sympy library to solve the equation.\n```python\nfrom sympy import symbols, Eq, solve\n\nx = symbols('x')\n# Define the expression\nexpr = 2 * x + 3\n\... |
[
{
"content": "In 5 years, Frank will be three times as old as Ty is now. Ty is currently 4 years more than two times as old as Carla is now. Carla is currently 2 years older than Karen is now. If Karen is currently 2 years old, how old will Frank be in 5 years?",
"role": "user"
},
{
"content": "Let'... |
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