conversations listlengths 2 2 |
|---|
[
{
"from": "human",
"value": "A restaurant sells small pizzas for $8, medium pizzas for $12, and large pizzas for $15. If they sell 8 small pizzas, 5 medium pizzas, and 4 large pizzas per day, how much money does the restaurant earn per week?"
},
{
"from": "gpt",
"value": "We are given the prices... |
[
{
"from": "human",
"value": "What is the value of $x$ in the equation $x + 2.43 = 1.2 + 5$?"
},
{
"from": "gpt",
"value": "We are given the equation:\n\n$$\nx + 2.43 = 1.2 + 5\n$$\n\n### Step 1: Simplify the right-hand side\n$$\n1.2 + 5 = 6.2\n$$\n\nSo the equation becomes:\n\n$$\nx + 2.43 = 6.2... |
[
{
"from": "human",
"value": "Find the value of $\\left(5^2-4^2\\right)^3$ modulo 10.\n\nThe new problem requires a different approach, as it involves finding the remainder of the expression when divided by 10. This requires knowledge of modular arithmetic and properties of exponents."
},
{
"from": "... |
[
{
"from": "human",
"value": "Principal Maria has to review 8 assignments for each student in her school. If she has 4 classes with 28 students in each class, how many assignments must she review in total?"
},
{
"from": "gpt",
"value": "We are given the following information:\n\n- Principal Maria... |
[
{
"from": "human",
"value": "Principal Maria has to review 8 assignments for each student in her school. If she has 4 classes with 28 students in each class, how many assignments must she review in total?"
},
{
"from": "gpt",
"value": "We are given the following information:\n\n- Principal Maria... |
[
{
"from": "human",
"value": "Find the value of x that makes the expression $\\frac{x}{15}+\\frac{3}{20}$ equal to $\\frac{2}{3}$."
},
{
"from": "gpt",
"value": "We are given the equation:\n\n$$\n\\frac{x}{15} + \\frac{3}{20} = \\frac{2}{3}\n$$\n\n### Step 1: Subtract $\\frac{3}{20}$ from both si... |
[
{
"from": "human",
"value": "Evaluate $(a^b)^a - (b^a)^b$ for $a = 2$ and $b = 3$."
},
{
"from": "gpt",
"value": "We are asked to evaluate the expression:\n\n$$\n(a^b)^a - (b^a)^b\n$$\n\nfor $ a = 2 $ and $ b = 3 $.\n\n---\n\n### Step 1: Substitute the values\n\nSubstitute $ a = 2 $ and $ b = 3 ... |
[
{
"from": "human",
"value": "A function f(x) is defined as f(x) = 3x + 1. If f(3) = 10, what is the value of f(f(3))?"
},
{
"from": "gpt",
"value": "We are given the function:\n\n$$\nf(x) = 3x + 1\n$$\n\nand we are told that:\n\n$$\nf(3) = 10\n$$\n\nWe are asked to find:\n\n$$\nf(f(3))\n$$\n\n--... |
[
{
"from": "human",
"value": "Consider the function $f(x) = x^2 + 2x - 3$. Evaluate $f(2) + 2f(-2)$.\n\nNote: The generated problem is similar in structure and requires a similar approach, evaluating the function at specific values and combining the results, while changing the coefficients and constants in ... |
[
{
"from": "human",
"value": "A bakery is making a special batch of cookies for a holiday sale. They need to package 432 cookies into boxes that hold 12 cookies each. How many boxes will they need to buy to package all the cookies?"
},
{
"from": "gpt",
"value": "To determine how many boxes are ne... |
[
{
"from": "human",
"value": "Find the value of $y$ such that $\\sqrt{y-3} = 5$."
},
{
"from": "gpt",
"value": "We are given the equation:\n\n$$\n\\sqrt{y - 3} = 5\n$$\n\n### Step 1: Eliminate the square root\nTo get rid of the square root, we square both sides of the equation:\n\n$$\n(\\sqrt{y -... |
[
{
"from": "human",
"value": "Emily has 8 sets of candles, with each set containing 15 candles. How many candles does Emily have?"
},
{
"from": "gpt",
"value": "We are given that Emily has **8 sets of candles**, and **each set contains 15 candles**.\n\n---\n\n### Step 1: Understand the problem\nW... |
[
{
"from": "human",
"value": "Samantha wants to buy 8 apples and 12 grapes. If apples cost $1.25 each and grapes cost $2 each, how much money does Samantha need to purchase 8 apples and 12 grapes?"
},
{
"from": "gpt",
"value": "Let's break the problem down step by step.\n\n### Step 1: Cost of app... |
[
{
"from": "human",
"value": "Simplify $\\frac{6x^2+4x}{2x^2-5x}$ when $x=2$."
},
{
"from": "gpt",
"value": "We are asked to simplify the expression:\n\n$$\n\\frac{6x^2 + 4x}{2x^2 - 5x}\n$$\n\nand evaluate it when $ x = 2 $.\n\n---\n\n### **Step 1: Substitute $ x = 2 $ into the expression**\n\nWe... |
[
{
"from": "human",
"value": "The operation $*$ is defined as $\\frac{a}{b}* \\frac{c}{d} = (a)(c)(\\frac{b}{d}).$ What is the simplified value of $\\frac{3}{5}*\\frac{9}{2}$?"
},
{
"from": "gpt",
"value": "We are given a custom operation $ * $ defined as:\n\n$$\n\\frac{a}{b} * \\frac{c}{d} = a ... |
[
{
"from": "human",
"value": "Savannah purchased 3 boxes of markers, with each box containing 8 markers, at a price of $1.50 per marker. What was the total cost of the markers that Savannah bought?"
},
{
"from": "gpt",
"value": "We are given the following information:\n\n- Savannah purchased **3 ... |
[
{
"from": "human",
"value": "Mr. Thompson teaches science in three levels of classes in his school. There are five times as many students in Mr. Thompson's second-level science class as in his fifth-level science class. The number of students in his third-level science class is three times that in the secon... |
[
{
"from": "human",
"value": "Mr. Thompson teaches science in three levels of classes in his school. There are five times as many students in Mr. Thompson's second-level science class as in his fifth-level science class. The number of students in his third-level science class is three times that in the secon... |
[
{
"from": "human",
"value": "Emily has $15. She spent $2.50 on a snack and then spent another $3.75 on a magazine. How much money, in dollars, does Emily have left?"
},
{
"from": "gpt",
"value": "Let's solve this step by step.\n\nEmily starts with **$15.00**.\n\n### Step 1: Subtract the cost of ... |
[
{
"from": "human",
"value": "Compute tan^2(45°) + cos^2(90°)."
},
{
"from": "gpt",
"value": "We are asked to compute:\n\n$$\n\\tan^2(45^\\circ) + \\cos^2(90^\\circ)\n$$\n\n---\n\n### Step 1: Evaluate $\\tan(45^\\circ)$\n\nWe know that:\n\n$$\n\\tan(45^\\circ) = 1\n$$\n\nSo:\n\n$$\n\\tan^2(45^\\c... |
[
{
"from": "human",
"value": "Find the result of (6t^2 - 3t + 2) - (4t^2 + 2t - 6)."
},
{
"from": "gpt",
"value": "We are asked to simplify the expression:\n\n$$\n(6t^2 - 3t + 2) - (4t^2 + 2t - 6)\n$$\n\n---\n\n### **Step 1: Distribute the negative sign**\n\nWe need to subtract the entire second ... |
[
{
"from": "human",
"value": "Given the function $f(x) = x^2 - 4$, what is the value of $f(2)$?"
},
{
"from": "gpt",
"value": "We are given the function:\n\n$$\nf(x) = x^2 - 4\n$$\n\nWe are asked to find the value of $ f(2) $.\n\n---\n\n### Step 1: Substitute $ x = 2 $ into the function\n\n$$\nf(... |
[
{
"from": "human",
"value": "Solve for $x$: $\\frac{5}{x} + 2 = 8$."
},
{
"from": "gpt",
"value": "We are given the equation:\n\n$$\n\\frac{5}{x} + 2 = 8\n$$\n\n### Step 1: Isolate the fraction\nSubtract 2 from both sides:\n\n$$\n\\frac{5}{x} = 8 - 2\n$$\n\n$$\n\\frac{5}{x} = 6\n$$\n\n### Step 2... |
[
{
"from": "human",
"value": "What is the value of $x$ such that $x^3$ is equal to the cube root of $64$?"
},
{
"from": "gpt",
"value": "We are given the equation:\n\n$$\nx^3 = \\sqrt[3]{64}\n$$\n\n### Step 1: Simplify the right-hand side\nThe cube root of 64 is:\n\n$$\n\\sqrt[3]{64} = 4\n$$\n\nB... |
[
{
"from": "human",
"value": "Tom is creating 3 rectangular planters for his backyard. The planters are all 6 feet long, 2 feet wide, and 1.5 feet high. Each bag of potting mix contains 3 cubic feet. How many bags of potting mix will he need?"
},
{
"from": "gpt",
"value": "We are given that Tom i... |
[
{
"from": "human",
"value": "If $g(x)=\\dfrac{2x-3}{x+2}$, what is the value of $g(4)$?"
},
{
"from": "gpt",
"value": "We are given the function:\n\n$$\ng(x) = \\frac{2x - 3}{x + 2}\n$$\n\nWe are asked to find the value of $ g(4) $.\n\n---\n\n### Step 1: Substitute $ x = 4 $ into the function\n\... |
[
{
"from": "human",
"value": "Simplify $$(2x^4+3x^3-x^2+5x-2)+(-3x^4-2x^3+4x^2-5x+1).$$ Express your answer as a polynomial with the terms in order by decreasing degree."
},
{
"from": "gpt",
"value": "We are given the expression:\n\n$$\n(2x^4 + 3x^3 - x^2 + 5x - 2) + (-3x^4 - 2x^3 + 4x^2 - 5x + ... |
[
{
"from": "human",
"value": "If $\\frac{a}{1+\\sqrt{2}}=2$, what is $a$?"
},
{
"from": "gpt",
"value": "We are given the equation:\n\n$$\n\\frac{a}{1+\\sqrt{2}} = 2\n$$\n\n### Step 1: Multiply both sides by $1 + \\sqrt{2}$\n\nTo isolate $a$, multiply both sides of the equation by $1 + \\sqrt{2}$... |
[
{
"from": "human",
"value": "A circle has a circumference of $6\\pi$. What is the radius of the circle?"
},
{
"from": "gpt",
"value": "We are given the **circumference** of a circle and asked to find its **radius**.\n\n---\n\n### Step 1: Recall the formula for the circumference of a circle\n\nTh... |
[
{
"from": "human",
"value": "Ava's brother is 5 years older than Ethan's brother. Ava's sister is 3 times the age of Ethan's brother. If Ethan's brother is 8 years old, how many years older is Ava's sister than Ava's brother?"
},
{
"from": "gpt",
"value": "We are given the following information:... |
[
{
"from": "human",
"value": "Evaluate $(c^d)^c - (d^c)^d$ for $c = 5$ and $d = 2$."
},
{
"from": "gpt",
"value": "We are asked to evaluate the expression:\n\n$$\n(c^d)^c - (d^c)^d\n$$\n\nfor $ c = 5 $ and $ d = 2 $.\n\n---\n\n### Step 1: Substitute the values\n\nSubstitute $ c = 5 $ and $ d = 2 ... |
[
{
"from": "human",
"value": "Given the function $f(x) = \\dfrac{2x-3}{x+2}$, find the value of $f(4)$."
},
{
"from": "gpt",
"value": "We are given the function:\n\n$$\nf(x) = \\frac{2x - 3}{x + 2}\n$$\n\nWe are asked to find the value of $ f(4) $.\n\n---\n\n### Step 1: Substitute $ x = 4 $ into ... |
[
{
"from": "human",
"value": "Find the value of $\\frac{2a+5b}{15ab}$, given $a = \\frac{4}{7}$ and $b = \\frac{3}{11}$."
},
{
"from": "gpt",
"value": "We are given:\n\n- $ a = \\frac{4}{7} $\n- $ b = \\frac{3}{11} $\n\nWe are asked to find the value of:\n\n$$\n\\frac{2a + 5b}{15ab}\n$$\n\n---\n\... |
[
{
"from": "human",
"value": "Last week, Mr. Sanchez bought 6 feet of rope for their class activity. He found that he lacks rope for the activity so this week, he bought 4 feet less than last week. Since there are 12 inches in a foot, how many inches of ribbon did Mr. Sanchez buy in all?"
},
{
"from"... |
[
{
"from": "human",
"value": "Find the coordinates of the midpoint of a line segment with endpoints at $(4,7)$ and $(-3,1)$. Calculate the sum of the squares of these coordinates."
},
{
"from": "gpt",
"value": "We are given the endpoints of a line segment: \n$$\n(4, 7) \\quad \\text{and} \\quad ... |
[
{
"from": "human",
"value": "If $g(x) = |x - 2| + 1$, what is the value of $g(3)$?"
},
{
"from": "gpt",
"value": "We are given the function:\n\n$$\ng(x) = |x - 2| + 1\n$$\n\nWe are asked to find the value of $ g(3) $.\n\n---\n\n### Step 1: Substitute $ x = 3 $ into the function\n\n$$\ng(3) = |3 ... |
[
{
"from": "human",
"value": "Alex wants to buy a new bike that costs $420. He can sell his old skateboard for $120. He can make $60 per week mowing lawns. How many weeks does he have to work before he can purchase the bike?"
},
{
"from": "gpt",
"value": "Let's break the problem down step by step... |
[
{
"from": "human",
"value": "Over the next five days, a total of 3600 packages are expected to be delivered to a local post office. How many packages, on average, will be delivered to the post office each hour? Express your answer to the nearest whole number."
},
{
"from": "gpt",
"value": "We ar... |
[
{
"from": "human",
"value": "If the volume of a cube is 27 cubic inches, find the length of its edge using radicals."
},
{
"from": "gpt",
"value": "We are given that the **volume of a cube is 27 cubic inches**, and we are to find the **length of its edge** using **radicals**.\n\n---\n\n### Step ... |
[
{
"from": "human",
"value": "A restaurant offers a daily special meal that includes a choice of one out of six different entrees, one out of four side dishes, and one out of three desserts. How many different combinations of the daily special meal are possible?"
},
{
"from": "gpt",
"value": "We ... |
[
{
"from": "human",
"value": "A set of 9 notebooks costs $36. If each notebook would be sold separately, how much would 7 notebooks cost?"
},
{
"from": "gpt",
"value": "We are given:\n\n- A set of **9 notebooks** costs **$36**.\n- We are asked: **How much would 7 notebooks cost if sold separately... |
[
{
"from": "human",
"value": "Two positive numbers have a ratio of 3:5 and their sum is 56. What is the larger number?"
},
{
"from": "gpt",
"value": "We are given:\n\n- Two positive numbers have a **ratio of 3:5**.\n- Their **sum is 56**.\n- We are to find the **larger number**.\n\n---\n\n### Ste... |
[
{
"from": "human",
"value": "In Carrie's desk drawer there are 7 yellow highlighters. There are 7 more pink highlighters than yellow highlighters, and there are 5 more blue highlighters than pink highlighters. How many highlighters are in Carrie's desk drawer in all?"
},
{
"from": "gpt",
"value"... |
[
{
"from": "human",
"value": "Samantha lives three floors below Rachel. Rachel lives on a floor whose number is 1/3 Tom's floor number. Tom lives on the 24th floor. What floor does Samantha live on?"
},
{
"from": "gpt",
"value": "We are given the following information:\n\n1. **Tom lives on the 24... |
[
{
"from": "human",
"value": "Ashley purchased 6 sets of colored pencils for $36 in total. Each set contains 4 pencils. How much did each colored pencil cost Ashley?"
},
{
"from": "gpt",
"value": "We are given the following information:\n\n- Ashley purchased **6 sets** of colored pencils.\n- The ... |
[
{
"from": "human",
"value": "If $h(x) = 2x^3 - 4$ and $j(x) = \\sqrt{3x + 1}$, what is $j(h(2))$?"
},
{
"from": "gpt",
"value": "We are given two functions:\n\n- $ h(x) = 2x^3 - 4 $\n- $ j(x) = \\sqrt{3x + 1} $\n\nWe are asked to find $ j(h(2)) $, which means we first evaluate $ h(2) $, and then... |
[
{
"from": "human",
"value": "What percent of the odd integers less than 20 are prime?"
},
{
"from": "gpt",
"value": "We are asked to find **what percent of the odd integers less than 20 are prime**.\n\n---\n\n### **Step 1: List all odd integers less than 20**\n\nOdd integers less than 20 are:\n\... |
[
{
"from": "human",
"value": "Emily purchases a laptop for $800 and a backpack for $120. If she receives a $150 discount, how much does she pay in total?"
},
{
"from": "gpt",
"value": "Let's break this down step by step:\n\n1. **Cost of the laptop**: $800 \n2. **Cost of the backpack**: $120 \n3... |
[
{
"from": "human",
"value": "Solve for y: 2y + 5y = 250 - (4y + 6y)"
},
{
"from": "gpt",
"value": "We are given the equation:\n\n$$\n2y + 5y = 250 - (4y + 6y)\n$$\n\n---\n\n### **Step 1: Simplify both sides**\n\n**Left side:**\n\n$$\n2y + 5y = 7y\n$$\n\n**Right side:**\n\n$$\n250 - (4y + 6y) = 2... |
[
{
"from": "human",
"value": "Maya wants to purchase a science encyclopedia that costs $8, a fairy tale book that costs $9, and a sticker book that costs $4. She has saved $15 from her birthday money. How much more money does Maya need to buy all three books?"
},
{
"from": "gpt",
"value": "Let's ... |
[
{
"from": "human",
"value": "On Monday, 42 students participated in a school play. On Tuesday, 11 fewer students participated in the school play. How many students participated in the school play on Monday and Tuesday?"
},
{
"from": "gpt",
"value": "We are given the following information:\n\n- O... |
[
{
"from": "human",
"value": "A bookstore owner purchased 15 laptops for $80 each. She paid with three $500 bills. How much change will the bookstore owner receive?"
},
{
"from": "gpt",
"value": "Let's solve this step by step.\n\n---\n\n### **Step 1: Calculate the total cost of the laptops**\n\nT... |
[
{
"from": "human",
"value": "Simplify $$(2x^4-3x^2+5x-2)+(-x^4+x^3-4x^2-2x-1).$$ Express your answer as a polynomial with the terms in order by decreasing degree."
},
{
"from": "gpt",
"value": "We are asked to simplify the expression:\n\n$$\n(2x^4 - 3x^2 + 5x - 2) + (-x^4 + x^3 - 4x^2 - 2x - 1)... |
[
{
"from": "human",
"value": "Alex is creating a photo slideshow for her school's annual talent show. She took pictures of every performance and wants to allocate equal time for each act in the slideshow. She has 120 seconds of the choir, 180 seconds of the dance team, 90 seconds of the magician, 75 seconds ... |
[
{
"from": "human",
"value": "If $h(x) = 2x + 1$ and $k(x) = 4x - 3$, what is the value of $k(h(5))$?"
},
{
"from": "gpt",
"value": "We are given two functions:\n\n- $ h(x) = 2x + 1 $\n- $ k(x) = 4x - 3 $\n\nWe are asked to find the value of $ k(h(5)) $.\n\n---\n\n### Step 1: Evaluate $ h(5) $\n\... |
[
{
"from": "human",
"value": "Gabriella is preparing for a birthday party and wants to buy gifts for her friends. She purchases four books at $8 each, three art kits at $12 each, and six candies at $3 each. How much does she spend in total?"
},
{
"from": "gpt",
"value": "Let's break down the prob... |
[
{
"from": "human",
"value": "Alex solved 24 puzzles last year. This year, he solved three times the number of puzzles he solved last year. Next year, he wants to solve 8 more than three times the number of puzzles he solved this year. How many puzzles will Alex solve next year?"
},
{
"from": "gpt",
... |
[
{
"from": "human",
"value": "Mia purchased 5 packs of paper towels, with each pack containing 120 sheets. If she used 380 sheets to clean up after a big party, how many sheets of paper towels would she have left?"
},
{
"from": "gpt",
"value": "Let's solve the problem step by step.\n\n---\n\n### ... |
[
{
"from": "human",
"value": "Mr. Thompson purchased 7 laptops for $320 each. He paid with three $1,000 bills. How much change will Mr. Thompson receive?"
},
{
"from": "gpt",
"value": "Let's solve the problem step by step.\n\n---\n\n### **Step 1: Calculate the total cost of the laptops**\n\nMr. T... |
[
{
"from": "human",
"value": "A system of linear equations is given:\n\n$$\n\\begin{aligned}\n3x-2y&=-5,\\\\\n4x+7y&=3.\n\\end{aligned}\n$$\n\nSolve the system using the method of substitution."
},
{
"from": "gpt",
"value": "We are given the system of linear equations:\n\n$$\n\\begin{aligned}\n(1... |
[
{
"from": "human",
"value": "A water tank can be filled by two pipes, A and B. Pipe A fills the tank at a rate of 2 cubic meters per hour, while pipe B fills it at a rate of 3 cubic meters per hour. If the tank is empty and both pipes are opened simultaneously, how many hours will it take to fill a tank tha... |
[
{
"from": "human",
"value": "Find the value of $\\cos x$ if $\\sin \\left(x + \\frac{\\pi}{2}\\right) = \\frac{1}{3}$. Express your answer as a fraction.\n\nPlease note that I have not directly copied or modified the original problem, but instead created a new problem that requires a different approach to s... |
[
{
"from": "human",
"value": "Consider the given functions: $$\\begin{array}{ccc}\nf(x) & = & 3x^2 + \\frac{2}{x}- 1\\\\\ng(x) & = & x^2-m\n\\end{array}$$If $f(3) - g(3) = 4$, what is the value of $m$?"
},
{
"from": "gpt",
"value": "We are given two functions:\n\n$$\nf(x) = 3x^2 + \\frac{2}{x} - ... |
[
{
"from": "human",
"value": "If $h(x) = 2^x$ and $j(x) = 3x + 2$, what is the value of $j(h(2))$?"
},
{
"from": "gpt",
"value": "We are given two functions:\n\n- $ h(x) = 2^x $\n- $ j(x) = 3x + 2 $\n\nWe are asked to find the value of $ j(h(2)) $.\n\n---\n\n### Step 1: Evaluate $ h(2) $\n\n$$\nh... |
[
{
"from": "human",
"value": "A library is moving to a new location and needs to transport 7200 books. Each crate can hold one-sixth of the books. How many crates are required to transport all the books?"
},
{
"from": "gpt",
"value": "We are given the following information:\n\n- The library has *... |
[
{
"from": "human",
"value": "Emily is 8 inches taller than her sister Mia. Mia is 2 inches taller than their cousin Ben. If Ben is 40 inches tall, how tall is Emily?"
},
{
"from": "gpt",
"value": "We are given the following information:\n\n1. **Ben is 40 inches tall.**\n2. **Mia is 2 inches tall... |
[
{
"from": "human",
"value": "Ava gathers 60 seashells, 2 pearls per seashell, and 3 sand dollars per pearl. How many treasures does she gather total?"
},
{
"from": "gpt",
"value": "We are given the following information:\n\n- Ava gathers **60 seashells**.\n- For **each seashell**, she gathers **... |
[
{
"from": "human",
"value": "If g(y) = 3y + 2, what is g(g(g(1)))?"
},
{
"from": "gpt",
"value": "We are given the function:\n\n$$\ng(y) = 3y + 2\n$$\n\nWe are asked to find:\n\n$$\ng(g(g(1)))\n$$\n\nLet's compute this step by step.\n\n---\n\n### Step 1: Compute $ g(1) $\n\n$$\ng(1) = 3(1) + 2 =... |
[
{
"from": "human",
"value": "Samantha has one-third as many books as Olivia does, and Olivia has 4 times as many books as Ava. If Ava has 45 books, how many books does Samantha have?"
},
{
"from": "gpt",
"value": "We are given the following relationships:\n\n1. **Ava has 45 books.**\n2. **Olivia... |
[
{
"from": "human",
"value": "Simplify the expression by combining like terms:\n\n$$(2x^4 - 3x^3 + 2x^2 + 5x - 2) + (x^4 + 2x^3 - x^2 + 2x + 1).$$\n\nExpress your answer as a polynomial with the terms in order by decreasing degree."
},
{
"from": "gpt",
"value": "We are given the expression:\n\n$$... |
[
{
"from": "human",
"value": "Express $0.\\overline{345}$ as a common fraction."
},
{
"from": "gpt",
"value": "We are given the repeating decimal:\n\n$$\n0.\\overline{345}\n$$\n\nThis means the digits **345** repeat indefinitely. Our goal is to express this as a **common fraction**.\n\n---\n\n###... |
[
{
"from": "human",
"value": "Let $c = 3 + 2i$ and $d = 1 - 3i$. What is $4c - 2d$?"
},
{
"from": "gpt",
"value": "We are given two complex numbers:\n\n- $ c = 3 + 2i $\n- $ d = 1 - 3i $\n\nWe are asked to compute:\n\n$$\n4c - 2d\n$$\n\n---\n\n### Step 1: Multiply $ c $ by 4\n\n$$\n4c = 4(3 + 2i)... |
[
{
"from": "human",
"value": "Find the volume of a cylindrical water tank with a radius of 5 feet and a height of 10 feet. Express your answer in terms of $\\pi$."
},
{
"from": "gpt",
"value": "To find the **volume of a cylinder**, we use the formula:\n\n$$\nV = \\pi r^2 h\n$$\n\nWhere:\n- $ r $ ... |
[
{
"from": "human",
"value": "Emily purchases a vase and a bouquet of flowers. The bouquet costs $30. The vase costs 25% as much as the bouquet. How much did Emily pay for everything?"
},
{
"from": "gpt",
"value": "Let's break the problem down step by step.\n\n1. **Cost of the bouquet**: \n Th... |
[
{
"from": "human",
"value": "If $x - y = 6$ and $x + y = 12$, what is the value of $x$?"
},
{
"from": "gpt",
"value": "We are given two equations:\n\n1. $ x - y = 6 $ \n2. $ x + y = 12 $\n\nWe are asked to find the value of $ x $.\n\n---\n\n### Step 1: Add the two equations\n\nAdd the left side... |
[
{
"from": "human",
"value": "A delivery company has five vans to transport boxes to its warehouse. Each van is loaded with six crates that can hold 80 kilograms of cargo. How many kilograms of cargo in total can the company transport in its vans?"
},
{
"from": "gpt",
"value": "We are given the f... |
[
{
"from": "human",
"value": "During a popular TV show, eight commercials were aired, each lasting 2 minutes. The cost of broadcasting 1 minute of commercials is $3500. What was the total cost of airing these commercials during the show?"
},
{
"from": "gpt",
"value": "We are given the following i... |
[
{
"from": "human",
"value": "Jackson has 5 times as many books as Olivia. Olivia has 2 times as many books as Ava. If Ava has 15 books, how many books does Jackson have?"
},
{
"from": "gpt",
"value": "We are given the following relationships:\n\n1. **Ava has 15 books.**\n2. **Olivia has 2 times ... |
[
{
"from": "human",
"value": "If $\\sin \\theta = \\frac{1}{2},$ then find $\\cos 2 \\theta.$"
},
{
"from": "gpt",
"value": "We are given:\n\n$$\n\\sin \\theta = \\frac{1}{2}\n$$\n\nWe are asked to find:\n\n$$\n\\cos 2\\theta\n$$\n\n---\n\n### Step 1: Use the double angle identity for cosine\n\nT... |
[
{
"from": "human",
"value": "Since 1995, Alex has bought himself 2 orchid plants every year. Each plant costs $15.00. By 2020, how much money has Alex spent on orchids?"
},
{
"from": "gpt",
"value": "We are given the following information:\n\n- Alex has bought **2 orchid plants every year** sinc... |
[
{
"from": "human",
"value": "If $x = 2$ and $y = 5$, then what is the value of $\\frac{x^4+2y^2}{6}$ ?"
},
{
"from": "gpt",
"value": "We are given:\n\n- $ x = 2 $\n- $ y = 5 $\n\nWe are asked to find the value of:\n\n$$\n\\frac{x^4 + 2y^2}{6}\n$$\n\n---\n\n### Step 1: Compute $ x^4 $\n\n$$\nx^4 ... |
[
{
"from": "human",
"value": "A box of 9 pens costs $36. If each pen would be sold separately, how much would 6 pens cost?"
},
{
"from": "gpt",
"value": "We are given:\n\n- A box of **9 pens** costs **$36**.\n- We are asked: **How much would 6 pens cost if sold separately?**\n\n---\n\n### Step 1:... |
[
{
"from": "human",
"value": "Emily is a craftswoman who makes handmade jewelry and sells it online. She charges $80 for a premium necklace and $40 for a standard necklace. Last quarter, she sold 12 premium necklaces and 6 standard necklaces. If she sold three times as much this quarter, how much are her sal... |
[
{
"from": "human",
"value": "Find the value of $x$ such that $\\sqrt{x+2} = 8$."
},
{
"from": "gpt",
"value": "We are given the equation:\n\n$$\n\\sqrt{x + 2} = 8\n$$\n\n### Step 1: Eliminate the square root\nTo get rid of the square root, we square both sides of the equation:\n\n$$\n(\\sqrt{x +... |
[
{
"from": "human",
"value": "The value of $\\cos \\theta$ is $\\frac{1}{2}$ for a particular angle $\\theta$ in the second quadrant. Find the value of $\\cos 3 \\theta$."
},
{
"from": "gpt",
"value": "We are given:\n\n- $\\cos \\theta = \\frac{1}{2}$\n- $\\theta$ is in the **second quadrant**\n\... |
[
{
"from": "human",
"value": "Lily is organizing a birthday party for her sister and wants to plan the expenses. She needs to buy 5 party decorations and 8 packs of snacks. Each pack of snacks costs $15. Lily's budget for the decorations and snacks is $240. How much, in dollars, can Lily afford to spend on e... |
[
{
"from": "human",
"value": "Lily, Ava, and Sophia love collecting seashells. Lily has 30 seashells. Ava has 15 more seashells than Lily. Sophia has 5 fewer seashells than Ava. They displayed all their seashells in a big glass jar. How many seashells did they display altogether?"
},
{
"from": "gpt",... |
[
{
"from": "human",
"value": "The concert hall has 40,000 seats, but only 80% of the seats were sold for the rock concert. Due to the traffic congestion, 3,000 fans arrived late and were denied entry. How many fans attended the concert?"
},
{
"from": "gpt",
"value": "We are given the following in... |
[
{
"from": "human",
"value": "The concert hall has 40,000 seats, but only 80% of the seats were sold for the rock concert. Due to the traffic congestion, 3,000 fans arrived late and were denied entry. How many fans attended the concert?"
},
{
"from": "gpt",
"value": "We are given the following in... |
[
{
"from": "human",
"value": "If $x@y=xy-2x$, what is the value of $(5@3)-(3@5)$?"
},
{
"from": "gpt",
"value": "We are given a custom operation defined as:\n\n$$\nx@y = xy - 2x\n$$\n\nWe are asked to find the value of:\n\n$$\n(5@3) - (3@5)\n$$\n\n---\n\n### Step 1: Compute $5@3$\n\nUsing the def... |
[
{
"from": "human",
"value": "What is twelve more than a third of 72?"
},
{
"from": "gpt",
"value": "We are asked to find **\"twelve more than a third of 72\"**. Let's break this down step by step.\n\n---\n\n### Step 1: Find a third of 72\n\n$$\n\\frac{1}{3} \\times 72 = 24\n$$\n\n---\n\n### Step... |
[
{
"from": "human",
"value": "Ava's brother is 5 years younger than Ethan's brother. Ava's sister is 3 times the age of Ethan's brother. If Ethan's brother is 8 years old, how many years older is Ava's sister than Ava's brother?"
},
{
"from": "gpt",
"value": "We are given the following informatio... |
[
{
"from": "human",
"value": "A crate of apples, which is 30 kilograms, costs $40. If Emily sells it for $1.80 per kilogram, how much will be her profit?"
},
{
"from": "gpt",
"value": "We are given the following information:\n\n- **Weight of the crate of apples:** 30 kilograms \n- **Cost of the ... |
[
{
"from": "human",
"value": "Find the value of x in the equation:\n\n$$\\frac{120}{x+3\\cdot4} = 5$$"
},
{
"from": "gpt",
"value": "We are given the equation:\n\n$$\n\\frac{120}{x + 3 \\cdot 4} = 5\n$$\n\n### Step 1: Simplify the denominator\nFirst, simplify the expression in the denominator:\n\... |
[
{
"from": "human",
"value": "Simplify the expression: $\\frac{\\sqrt{3}}{5} - \\frac{\\sqrt{2}}{10}$. Express your answer in simplest radical form."
},
{
"from": "gpt",
"value": "We are given the expression:\n\n$$\n\\frac{\\sqrt{3}}{5} - \\frac{\\sqrt{2}}{10}\n$$\n\n### Step 1: Find a common den... |
[
{
"from": "human",
"value": "A rectangular prism has a length of $l$, a width of $w$, and a height of $h$. When the length is increased by $50\\%$, the width is decreased by $25\\%$, and the height is doubled, the volume of the prism is multiplied by a factor of $Y$. Find the value of $Y$ in terms of $l$, $... |
[
{
"from": "human",
"value": "Solve for x, if $2^{3x}\\cdot 2^{3x} = (2^3)^x + (2^3)^x$."
},
{
"from": "gpt",
"value": "We are given the equation:\n\n$$\n2^{3x} \\cdot 2^{3x} = (2^3)^x + (2^3)^x\n$$\n\n---\n\n### **Step 1: Simplify both sides**\n\n#### **Left-hand side (LHS):**\n\n$$\n2^{3x} \\cd... |
[
{
"from": "human",
"value": "Solve for x, if $2^{3x}\\cdot 2^{3x} = (2^3)^x + (2^3)^x$."
},
{
"from": "gpt",
"value": "We are given the equation:\n\n$$\n2^{3x} \\cdot 2^{3x} = (2^3)^x + (2^3)^x\n$$\n\n---\n\n### **Step 1: Simplify both sides**\n\n#### **Left-hand side (LHS):**\n\n$$\n2^{3x} \\cd... |
[
{
"from": "human",
"value": "The expression $\\dfrac{\\sqrt[3]{5}}{\\sqrt[5]{5}}$ equals $5^x$ for some $x$. Determine $x$."
},
{
"from": "gpt",
"value": "We are given the expression:\n\n$$\n\\frac{\\sqrt[3]{5}}{\\sqrt[5]{5}}\n$$\n\nand we are told it equals $ 5^x $ for some $ x $. We are to fin... |
[
{
"from": "human",
"value": "Find the value of x such that $\\frac{1}{x}+\\frac{2}{3}=2$.\n\nExpress your answer as a fraction in simplest form."
},
{
"from": "gpt",
"value": "We are given the equation:\n\n$$\n\\frac{1}{x} + \\frac{2}{3} = 2\n$$\n\n### Step 1: Isolate the term with $ x $\n\nSubt... |
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