Diffusion

🔍

question:Adam’s wardrobe is too crowded so he decides to donate some of his clothes to a charity shop. He takes out 4 pairs of pants, 4 jumpers, 4 pajama sets (top and bottom), and 20 t-shirts, then asks his friends if they have anything they want to donate. x of his friends donate the same amount of clothing as Adam each. Then he takes another look over his clothing and decides that he actually wants to keep half of his clothes. How many articles of clothing are being donated in total? If we know the answer to the above question is 126, what is the value of unknown variable x?

answer:Adam donates 4 pairs of pants, 4 jumpers, 4 pajama sets, and 20 t-shirts, which is a total of 4 + 4 + 4 + 20 = 32 articles of clothing. His friends donate the same amount of clothing as Adam each, so the total number of articles of clothing donated by his friends is x * 32. After deciding to keep half of his clothes, Adam keeps 32/2 = 16 articles of clothing. The total number of articles of clothing being donated is the sum of the number of articles donated by Adam and his friends: 32 + x * 32 = 32(1 + x). We are given that the total number of articles of clothing being donated is 126, so we can write: 32(1 + x) = 126. Dividing both sides by 32, we get: 1 + x = 126/32. Subtracting 1 from both sides, we get: x = 126/32 - 1. Simplifying the right side, we get: x = 3. The value of x is 3. 3 The answer is: 3

question:What is the simplified form of (5^7+3^6)(1^5-(-1)^4)^{10}?

answer:First, let's simplify the expression inside the parentheses: (1^5 - (-1)^4)^{10} = (1 - 1)^{10} = 0^{10} = 0. Now, we can simplify the entire expression: (5^7 + 3^6)(1^5 - (-1)^4)^{10} = (5^7 + 3^6)(0) = boxed{0}. The answer is: 0

question:Quinn's library was hosting a summer reading challenge. For every 5 books you read, you a coupon for a free donut at a nearby bakery. Quinn decided he could read x books a week for 10 weeks total. How many free donuts would Quinn be eligible for? If we know the answer to the above question is 4, what is the value of unknown variable x?

answer:Quinn can read x books a week for 10 weeks, which means he can read a total of 10x books. For every 5 books he reads, he gets a coupon for a free donut. So the number of free donuts Quinn would be eligible for is: (10x) / 5 = 2x. We are given that the number of free donuts is 4, so we can write: 2x = 4. Solving for x, we get: x = 2. The value of x is 2. 2 The answer is: 2

question:A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits (spadesuit, heartsuit, diamondsuit, and clubsuit), such that there is exactly one card for any given rank and suit. Two of the suits (spadesuit and clubsuit) are black and the other two suits (heartsuit and diamondsuit) are red. The deck is randomly arranged. What is the probability that the top three cards are all spadesuits?

answer:There are a total of 52 cards in the deck, and 13 of them are spadesuits. So, the probability that the first card drawn is a spadesuit is frac{13}{52}. After one spadesuit is drawn, there are 51 cards left in the deck, and 12 of them are spadesuits. So, the probability that the second card drawn is a spadesuit is frac{12}{51}. After two spadesuits are drawn, there are 50 cards left in the deck, and 11 of them are spadesuits. So, the probability that the third card drawn is a spadesuit is frac{11}{50}. To find the probability that all three cards are spadesuits, we multiply the probabilities of each event happening: [frac{13}{52} times frac{12}{51} times frac{11}{50} = frac{11}{850}.] Therefore, the probability that the top three cards are all spadesuits is boxed{frac{11}{850}}.The answer is: frac{11}{850}