Diffusion

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question:the baking contest, x times as many people voted for the unicorn cake compared to the witch cake, and the number of votes for the dragon cake was 25 more than the number of votes for the witch cake. If 7 people voted for the witch cake, how many votes were cast total? If we know the answer to the above question is 60, what is the value of unknown variable x?

answer:We are given that 7 people voted for the witch cake. We are also given that the number of votes for the unicorn cake is x times as many as the number of votes for the witch cake, which means x * 7 people voted for the unicorn cake. The number of votes for the dragon cake is 25 more than the number of votes for the witch cake, which means 7 + 25 = 32 people voted for the dragon cake. The total number of votes cast is the sum of the votes for all three cakes: 7 + x * 7 + 32. We are given that the total number of votes is 60, so we can write: 7 + x * 7 + 32 = 60. Simplifying the left side, we get: 39 + x * 7 = 60. Subtracting 39 from both sides, we get: x * 7 = 21. Dividing both sides by 7, we get: x = 3. The value of x is 3. 3 The answer is: 3

question:Frank, Betty, and Bill went to their farm and picked oranges. Betty picked 15 oranges and Bill picked 12 oranges. Frank picked three times the combined number of oranges picked by Betty and Bill. Frank then planted 2 seeds from each of his oranges and waited for 20 years for each seed to grow into an orange tree. Each orange tree contains 5 oranges for Frank's son Philip to pick. How many oranges are there in total for Philip to pick?

answer:Betty picked 15 oranges and Bill picked 12 oranges, so the total number of oranges picked by both of them is 15 + 12 = 27. Frank picked three times the combined number of oranges picked by Betty and Bill, so he picked 3 * 27 = 81 oranges. Frank planted 2 seeds from each of his oranges, so he planted 81 * 2 = 162 seeds. After 20 years, each seed grew into an orange tree, so there are 162 orange trees. Each orange tree contains 5 oranges for Philip to pick, so Philip can pick a total of 162 * 5 = 810 oranges. 810 The answer is: 810

question:f Jimmy bought 3 pens for 1 each, 4 notebooks for 3 each, and 2 folders for 5 each, and paid with a 50 bill, what is the amount of change he will receive?

answer:Jimmy bought 3 pens for 1 each, so he spent 3 * 1 = 3 on pens. He bought 4 notebooks for 3 each, so he spent 4 * 3 = 12 on notebooks. He bought 2 folders for 5 each, so he spent 2 * 5 = 10 on folders. In total, Jimmy spent 3 + 12 + 10 = 25. He paid with a 50 bill, so he will receive 50 - 25 = 25 in change. 25 The answer is: 25

question:We roll a fair 6-sided die 5 times. What is the probability that we get an odd number in exactly 4 of the 5 rolls?

answer:There are binom{5}{4} ways to choose which rolls will be odd. For each of these rolls, there are 3 odd numbers that could appear, and 3 even numbers that could not appear. For the remaining roll, there are 3 even numbers that could appear. So, the probability is binom{5}{4}cdotleft(frac{3}{6}right)^4 cdot left(frac{3}{6}right)^1 = binom{5}{4}cdotleft(frac{1}{2}right)^5 = boxed{frac{5}{32}}. The answer is: frac{5}{32}