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question:f two different integers are chosen at random from 1 to 20 inclusive, what is the probability that both numbers are prime? Express your answer as a common fraction.
answer:There are 8 prime numbers between 1 and 20: 2, 3, 5, 7, 11, 13, 17, and 19. There are 20 numbers to choose from in total. The probability of choosing a prime number for the first number is frac{8}{20}=frac{2}{5}. After one prime number has been chosen, there are now 7 prime numbers left and 19 total numbers left to choose from. The probability of choosing a prime number for the second number is frac{7}{19}. Therefore, the probability of choosing two prime numbers is frac{2}{5}cdotfrac{7}{19}=boxed{frac{14}{95}}. The answer is: frac{14}{95}
question:f your mom bought a refrigerator for 4275 and a washing machine that is 1490 less than the price of the refrigerator, what is the total cost of the purchases in dollars?
answer:The washing machine is 1490 less than the refrigerator, so the price of the washing machine is 4275 - 1490 = 2785. The total cost of the purchases is 4275 + 2785 = 7060. 7060 The answer is: 7060
question:Victor has 8 flower stickers. He has 2 fewer animal stickers than flower stickers. How many stickers does Victor have in total?
answer:Victor has 2 fewer animal stickers than flower stickers, so he has 8 - 2 = 6 animal stickers. In total, Victor has 8 flower stickers + 6 animal stickers = 14 stickers. 14 The answer is: 14
question:Mr. Wong harvested 560 mangoes from the tree outside his house. He sold half of it at the market and distributed the rest evenly among x of his neighbors. How many mangoes does each neighbor receive? If we know the answer to the above question is 35, what is the value of unknown variable x?
answer:Mr. Wong harvested 560 mangoes. He sold half of it at the market, which means he sold 560/2 = 280 mangoes. He distributed the rest evenly among x of his neighbors, which means each neighbor received (560-280)/x = 280/x mangoes. We are given that each neighbor received 35 mangoes, so we can write: 280/x = 35. Simplifying the equation, we get: x = 8. The value of x is 8. 8 The answer is: 8