MIT

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question:My co-worker Erich is very odd. He only likes numbers that are divisible by 5. How many different last digits are possible in numbers that Erich likes?

answer:To determine the possible last digits of numbers divisible by 5, we need to look at the multiples of 5 and see what the last digit is. The multiples of 5 have a pattern of 5, 0, 5, 0, 5, 0,... So the possible last digits are 5 and 0. Therefore, there are boxed{2} different last digits possible in numbers that Erich likes.The answer is: 2

question:f c is a constant such that x^2+100x+c is equal to the square of a binomial, then what is c?

answer:If x^2 + 100x + c is equal to the square of a binomial, then the binomial must be of the form x + a, where a is a constant. Expanding (x + a)^2, we get x^2 + 2ax + a^2. So we must have 2ax = 100x, which implies 2a = 100 and a = 50. Therefore, c = (50)^2 = boxed{2500}. The answer is: 2500

question:Ten more than twice the number of birds on the fence is 50. How many birds are on the fence?

answer:Let's represent the number of birds on the fence as x. Twice the number of birds on the fence is 2x. Ten more than twice the number of birds on the fence is 2x + 10. According to the problem, 2x + 10 = 50. Subtracting 10 from both sides, 2x = 40. Dividing both sides by 2, x = 20. Therefore, there are 20 birds on the fence. 20 The answer is: 20

question:f there were beacon towers positioned at 5 kilometer intervals along the 7300 kilometer-long Great Wall in ancient China, and each tower had two soldiers, what was the total number of soldiers in the beacon towers on the Great Wall?

answer:If there were beacon towers positioned at 5 kilometer intervals along the 7300 kilometer-long Great Wall, then there were 7300/5 = 1460 beacon towers. If each tower had two soldiers, then there were 1460 x 2 = 2920 soldiers in the beacon towers on the Great Wall. 2920 The answer is: 2920