Suppose that p is a random variable equal to profits from an ice cream stand at the beach and that p has the following probability distributions:
$70,000 with probability 0.05
$50,000 with probability 0.25
$30,000 with probability 0.35
$10,000 with probability 0.20
$10,000 with probability 0.15
what is the expected value of profits?

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?