Carolina goes to a paintball field that charges an entrance fee of \$18 dollar sign, 18 and \$0.08 dollar sign, 0, point, 08 per ball. The field has a promotion that says, "Get \$10 dollar sign, 10 off if you spend \$75 dollar sign, 75 or more!" Carolina wonders how many paintballs she needs to buy along with the entrance fee to get the promotion. Let B represent the number of paintballs that Carolina buys

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?