At a summer camp, the following juices are available at breakfast: blueberries, apples, bananas, and pears. Also, the following juices are available: blackberry, raspberry, orange, and pineapple. How many combinations of one fruit and one juice involve one or more types of berries. Its not (16 combinations)​

Orly uses 2 cups of raisins for every 12 cups of trail mix she makes. how many cups of trail mix will she make if she uses 8 cups of raisins?

The u-drive rent-a-truck company plans to spend $13 million on 320 new vehicles. each commercial van will cost $25 comma 000, each small truck $50 comma 000, and each large truck  $80 comma 000. past experience shows that they need twice as many vans as small trucks. how many of each type of vehicle can they buy?

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?