Janae has a soap bottle that has $474$ mL of liquid soap. Each push of the pump uses $8$ mL of soap. There needs to be at least $50$ mL of soap in the bottle for the pump to work.

Astore has clearance items that have been marked down by 60%. they are having a sale, advertising an additional 55% off clearance items. what percent of the original price do you end up paying?

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?

A50% increase followed by 33 1/2% decrease