A movie theater offers three types of tickets: child, student, and adult. Ticket sales for two movies are shown in the table. Ticket Type Child Student Adult Total Movie Title The Ransom 12 38 70 100 Space Force 34 42 56 132 Total 46 80 126 232 If a ticket was sold for Space Force, what is the probability it was a student ticket? StartFraction 42 Over 232 EndFraction StartFraction 42 Over 132 EndFraction StartFraction 80 Over 232 EndFraction

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?