Hannah’s favorite toy character is sold wearing one of many outfits. An outfit consists of one shirt, one pair of pants, and one cap. The shirt can be striped, plain, or polka-dotted. The pants may be denim or plaid. The cap may be a cowboy hat or a baseball cap. If Hannah picks a toy at random from the shelf and there are an equal number of toys wearing each outfit, what is the probability that the toy is dressed in a polka-dotted shirt and a cowboy hat? A. 1/8 B. 1/6 C. 1/4 D. 1/3 E. 1/2

1- 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.2- 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 the first question?