Event a: spinning violet or yellow on the spinner shown. event b: rolling an even number on a number cube. what is p(a and b)?  

What is the remainder when 2872 is divided by 76? a) 51 b) 57 c) 60 d) 63

If a || b and b | y, then ? a) x || y. b) x | a. c) a | y. d) a || y.

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?