Item 3 in a particular game, a spinner with four equally-sized sectors labeled 1, 3, 4, and 6 is spun twice. one turn is considered 2 spins of the spinner. if the sum of the spins is even, you move forward 6 spaces. otherwise, you move back 2 spaces. what is the mathematical expectation for the number of spaces moved in one turn? 2 spaces backward 2 spaces forward 1 space forward 1 space backward

Adam drew two same size rectangles and divided them into the same number of equal parts. he shaded 1/3 of one rectangle and 1/4 of the other rectangle. what is the least number of parts into which both rectangles could be divided into?

What is the absolute value of the complex number -4-sqrt2i

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?