List all the elements of the sample space for the following experiment: you roll a die and toss a penny.
a. (1, h), (2, h), (3, h), (4, h), (5, h), (6, h), (1, t), (2, t), (3, t), (4, t), (5, t), (6, t)
b. (1, h), (2, h), (3, h), (4, h), (5, h), (6, h), (1, h), (2, h), (3, h), (4, h), (5, h), (6, h)
c. (1, t), (2, t), (3, t), (4, t), (5, t), (6, t), (1, t), (2, t), (3, t), (4, t), (5, t), (6, t)
d. (1, h), (3, h), (5, h), (2, t), (4, t), (6, t)

Scrub a dub toothbrushes are $4.00 each. there is a 10% discount, but there is also a 6% sales tax after the discount is applied. what is the new price after tax? round to the nearest penny

Marina baked cookies. she gave 3/4 of the cookies to the scout bake sale. she shared the remaining 6 cookies with her friends. how many cookies did marina bake?

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?