you are going to roll two dice what are the outcomes in the sample space?

a) {1, 2, 3, 4, 5, 6}
b) {2, 4, 6, 8, 10, 12}
c) {1-1, 2-2, 3-3, 4-4, 5-5, 6-6}
d) {1-1, 1-2, 1-3, 1-4, 1-5, 1-6, 2-2, 2-3, 2-4, 2-5, 2-6, 3-3, 3-4, 3-5, 3-6, 4-4, 4-5, 4-6, 5-5, 5-6, 6-6}

If f(x)=-x^2+6x-1 and g(x)=3x^2-4x-1,find(f+g)(x)

Teams of 4 are competing in a 1/4 mile relay race. each runner must run the same exact distance. what is the distance each teammate runs?

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?