At a fair, each person can spin two wheels of chance. the fist wheel has numbers 1,2, and 3. the second wheel has the letters a and b. (a) list all the possible outcomes of the computed event. (b) if you spin both wheels, what is the probability that you get either a 1 or an a? explain.

Offering 30 if a plus b plus c equals 68 and ab plus bc plus ca equals 1121, where a, b, and c are all prime numbers, find the value of abc. the answer is 1978 but i need an explanation on how to get that.

Thee blue triangle has rotated from quadrant i to quadrant iii about the origin. describe the effects of the rotation on the coordinates of the blue triangle.

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?