GEOMETRY-A.9 MUTUALLY EXCLUSIVE/OVERLAPPING EVENTS Determine whether the events are disjoint(mutually exclusive) or overlapping. Explain your reasoning

1. Roll a pair of dice and get getting doubles or a sum of 8

2.

Draw a card that is a face card or less than 8

3.

Select a card from a deck of cards that is a heart or a 2

4

A person on student council who is a senior or a male

From the integers 1 - 50, selecting a multiple of 7 or a multiple of 8

This is the number of parts out of 100, the numerator of a fraction where the denominator is 100. submit

Find the equation of the line with slope =8 and passing through (6,53) write your equation in the form y=mx+b

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?