1. prove the following:
if n2 is not divisible by 3, then n is not divisible by 3.
(a) what kind of proof will you use to show this fact (proof by contrapositive? proof by contradiction? direct proof? proof by cases? etc.)
(b) show the fact.
2. identify the problem in the following proof that if n2 is rational, then n is rational (note: that fact is not true. consider \sqrt{2} ).
suppose n2 is rational. then n2 = \frac{a^{2}}{b^{2}} , so n = \frac{a}{b} . thus n is rational.

The floor plan of a room has a scale of 2.5 in.: 35 ft. in the drawing, the length of the room is 8 in. and the width of the room is 6 in. what is the perimeter of the actual room?

Me on this one i will give you 20pts. answer should be in detail . this is the discussion topic. one of the most fiercely debated topics in sports is the hot hand theory. the hot hand theory says that success breeds success. in other words, rather than each shot a basketball player takes or each at-bat a baseball player has being an independent event, the outcome of one event affects the next event. that is, a player can get hot and make a lot of shots in a row or get a lot of hits in a row. the hot hand theory, however, has been shown to be false in numerous academic studies. read this article, which discusses the hot hand theory as it relates to a professional basketball player. state whether you agree or disagree with the hot hand theory, and give reasons for your opinion. be sure to use some of the terms you’ve learned in this unit, such as independent event, dependent event, and conditional probability, in your answer.

Which expression will have the same sum as 3_8 + 1/4?