Clear

Well, if you want to do this the 'lazy' way, you can just eyeball it.

I'd say about a quarter of those are behind the 20 line, so your answer would be B, 106. :D

Huh! Maybe someone smarter than me can come help out.

Another great way to solve it!

It's always reassuring when two people get the same answer. :)

2. Same thing, average all the numbers with an additional 9. You will get 4.63636363636 or 51/11 .

3. Well, you know the drill  by now; average! When there are two extra 9's, we get 5 as the expected value.

4. When you add 6 extra 9's you get 6 as the expected value. 

:D I hope this helps you!

1. Simply average all the numbers: you get 4.2!

I think you were trying to use LaTeX for your numbers, which is really a nice touch, but it isn't showing up.

I can try and help you... once you add in those numbers.

(It is just a liiiitttle hard to solve math problems where all the numbers are excluded.) 

The answer is: (x y + 2 x - y + 2) (x y - 2 x + y + 2)

Hope this helps!

-Clear

There is a 2/3 chance each time that the roll will NOT be a multiple of 3, so (2/3)^4 is the probability that none of them will be a multiple of 3.

If we subtract this from 1, we will get the probablility that at least one of the rolls is a multiple of 3. This is equal to 65/81, option D.

I hope this helps you, best of luck!

There are 66 ways... I can come add an explanation here later. 

Hope this helps!