Answer:



Step-by-step explanation:
Given
--- 8 friends
--- proportion that one-time fling
This question is an illustration of binomial probability, and it is represented as:

Solving (a): P(x = 0) --- None has done one time fling




Solving (b): 
To do this, we make use of compliment rule:

Rewrite as:



Solving (c):
--- Not more than 2 has one time fling
This is calculated as:

We have:







So:



The answer to 8a. is 17, the answer to 8b. is 3.9, the answer to 8c. is 1 / 2, the answer to 8d. is 7 7 / 8, the answer to 9a. is commutative property, the answer to 9b. is multiplicative identity property, the answer to 9c. is associative property, and the answer to 9d. is additive inverse property.
Regarding the whole "explain using mental math" thing, I pretty much just used the fact that 8a. and 8b. both had the same number of decimal places. For 8c., I just made each number have a denominator of 10. And last, for 8d., all of the denominators were already the same, which made it pretty easy. I apologize for this section of my answer being so informal lol, I haven't had to do these kinds of problems in like 5 years <span />
1 1/2 I think is the answer
If Carly had more DVDs than Rob then you would subtract her amount away from the total. 42-4=38