CubeyThePenguin

I answered these questions a few seconds ago.

1. We are counting the derangements of 6, so the probability is 265/720 = 53/144

2. (1/2)^4 = 1/16

3. There is only two ways to seat them: BG BG BG BG BG or GB GB GB GB GB. This can happen in 2 * 5!  = 240 ways.

Because the table is circular, we have 10!/10 = 362880 total ways to seat them, and the probability is 240/362880 = 1/1512. (i'm a bit unsure of this)

4. Count the cases where the keys are together: GG _ _ _ _ _ _ (underscores represent other keys) If we count GG as a single block, there are 2 * 7! ways out of a total 8! ways, which is 1/4.

The value of the entire tower is 4, so we can substitute that:

\((\sqrt[4]{x})^4 = 4\)

\(\boxed{x = 4}\)

1. The common difference is 5, so add 5 every term: 3, 8, 13, 18, ...

The answer is D.

2. The bacteria triples every hour, so this is an exponential function. It also starts with 5 bacteria, so the answer is D.

One year has 365 * 24 = 8760 hours.

Izzy: 1 book every 2 hours ==> 4380 books

Bachukas: 8 books every 36 hours ==> 1946 2/3 books

Fantasy Lover: 1 book every 36240 hours ==> 0.241 books

Add to get 6326.9 books.

Sally's number, AB, can be represented as 10A + B, where A and B are the individual digits.

AB = (10A + B)/2

AB - 5A - B/2 = 0

2AB - 10A - B = 0

(2A - 1)(B - 5) = 5

Case 1: 2A - 1 = 5 and B - 5 = 1

A = 3, B = 6

Case 2: 2A - 1 = 1 and B - 5 = 5

B = 10, so this doesn't work.

The number is 36.

2/3 + 8/9 + 26/27 + 80/81 + 242/243

= 5(1) - (1/3 + 1/9 + 1/27 + 1/81 + 1/243)

 = 5 - 121/243

= 1094/243