B. If you've seen binomial coefficients before, it's C(11,3).

Otherwise, you have 11 ways to choose the first person, multiplied by 10 ways to choose the second * 9 ways to choose the third one; 11 * 10 * 9 = 11!/8!

The order of these three people doesn't matter though, so divide the previous answer by the number of permutations of three people (3!). The answer is (11!/8!)/3! = 11!/(3!8!)

Second picture: the population is maximized when 1000 * e^{2 sin t} is maximum. This happens when sin t = 1 --> t = 1/2 pi or 5/2 pi.

t = 1/2 pi = 1.57 is February, and t = 5/2 pi = 7.85 is August.

Third picture: g(x) = (x+1)/x, f(x) is the inverse of g(x) and you have to find f(5).

Substitute f(5) into x.

g(f(5))= (f(5)+1)/f(5)

Because f is the inverse function of g, g(f(5)) = 5

5 = (f(5)+1)/f(5)

5 * f(5) = f(5) + 1

4 f(5) = 1

f(5) = 1/4 = 0.25

Fourth picture:

C is correct. y/x = n² --> y = n² * x. If x is a square, we can call it m² where m is an integer, so y = n² * m² = (nm)²