I am assuming 33 is B^(2/3) times B^(1/2)
See the following image
Yes, your answer is correct.
As a ratio, 5:86 represents students to teachers
We can set up the equation as 5/86=x/9460
Multiply 9460 to both sides
5x9460/86=x
47300/86=x
x=550
There are 550 professors
The answer is 6
h = 2 A/a+b = 2 51/10+7 = 6