Using the defining equation with n = 3, you have
Thus, .
Use the calculator: . Thus, x 4 ≈ 5.29.
39 . D
The area of any triangle is . Call the base of triangle ABC side AC and say that the
height drawn from point B to base AC meets base AC at point D.
Base AC of triangle ABC is a radius of the circle. The area of the semicircle is 8π. So if the
radius of the semicircle is r (in particular, r = AC = BC), then , πr^2 = 16π, r^2 = 16 ,
and r = 4. So AC = 4 and BC = 4.
You can find the height BD of the triangle in terms of θ by saying that , so BD =
BC sin θ = 4 sin θ. Thus the base AC is 4, and the height BD is 4 sin θ. The area of the triangle is
40 . B
When two or more events are independent, the probability that all the events occur is equal
to the product of the probabilities that each event occurs. The decimal equivalent of 70% is
0.7. In this question, the probability that a person selected at random from each room is a
senior at university X is 0.7. So the probability that each of the 3 people selected is a senior at
university X is (0.7)(0.7)(0.7) = 0.343.
41 . E