5 and 4
5 and 6
6 and 5
That’s 10 favorable outcomes:
34 . B
The equation of an ellipse centered at the point (p, q) and with axes 2a and 2b is
Here p = −2, q = 3 , a = 2, and b = 3, so the equation is
which is the same as choice (B).
35 . E
Don’t let the functions symbolism confuse you. Just think of these as two quantities—f(x)
and g(x)—that are both nonnegative. Statement I says their sum is nonnegative. That’s true
—add any two nonnegatives and you’ll get a nonnegative sum. Statement II says the
difference f(x) − g(x) is nonnegative. Well, that’s true only if f(x) ≥ g(x). But there’s no reason
that g(x) couldn’t be greater than f(x). Statement III says their product is nonnegative. That’s
true—multiply any two nonnegatives and you’ll get a nonnegative product. Statements I and
III are true.
36 . C
Express cosecant as 1 over sine: