Let X = {n ∈ N : 10 ≤ n < 20}. Find examples of sets with the properties below and very briefly explain why your examples work. (a) A set A ⊆N with |A| = 10 such that X \A = {10,12,14}.

(b) A set B ∈P(X) with |B| = 5.

(c) A set C ⊆P(X) with |C| = 5.

(d) A set D ⊆ X ×X with |D| = 5

(e) A set E ⊆ X such that |E|∈ E.

Suppose that f(0) = −3 and f '(x) ≤ 8 for all values of x. how large can f(4) possibly be? solution we are given that f is differentiable (and therefore continuous) everywhere. in particular, we can apply the mean value theorem on the interval [0, 4] . there exists a number c such that

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.

What number line represents the solution set for the inequality -1/2 greater than or equal to 4