2. recall that we say that f(n) is o(g(n)) if and only if for some constants c > 0 and n0 ≥ 0, for all n > n0, f(n) ≤ cg(n). for each of the following pairs of functions, find values of c and n0 that demonstrate that f(n) is o(g(

(a) f(n) = 3n + 5, g(n) = n
(b) f(n) = n 2 + 10n + 21, g(n) = n 2
(c) f(n) = 2n + 12, g(n) = n
(d) f(n) = 2n + 12, g(n) = n 2
(e) f(n) = 3n 3 + 2n 2 + n + 1, g(n) = n 3

Two sides of a right triangle measure 2 units and 4 units. what is the area of the square that shares a side with the third side of the triangle?

The resumâ´es of two male applicants for a college teaching position in chemistry are placed in the same file as the resumâ´es of two female applicants. two positions become available, and the first, at the rank of assistant professor, is filled by selecting one of the four applicants at random. the second position, at the rank of instructor, is then filled by selecting at random one of the remaining three applicants. using the notation m2f1, for example, to denote the simple event that the first position is filled by the second male applicant and the second position is then filled by the first female applicant, (a) list the elements of a sample space s; (b) list the elements of s corresponding to event a that the position of assistant professor is filled by a male applicant; (c) list the elements of s corresponding to event b that exactly one of the two positions is filled by a male applicant; (d) list the elements of s corresponding to event c that neither position is filled by a male applicant; (e) list the elements of s corresponding to the event a â© b; (f) list the elements of s corresponding to the event a âş c; (g) construct a venn diagram to illustrate the intersections and unions of the events a, b, and c.

What's for breakfast? all people who ate at a certain restaurant were surveyed as to what they ordered on a particular sunday morning. 40 ate eggs 42 ate sausage 32 ate pancakes 13 ate sausage and eggs 15 ate pancakes and sausage 11 ate eggs and pancakes 6 ate all three items 3 people didn't eat any of the items how many people ate only pancakes? how many people ate at the resturant that morning? how many people didn't eat eggs?