Find a trivial lower-bound class for each of the following problems and indicate, if you can, whether this bound is tight.
a. finding the largest element in an array
b. checking completeness of a graph represented by its adjacency matrix
c. generating all the subsets of an n-element set
d. determining whether n given real numbers are all distinct

Using pert, adam munson was able to determine that the expected project completion time for the construction of a pleasure yacht is 21 months, and the project variance is 4. a) what is the probability that the project will be completed in 17 months? b) what is the probability that the project will be completed in 20 months? c) what is the probability that the project will be completed in 23 months? d) what is the probability that the project will be completed in 25 months? e) what is the due date that yields a 95% chance of completion?

The equation shown below represents function f. f(x)= -2x+5 the graph shown below represents function g. which of the following statements is true? a. over the interval [2, 4], the average rate of change of f is the same as the average rate of change of g. the y-intercept of function f is less than the y-intercept of function g. b. over the interval [2, 4], the average rate of change of f is greater than the average rate of change of g. the y-intercept of function f is greater than the y-intercept of function g. c. over the interval [2, 4], the average rate of change of f is the same as the average rate of change of g. the y-intercept of function f is greater than the y-intercept of function g. d. over the interval [2, 4], the average rate of change of f is less than the average rate of change of g. the y-intercept of function f is the same as the y-intercept of function g.

One side of a rectangle is 7 centimeters shorter than six times the other side. find the length of the longer side if we also know that the perimeter of the rectangle is 266 centimeters.