Show that there are at most dn/2 h+1e nodes of height h in any n-element heap.
(b) for a min heap with n elements, what are the possible array subscript locations for the third smallest value in the heap? assume the array index begins at 1, and that all values are distinct. justify your answer.
(c) a d-ary heap is similar to a binary heap, except that nodes have d children instead of two children. justify your answers to the questions below.
i. what is the height of the tree representing a d-ary heap with n elements?
ii. what is the time taken for an insert operation in a d-ary heap? how does it compare with that for a binary heap?
iii. what is the time taken for a delete-max operation in a d-ary heap?

The total revenues for a company are $150,223 and the total expenses were 125,766. if you are calculating the net income, which of these spreadsheets would you use? insert a spreadsheet with $150,223 in cell b2 and 125, 766 in cell b3. enter a formula =b2-b3. the formula should be showing in the formula bar. insert a spreadsheet with $150,223 in cell b2 and 125, 766 in cell b3. enter a formula =b2+b3. the formula should be showing in the formula bar. insert a spreadsheet with $150,223 in cell b2 and 125, 766 in cell b3. enter a formula =b2/b3. the formula should be showing in the formula bar. insert a spreadsheet with $150,223 in cell b2 and 125, 766 in cell b3. enter a formula =b2*b3. the formula should be showing in the formula bar.

Budgets you to do all of the following expect a) send frivolously b) avoid over spending c) gain financial independence d) examine your priorities and goals

When early motion pictures played in movie theaters, they were often accompanied by live organ or piano music. which of the following are the most likely reasons that this happened? (select all that apply). the music was provided to distract audience members from the loud sounds made when filmstrips were changed. the music accompanied the movies because the movies were silent and audiences were used to hearing music during plays in theaters. the music usually was played before, and sometimes after the movie, as an alternative form of entertainment. the music viewers to interpret the dramatic action in the films.