Estimate how many searches will be needed to justify time spent on presorting an array of 101 elements if sorting is done by mergesort and searching is done by binary search. You may assume that all searches are for elements known to be in the array. What about an array of 105 elements?

Show that there is a language a ⚆ {0, 1} â— with the following properties: 1. for all x â a, |x| ≤ 5. 2. no dfa with fewer than 9 states recognizes a. hint: you don’t have to define a explicitly; just show that it has to exist. count the number of languages satisfying (1) and the number of dfas satisfying (2), and argue that there aren’t enough dfas to recognize all those languages. to count the number of languages satisfying (1), think about writing down all the strings of length at most 5, and then to define such a language, you have to make a binary decision for each string about whether to include it in the language or not. how many ways are there to make these choices? to count the number of dfas satisfying (2), consider that a dfa behaves identically even if you rename all the states, so you can assume without loss of generality that any dfa with k states has the state set {q1, q2, . . , qk}. now think about how to count how many ways there are to choose the other four parts of the dfa.

Awide variety of “ apps “ are available to customize devices. which category of app does the word processing software fall into?

The head restraint should be adjusted so that it reaches a. the top of your ears b. the base of your skull c. the top of the head