What is the Internet?

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.

Aconstruction company is creating a powerpoint presentation describing how they calculate costs during each construction step. they plan to email this presentation to clients. the individual clients will be watching the presentation slide show on their own personal computers. what is the most important formatting step the company should take to make the text readable and pleasing to the eye?

Carlos, an algebra teacher, is creating a series of powerpoint presentations to use during class lectures. after writing, formatting, and stylizing the first presentation, he would like to begin writing the next presentation. he plans to insert all-new content, but he wants to have the same formatting and style as in the first one. what would be the most efficient way for carlos to begin creating the new presentation? going under the file tab and opening the first presentation, deleting all content from each page, and adding new content going under the file tab and clicking on new in the left pane, then choosing new from existing going under the design tab and clicking on themes, then selecting the theme that was used for the first template going under the design tab and opening the template that was created for the first presentation