An algorithm takes 5 seconds for input size 200. How long will it take for input size 1000 if the running time is linear (assume low-order terms are negligible).

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.

The graph shows median weekly earnings for full-time workers according to education level. which can you not conclude?

Alex’s family members live in different parts of the world. they would like to discuss the wedding plans of one of their distant relatives. however, alex wants all the family members to talk to each other simultaneously so that they can make decisions quickly. which mode of internet communication should they use? a. blog b. email c. wiki d. message board e. instant messaging