(50 points) What animes should I watch?

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.

Which of the following is a way that advancements in technology improve humans' ability to measure air quality and protect human health? a. air quality data gathered by new instruments can be used to reduce exposure to pollutants. b. new technologies enable natural and human-made pollution sources to be located and monitored. c. air quality data gathered by new instruments can be used to predict trends in pollution over time. d. new technologies allow governments to make informed decisions about the regulation of pollution. (choose more than one)

Technician a says engine assemblies can be mounted longitudinally in a chassis. technician b says engine assemblies can be mounted transversely in a chassis. who is correct?