You are working on a statewide Colorado project and decide to define a custom coordinate system. Start with one of the State Plane zones and modify it slightly to make it better for the whole state. Explain your approach and Capture the window showing the custom coordinate system description you created.

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 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

1. you have a small business that is divided into 3 departments: accounting, sales, and administration. these departments have the following number of devices (computers, printers, etc.): accounting-31, sales-28, and administration-13. using a class c private network, subnet the network so that each department will have their own subnet. you must show/explain how you arrived at your conclusion and also show the following: all available device addresses for each department, the broadcast address for each department, and the network address for each department. also, determine how many "wasted" (not usable) addresses resulted from your subnetting (enumerate them).