Allison takes a trip to a “Cent Store” where all items cost less than one dollar and she purchases one item. Ask for the cost of the item in cents. Remember that the cost will be less than one dollar. Display the minimum number of coins needed to make change for Allison’s purchase from one dollar. Also display the number of each type of coin. (Possible coins are pennies, nickels, dimes, and quarters.) (Java)

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.

Jackson is teaching the decimal number system. he wants his students to know how to expand numbers by powers of 10. which is the correct order in which digits are assigned values in the decimal number system?

1. technician a says horsepower information can be used by consumers to compare the power of different automobile engines. technician b says that manufacturers will often list the horsepower output of their engines in the online service information. who is right?