Round the given number to the indicated place value. (a) Round 5,473.38275 to the nearest tenth. (b) Round 5,473.38275 to the nearest hundredth. (c) Round 5,473.38275 to the nearest thousandth.

The Wray family (a family of 5) is planning their family vacation to Seattle, Washington. The distance is approximately 2,300 miles. The average price of gasoline is $3.99 per gallon. They plan to stay in a hotel for six nights and budget the cost of meals to be about $60 per person per day. The trip will be a total of 7 days. (a) If their van averages 25 miles per gallon, estimate the total cost of the gas for the trip. Remember that they must drive there and back! Round to the nearest cent. (b) If the hotel will cost $139.99 per night plus 18% hotel tax, determine how much they should budget for the total cost of the hotel. Round your answer to the nearest cent. (c) How much should they budget for the total cost of meals for their trip?

The following is a toy grammar of English. Explain why we need the two non-terminal nodes T and I. What do they do, and why can’t we just have one terminal node to cover both? S → N IS → N T NN→ MaryN→ JohnN→ SamI → laughedI → criedT → helpedT → liked

Write the regular expression for this language: The set of strings that are composed of one or more 0s followed by one or more 1s.

Identify the string that belongs to the language a*b*.

Set A has 4 members and set B has 3 members. We also know that A∩B has 2 members. How many members does AUB have?

Write a regular expression that is equivalent to the following grammar. S→ABA→AaA→ϵB→BbB→ϵ

If p means “John likes Sushi” and q means “John likes pizza”, what exactly does (p∧q)∨(¬p∧¬q) mean?

Which of these well-formed formulas corresponds to the truth table? p q ? T T T T F F F T T F F F

9. Is this a tautology (always true), a contingency (sometimes true), or a contradiction (never true)? a∧(¬a∧¬b)