Michael and Derek enjoy playing tennis, and before every match they estimate how long it will take. The actual match time is always greater than the time Michael and Derek estimate. They recorded the times for four matches, but some of the information has been lost. Complete the table. Round to the nearest tenth if necessary.

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

Given abc find the values of x and y. in your final answer, include all of your calculations.

For each given situation, determine if the method of randomization is either appropriate or not appropriate