The smiths spend 12% of their budget on entertainment. their total budget this year is $2,000 more than last year, and this year they plan to spend $5,640 on entertainment. what was their total budget last year?

Which of the following is the formula for the sequence graphed below

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."

Afamily has five members. a mom, a dad, two sisters, & a brother. the family lines up single file. what is the probabillity that the mom is at the front of the line