Mrs. grady surveyed 30 students, 12 of which said they liked basketball, 16 of which said they liked hockey, and 4 of which said they liked both sports. (a) how many students did not like either sport?

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."

Student price tickets to a movie are $1 and non student tickets are $2 . 350 tickets are sold and the total amount made is $450. there were 250 student tickets sold . true or false .

20 points 1. your friend, taylor, missed class today and needs some identifying solutions to systems. explain to taylor how to find the solution(s) of any system using its graph. 2. taylor graphs the system below on her graphing calculator and decides that f(x)=g(x) at x=0, x=1, and x=3. provide taylor some feedback that explains which part of her answer is incorrect and why it is incorrect. f(x)=2x+1 g(x)=2x^2+1