The distance between city a and city b is 22 miles. the distance between city b and city c is 54 miles. the distance between city a and city c is 51 miles.

what type of triangle is created by the three cities?

an acute triangle, because 222 + 542 > 512
an acute triangle, because 222 + 512 > 542
an obtuse triangle, because 222 + 542 > 512
an obtuse triangle, because 222 + 512 > 542

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."

33% of college students say they use credit cards because of the rewards program. you randomly select 10 college students and ask each to name the reason he or she uses credit cards. find the probability that the number of college students who say they use credit cards because of the rewards program is (a) exactly two, (b) more than two, and (c) between two and five inclusive. if convenient, use technology to find the probabilities.

List the sides of δrst in ascending order (shortest to longest) if: m∠r =x+28°, m∠s = 2x+16°, and m∠t = x+12