Katrina and amanda are studying the same class. on monday, katrina solved 35 math problems and amanda solved 21 math problems. on wednesday katrina solved 16 math problems and amanda solved 20 math problems. on thursday, katrina solved 40 math problems and amanda solved 24 math problems. on saturday, katrina solved 18 math problems and amanda solved 24 math problems. on which day did katrina and amanda have the same ratio of problems as monday?

In a circle, a 45° sector has an area of 32π cm2. what is the radius of this circle? 32 cm 12 cm 16 cm 8 cm

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."

Find the area of the unshaded square