An experiment was designed to see whether laboratory rats would, on average, eat more when confined to a crowded cage or an uncrowded one. To minimize the effect of genetic differences, two rats were chosen from each of 30 litters. One of each pair of rats was randomly assigned to a crowded cage, the other rat to an uncrowded cage. The data to be collected were the 30 differences in the amount of food consumed between the "crowded" and the "uncrowded" rat from each litter.

What is the natural null hypothesis for this experiment?

?If so, which direction should be chosen?

Part a : solve - vp + 40 < 65 for v . part b : solve 7w - 3r = 15 for r show your work!

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."

Atriangle has an area of 72 square inches. if the base of the triangle has a length of 18 inches, what is the height of the triangle? use the formula for the area of a triangle: area = (base)(height) type a numerical answer in the space provided. do not include the units or spaces in your answer.