The mean length of a candy bar is 43 millimeters. there is concern that the settings of the machine cutting the bars have changed. test the claim at the 0.02 level that there has been no change in the mean length. the alternate hypothesis is that there has been a change. twelve bars (n = 12) were selected at random and their lengths recorded. the lengths are (in millimeters) 42, 39, 42, 45, 43, 40, 39, 41, 40, 42, 43, and 42. the mean of the sample is 41.5 and the standard deviation is 1.784. computed t = -2.913. has there been a statistically significant change in the mean length of the bars?

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."

You and a friend went to the movies.you spent half your money on tickets. then you spent 1/4 of the money on popcorn, $2 on candy, and $3 on a soda. if you have $1 left, hiw much money did u take to the movies?

Which equation expression the relationship between the number of boxes b and the number of cans c and the proportion is 48