Casey read a report that said the probability that a randomly selected American is left-handed is 14 % , percent. She was curious how many left-handed students to expect in a class of 30 students. She simulated 50 classes of 30 students where each student selected had a 0.14 point, 14 probability of being left-handed. Casey counted how many left-handed students were in each simulated class. Here are her results: 0 1 2 3 4 5 6 7 8 # of left-handed students Use her results to estimate the probability that there are more than 5 left-handed students in a class of 30 30 students. Give your answer as either a fraction or a decimal.

Use the matrix-column representation of the product to write each column of ab as a linear combination of the columns of a.

Which expression is equivalent to (3^2)^-2 a.-81 b.-12 c.1/81 d.1/12

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."