Aparticular brand of dishwasher soap is sold in three sizes: 25 oz, 40 oz, and 65 oz. twenty percent of all purchasers select a 25-oz box, 50% select a 40-oz box, and the remaining 30% choose a 65-oz box. let x1 and x2 denote the package sizes selected by two independently selected purchasers. a. determine the sampling distribution of x, calculate e(x), and compare to m. b. determine the sampling distribution of the sample variance s2 , calculate e(s2 ), and compare to s2 .

The hypotenuse of an isosceles right triangle is $14\sqrt 2$. what is the area of the triangle?

In a sample of 2023 u.s. adults, 373 said franklin roosevelt was the best president since world war ii. two u.s. adults are selected at random from the population of all u.s. adults without replacement. assuming the sample is representative of all u.s. adults, complete parts (a) through (d). (a) find the probability that both adults say franklin roosevelt was the best president since world war ii. the probability that both adults say franklin roosevelt was the best president since world war ii is (round to three decimal places as needed.) (b) find the probability that neither adult says franklin roosevelt was the best president since world war ii. the probability that neither adult says franklin roosevelt was the best president since world war ii is (round to three decimal places as needed.) (c) find the probability that at least one of the two adults says franklin roosevelt was the best president since world war ii. the probability that at least one of the two adults says franklin roosevelt was the best president since world war ii is (round to three decimal places as needed.) (d) which of the events can be considered unusual? explain. select all that apply. the event in part left parenthesis a right parenthesis is unusual because its probability is less than or equal to 0.05. the event in part (b) is unusual because its probability is less than or equal to 0.05. none of these events are unusual. the event in part (c) is unusual because its probability is less than or equal to 0.05.

Select the two pairs of figures that are similar.