The figure shows two triangles on the coordinate grid: What set of transformations is performed on triangle ABC to form triangle A′B′C′?

a.
A translation 5 units down, followed by a 180-degree counterclockwise rotation about the origin

b.
A translation 5 units down, followed by a 270-degree counterclockwise rotation about the origin

c.
A 180-degree counterclockwise rotation about the origin, followed by a translation 5 units down

d.
A 270-degree counterclockwise rotation about the origin, followed by a translation 5 units down

Let f (x) = x e8x. find a formula for the nth derivative of f, where n is any positive integer. use x and n in your answer if needed. f (n)(x) =

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.

How many credit hours will a student have to take for the two tuition costs to be equal? round the answer to the nearest tenth of an hour.