state the various transformations applied to the base function ƒ(x) = |x| to obtain a graph of the function g(x) = 3[|x − 1| + 2].
horizontal shift of 1 unit to the right, a vertical shift upward of 6 units, and a vertical stretch by a factor of 3.
horizontal shift of 3 units to the right, a vertical shift downward of 2 units, and a vertical stretch by a factor of 3.
horizontal shift of 3 units to the left, a vertical shift upward of 2 units, and a vertical stretch by a factor of 3.
horizontal shift of 1 unit to the left, a vertical shift downward of 6 units, and a vertical stretch by a factor of 3.

On average, how many more hits will he get when he bats 100 times at home during the day as opposed to 100 times away at night?

The accompanying table shows the numbers of male and female students in a particular country who received bachelor's degrees in business in a recent year. complete parts (a) and (b) below. business degrees nonbusiness degrees total male 189131 634650 823781 female 169539 885329 1054868 total 358670 1519979 1878649 (a) find the probability that a randomly selected student is male, given that the student received a business degree. the probability that a randomly selected student is male, given that the student received a business degree, is nothing. (round to three decimal places as needed.) (b) find the probability that a randomly selected student received a business degree, given that the student is female. the probability that a randomly selected student received a business degree, given that the student is female, is nothing. (round to three decimal places as needed.)

The width of a rectangle is half as long as the length. the rectangle has an area of 18 square feet. what are the length and width of the rectangle?