Rug with a perimeter of 18 feet. she decides to place a border around the rug so that the new length of the rug is 8 feet and the width is 4 feet. the border is the same width all the way around. the equation which represents x, the width of the border is 2(8-2x)+2(4-2x)=18. what is the width of the border?

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.)

Evaluate the expression for the given value of the variable. ∣-4b-8∣+∣-1-b^2 ∣+2b^3 ; b=-2

The given diagram shows the parts of a right triangle with an altitude to the hypotenuse. using the two given  measures, find the other four.