Shown in the figure is part of a design for a water slide. find the total length of the slide to the nearest foot, if α = 25°, β = 31°, a = 35 ft, and b = 170 ft.

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.)

1. suppose that scores on a knowledge test are normally distributed with a mean of 71 and a standard deviation of 6. a. label the curve: show the mean and the value at each standard deviation: b. if angelica scored a 76 on the test, what is her z-score? (draw her score on the curve above and label) c. what percent of students did angelica score higher than? how can you tell? d. if 185 students took the test, how many students scored higher than angelica?

If the coefficient of determination for a data set containing 24 points is 0.5,12 of the data points must lie on the regression line for the data set. true or false?