Ariana is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Arians will earn $40 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. Ariana earned a total of $500 in royalties on 9 commercials and movies. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Arianas songs were played. Define the variables that you use to write the system.

If h(x) = f[tex]h(x) = f[/tex] ° [tex]g) (x)[/tex] and [tex]h(x) = \sqrt[3]{x+3}[/tex], find [tex]g(x)[/tex] if [tex]f(x) = \sqrt[3]{x +2}[/tex] ·

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.)

Is triangle jkl congruent to triangle rst? if so, what is the scale factor?