Liam bought 2 vintage movie posters, 2 rock posters, and 1 rap poster. he applied a $35 gift card to the total purchase and a half-off coupon to the rap poster. write and evaluate a numerical expression to show how much liam paid for the posters.

Peter applied to an accounting firm and a consulting firm. he knows that 30% of similarly qualified applicants receive job offers from the accounting firm, while only 20% of similarly qualified applicants receive job offers from the consulting firm. assume that receiving an offer from one firm is independent of receiving an offer from the other. what is the probability that both firms offer peter a job?

Prove sin2a + cos2a - 1 / sin2a + cos2a + 1 = 1 - tana / 1 + cota

Which of the following circles have their centers in the third quadrant? check all that apply.