You are selling tickets to a play. You have sold (3t+2) tickets for $5 each and (2t+5) tickets for $7 each. When t=3 what is the total amount of money received?

Which sum or difference identity would you use to verify that cos (180° - q) = -cos q? a.) sin (a -b) = sin a cos b – cos a sin b b.) cos (a -b) = cos a cos b – sin a sin b c.) cos (a -b) = cos a cosb + sin a sin b d.) sin (a + b) = sin a cos b + cos a sin b

Aking and his army will attempt to capture a fortress. the left and right flanks break off from the main group to attack the west and east guard towers. suppose the left flank has a 60% chance of success and the right flank has a 75% chance of success, independently of one another. if both flanks capture their respective targets, then the king has a 98% chance of successfully taking the fort. if, however, only the left flank captures its tower, the king has an 80% chance of success; if only the right flank succeeds, the king has a 50% chance. if both flanks fail, then the king's chance of capturing the fort drops to 20%. it turns out the king captures the fort. what is the probability that one, and only one, flank was successful (either the left, or the right, but not both)? (round your answer to 3 decimal places)

3. mr. sanchez’s class sold fruit pies for $1.65 each and mr. kelly’s class sold bottles of fruit juice for $1.36 each. together, the classes sold 79 items and earned $118.17 for their school. (a) write and solve a system of equations that model the problem. show all your work. (b) which class earned more money? (c) how much more money did that class earn?