Mary started the week with 32 bananas. On Tuesday her family ate half of them. On Wednesday they ate half of the remaining bananas. If they continue doing this each day, on which day of the week will only one banana be left?

If cos(2x) = tan^2(y), show that cos(2y) = tan^2(x).

Carla was trying to decide what to do saturday evening. she has $100 available to spend for the evening. she has narrowed her choices down to these events: braves game, a concert of an artist she likes, or the georgia aquarium. admission to the braves game is $25, hot dogs cost $10, sodas cost $5. the concert costs $25 for admission, $20 for a souvernir t-shirt, and $10 for a soda. the georgia aquarium has the show of a lifetime with an all you can eat and drink that costs $100. carla does not want to take any driving chances, so in addition to the cost of the aquarium, she will also need to pay for her uber/lyft, which is $15 each way. which option should carla choose if she wants to spend the least? based on that choice, what then is carla's oppotunity cost? fully explain your answer in at least one paragraph.

Vinny is interviewing for a job.he wants his take home pay to be at least $42,000.what is the least salary he can earn if he pays 25% income tax?