The newly elected president needs to decide the remaining 33 spots available in the cabinet he/she is appointing. If there are 1313 eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed?

What numbers are included in the set of integers? what numbers are not included?

Two airplanes start at the same place and travel in opposite directions,one at 395 miles per hour and the other at 422 miles per hour. how many hours will it take for the planes to be 2451 miles apart?

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.