Professors Gupta and Rudich each independently pick k problems uniformly at random from a set of k 2 problems to place on an exam. How many problems do we expect will be picked by both of them

Find the greatest common factor of -30x 4 yz 3 and 75x 4 z 2.

Sara can take no more than 22 pounds of luggage on a trip.her suitcase weighs 112 ounces.how many more pounds can she pack without going over the limit?

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.