Sandra swims the 100-meter freestyle for her school’s swim team. her state’s ranking system awards 3 points for first place, 2 points for second, 1 point for third, and 0 points if she does not place. her coach used her statistics from last season to design a simulation using a random number generator to predict how many points she would receive in her first race this season
integer value points awarded frequency
1 - 8 3 20
9 - 15 2 12
16 - 19 1 6
20 0 2
  what is sandra’s expected value of points awarded for a race?

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.