Suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 22 and a mean diameter of 200200 inches. If 8383 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.20.2 inches? Round your answer to four decimal places. Answer

Simplify. (-2)^-3 a. -8 b. -1/8 c. 1/8 d. 8

Sue's average score for three bowling games was 162. in the second game, sue scored 10 less than in the first game. in the third game, she scored 13 less than in the second game. what was her score in the first game?

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.