Adrian hopes that his new training methods have improved his batting average. Before starting his new regimen, he was batting 0.250 in a random sample of 52 at bats. For a random sample of 25 at bats since changing his training techniques, his batting average is 0.480. Determine if there is sufficient evidence to say that his batting average has improved at the 0.10 level of significance. Let the results before starting the new regimen be Population 1 and let the results after the training be Population 2. Step 1 of 3 :
State the null and alternative hypotheses for the test. Fill in the blank below.
H0Ha: p1=p2: p1⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯p2

Suppose you just purchased a digital music player and have put 8 tracks on it. after listening to them you decide that you like 4 of the songs. with the random feature on your player, each of the 8 songs is played once in random order. find the probability that among the first two songs played (a) you like both of them. would this be unusual? (b) you like neither of them. (c) you like exactly one of them. (d) redo () if a song can be replayed before all 8 songs are played.

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.

9.4.34  question   to estimate the height of a stone  figure, an observer holds a small square up to her eyes and walks backward from the figure. she stops when the bottom of the figure aligns with the bottom edge of the  square, and when the top of the figure aligns with the top edge of the square. her eye level is 1.811.81 m from the ground. she is 3.703.70 m from the figure. what is the height of the figure to the nearest hundredth of a  meter?