A counselor at a large high school wants to estimate the mean amount of sleep μ that students got the previous night. She selects a random sample of 10 students and asks them to record the number of hours they slept last night. Based on this sample, the 95% confidence interval for the population mean amount of sleep for all students at the high school is (5.39, 7.81) hours. (a) Interpret the confidence interval. (b) What is the point estimate that was used to create the interval? What is the margin of error? (c) It is recommended that high school students get 8 hours or more of sleep each night. Based on this survey, the students claim that, on average, students at this high school are not getting the recommended amount of sleep. Use the confidence interval to evaluate this claim.

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.

Kristen is wrapping presents for the holidays. she has a box that measures 4 ft. x 2 ft. x 2 ft. how many square feet of wrapping paper does she need to cover the box without overlapping?

Triangles abc and dfg are given. find the lengths of all other sides of these triangles if: b ∠a≅∠d, ab·dg=ac·df, ac=7 cm, bc=15 cm, fg=20 cm, and df-ab=3 cm.