Draw vector diagrams based on the given scenarios, and solve the problems involving vectors. a) Karina travels 5 miles at a bearing of 30° east of north to get to the supermarket. She then travels 10
miles 15° south of east to go to Anissa's house. How far away and in what direction is Karina's house
from Anissa's house? Draw a diagram and show your work to justify your answer. Round the distance
to the nearest hundredth and the direction to the nearest degree.

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.