In triangle abc, the measure of angle b is 90 degrees, bc=16, and ac=20. triangle def is similar to triangle abc, where vertices d, e, and f corresponds to vertices a, b, and c, respectively, and each side of triangle def is 1/3 the length of the corresponding side of triangle abc. what is the value of sinf?
( show your work)

Convert 2000 swiss francs to dutch guilders

In need of in the diagram, ∠abc is a right angle. ∠dbc = 30°27'40". find the measure of ∠abd.

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.