If cot(x) = 5/7, find tan(x)

Haruka hiked several kilometers in the morning. she hiked only 66 kilometers in the afternoon, which was 25% less than she had hiked in the morning. how many kilometers did haruka hike in all?

Merrida uses a pattern in the multiplication table below to find ratios that are equivalent to 7: 9. if merrida multiplies the first term, 7, by a factor of 6, what should she do to find the other term for the equivalent ratio? multiply 9 by 1. multiply 9 by 6. multiply 9 by 7. multiply 9 by 9.

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.