∠e and ∠f are vertical angles with m∠e=5x+10 and m∠f=7x−12 . what is the value for x? enter your answer in the box.

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.

Rhombus adef is inscribed into a triangle abc so that they share angle a and the vertex e lies on the side bc . what is the length of the side of the rhombus if ab=c, and ac=b.

The students in a class were asked how many siblings they have. the data obtained is represented in the dot plot. the number of students who have no siblings is . the number of students who have three or more siblings is .