The number of miles y in a measure varies directly as the number of kilometers x. Write a direct variation equation that can be used to convert kilometers to miles, if 5 kilometers is about 3.1075 miles.

Afactory makes propeller drive shafts for ships. a quality assurance engineer at the factory needs to estimate the true mean length of the shafts. she randomly selects four drive shafts made at the factory, measures their lengths, and finds their sample mean to be 1000 mm. the lengths are known to follow a normal distribution whose standard deviation is 2 mm. calculate a 95% confidence interval for the true mean length of the shafts. input your answers for the margin of error, lower bound, and upper bound.

An investment decreases in value by 30% in the first year and decreases by 40% in the second year. what is the percent decrease in percentage in the investment after two years

For the quadratic function [tex]y=(x+4)^2-1[/tex] , do the following: a) rewrite the function in the standard form, b) rewrite the function in intercept form, c) find the vertex, d) find the y-intercept, e) find the x-intercepts.