The line ab has equation

the point a has coordinates (1, -1) and the point b has coordinates (3, k)

a) find the value of k

b) find an equation for the line through a which is perpendicular to ab

c) the point c has coordinates (-6 ,-2). show that ac has length

stating the value of p

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.