The number of lawns l that a volunteer can mow in a day varies inversely with the number of shrubs s that need to be pruned that day. If the volunteer can prune 6 shrubs and mow 8 lawns in one day, then how many lawns can be mowed if there are only 3 shrubs to be pruned?

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.

(c) the diagram shows the first three shapes of a matchsticks arrangement.first shape = 3second shape = 5third shape = 7given m represents the number of matchstick used to arrange the n'th shape.(i) write a formula to represent the relation between m and n. express m as the subjectof the formula.(ii) 19 matchsticks are used to make the p'th shape. find the value of p.

Jake bakes and sell apple pies. he sells each pie for $5.75 . the materials to make the pies cost $40. the boxes jake puts the pies in cost & 12.50 total. how many pies does jake need to sell to earn a profit of $50