James has 4/3/4 feet of rope he plans to cut off 1/1/2 feet from the rope will be left

There is a line with slope 1/a going through the point (a, a²). find the equation of the line perpendicular to this line at this point. (don’t let this problem intimidate you! solve the problem as you would if i’d given you specific values. just use variables instead.)

Atextile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. the company wishes to test the hypothesis upper h subscript 0 baseline colon mu equals 12 against upper h subscript 1 baseline colon mu less-than 12 using a random sample of n equals 4 specimens. calculate the p-value if the observed statistic is x overbar equals 11.8. round your final answer to five decimal places (e.g. 98.76543).

Captain umaima has a ship, the h.m.s. khan. the ship is two furlongs from the dread pirate nadia and her merciless band of thieves. the captain has probability 3/7 of hitting the pirate ship. the pirate only has one good eye, so she hits the captain's ship with probability 2/5. if both fire their cannons at the same time, what is the probability that the captain hits the pirate ship, but the pirate misses.