20. a soccer player jumps up and heads the ball while it is 4 feet above the ground. it bounces up at a
velocity of 12 feet per second. how long will it take the ball to hit the ground? use the projectile motion
formula. show all steps. simplify completely and label answer. g = -16t2 + vt + h

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.

Afarmer has a large field that is x feet in length. he wants to fence in a rectangular section in the middle of the field , leaving a length of 100 feet of open field behind each end of the fenced rectangle.he also wants the width of the fenced-in space to be 100 feet less than its length. find the expressions to represent the length and width of the fenced section of the field

The? half-life of a radioactive substance is 20 years. if you start with some amount of this? substance, what fraction will remain in 120 ? years