The lifetime (in hours) of a 60-watt light bulb is a random variable that has a normal distribution with σ = 30 hours. a random sample of 25 bulbs put on test produced a sample mean lifetime of = 1038 hours. if in the study of the lifetime of 60-watt light bulbs it was desired to have a margin of error no larger than 6 hours with 99% confidence, how many randomly selected 60-watt light bulbs should be tested to achieve this result?

Aboat radioed a distress call to a coast guard station. at the time of the call, a vector a from the station to the boat had a magnitude of 45.0 km and was directed 15.0° east of north. a vector from the station to the point where the boat was later found is = 30.0 km, 15.0° north of east. what are the components of the vector from the point where the distress call was made to point where the boat was found? in other words, what are the components of vector c = b - a?

A1-lb collar is attached to a spring and slides without friction along a circular rod in a vertical plane. the spring has an undeformed length of 5 in. and a constant k =25 lb/ft. knowing that the collar is released from being held at a determine, the speed of the collar and the normal force between the collar and the rod as the collar passes through b.

Aprisoner is forced to go into one of three rooms, but he can choose which room. the first room is ablaze with fire. the second one is rigged with explosives that will go off as soon as he enters. the third contains a pair of lions who haven't eaten in years. which room should he choose to survive?