For safety reasons, four different alarm systems were installed in the vault containing the safety deposit boxes at a beverly hills bank. each of the four systems detects theft with a probability of .99 independently of the others. the bank, obviously, is interested in the probability that when a theft occurs, at least oneof the four systems will detect it. this probability is equal to:

Aspacecraft can attain a stable orbit 300 kilometers above earth if it reaches a velocity of 7.7 kilometers per second. the formula for a rocket's maximum velocity v in kilometers per second is vequalsminus0.0098tplusc ln upper r, where t is the firing time in seconds, c is the velocity of the exhaust in kilometers per second, and r is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. find the velocity of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.1 km/s, and a firing time of 15 s. can the spacecraft achieve a stable orbit 300 km above earth?