Johnson Chemicals is considering two options for its supplier portfolio. Option 1 uses two local suppliers. Each has a "unique-event" risk of 5.8%, and the probability of a "super-event" that would disable both at the same time is estimated to be 1.6%. Option 2 uses two suppliers located in different countries. Each has a "unique-event" risk of 14%, and the probability of a "super-event" that would disable both at the same time is estimated to be 0.24%.

(a) The probability that both suppliers will be disrupted using option 1 is
(b) The probability that both suppliers will be disrupted using option 2 is

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?