The process of producing vitamins yields capsules with varying amounts of the active ingredient. It is claimed that the average amount of active ingredient per tablet is at least 50 milligrams. The Consumer Watchdog Bureau tests a random sample of 75 tablets. The mean content of the active ingredient for this sample is 46.6 milligrams and the standard deviation is 9 milligrams. What is the approximate p-value for the appropriate test? (4 points)

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?