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miss charlene made keychains for a donation drive
of the keychains
were packed into 14 small bags and 4 medium bags. 7 of the
laining keychains were packed into 6 big bags. the rest of the
keychains were given out as free samples. each medium bag
contained 4 times as many keychains as each small bag. each big bag
contained 6 more keychains than each small bag.
(a) what fraction of the keychains were given out as free samples?
(give your answer in its simplest form.)
(b) how many keychains were there in all the big bags?

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?