You are offered the following gamble: Flip two fair coins. If at least one head comes up, you win $12. If not, you lose $24. What is the expected value of this gamble?

Write an algebraic expression to match each statement a. four less than 8 times a number b. twice the difference of a number and six c. nine from a number squared

What are the excluded values? m+5/mn+3m

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?