A sociologist was interested in determining if there was a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred. A random sample of 93 adults revealed the following data. Use a Chi-Square independence test to determine if age and type of movie preferred are independent at the 5% level of significance. 18-23 years old 24-29 years old 30-35 years old Totals Drama 8 15 11 34 Science Fiction 12 10 8 30 Comedy 9 8 12 29 Totals 29 33 31 93 Provided the assumptions of the test are satisfied, determine the critical value for the test.

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?