At a local community college, 55% of students who enter the college as freshmen go on to graduate. four freshmen are randomly selected.

a. what is the probability that none of them graduates from the local college? (round your intermediate calculations and final answer to 4 decimal places.)

b. what is the probability that at most three will graduate from the local college? (round your intermediate calculations and final answer to 4 decimal places.)

c. what is the expected number that will graduate? (round your final answer to the nearest whole number.)

Jonathan pays $1.90 per pound for potatoes. he buys 8.3 pounds of potatoes. he determines that he will pay $15.77, before tax, for the potatoes. which best describes the reasonableness of jonathan’s solution? jonathan’s answer is reasonable because there are two decimal places in the factors and two in the product. jonathan’s answer is unreasonable because there are three decimal places in the factors and two in the product. jonathan’s answer is reasonable because is 16, and 16 is close to 15.77. jonathan’s answer is unreasonable because is 8, and 8 is not very close to 15.77.

I’ve been trying all day to figure this puzzle out. i need the work for it aswell. it is a factoring polynomials tarsia. the image is below.

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?