Suppose that news spreads through a city of fixed size of 900000 people at a time rate proportional to the number of people who have not heard the news. a. Formulate a differential equation and initial condition for y(t) , the number of people who have heard the news t days after it has happened. No one has heard the news at first, so y(0)=0.dy/dt = k ( what ) , where k is the proportionality constantb.) 8 days after a scandal in City Hall was reported, a poll showed that 100000 people have heard the news. Using this information and the differential equation, solve for the number of people who have heard the news after t days. y(t) = what

An engineer is going to redesign an ejection seat for an airplane. the seat was designed for pilots weighing between 120 lb and 161 lb. the new population of pilots has normally distributed weights with a mean of 125 lb and a standard deviation of 28.1 lb. a)if a pilot is randomly selected, find the probability that his weight is between 120 lb and 161 lb. the probability is approximately? b. if 36 different pilots are randomly selected, find the probability that their mean weight is between 120 lb and 161 lb. the probability is approximately? c. when redesigning the ejection seat, which probability is more relevant? . part (b) because the seat performance for a single pilot is more important. b. part (b) because the seat performance for a sample of pilots is more important. c. part (a) because the seat performance for a sample of pilots is more important. d. part (a) because the seat performance for a single pilot is more important.