College professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let X = the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is as follows. f(x) = kx^2 0 ? x ? 20 otherwise(a) Find the value of k. (Enter your answer to three decimal places.).375(B) What is the probability that the lecture ends within 1 min of the end of the hour? (Enter your answer to three decimal places.).125c) What is the probability that the lecture continues beyond the hour for between 15 and 45 sec? (Round your answer to four decimal places.)(d) What is the probability that the lecture continues for at least 75 sec beyond the end of the hour? (Round your answer to four decimal places.)

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)

answer: 3 x 2 = 6 and 6+0

step-by-step explanation: sum equals addition and twice is multiplication so its

3 x 2 = 6

6+0= 6

identity property of zero