Acollege 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.
(a) f(x) = kx^2 for 0 (b) f(x) = 0 for otherwise.
find the value of k and draw the corresponding density curve

Suppose there is a simple index of three stocks, stock abc, stock xyz, and stock qrs. stock abc opens on day 1 with 4000 shares at $3.15 per share. stock xyz opens on day 1 with 5000 shares at $4.30 per share. stock qrs opens on day 1 with 6000 shares at $4.60 per share. the price of stock abc on day 8 begins at $3.50. the price of stock xyz on day 8 begins at $3.90. stock qrs opens on day 8 with a price of $4.50 per share. assume that each stock has the same number of shares that it opened with on day 1. what is the rate of change of this simple index over 1 week?

Four individuals pool money together to start a new business and agree to split the profits equally. n invests $6,000, x invests $2,000, y invests $8,000 and z invests $4,000. if the profits for the first month were $100,000, y receives than if the profits were divided in proportion to how much they invested.

Evaluate the expression for the given value of the variable. ∣-4b-8∣+∣-1-b^2 ∣+2b^3 ; b=-2