1 Let X and Y be two continuous random variables with joint probability
density function
f(x, y) = 0.25x^2 + y/c; -1<= x
<= 1, 0; otherwise.

a) Compute the value of c.
b) Produce the marginal probability density function of Y.
c) Calculate P(X > 0,Y <1).
d) Calculate P(X>0|Y <1).
e) Calculate P(X + Y > 0).

The amount of energy it takes to lift a box might be a function of which of the following

1. what expression would be the same as 6x+x+0 2. find the prime factorization of 60 3. write the expression for 6 + x in words.

In one day there are too high tides into low tides and equally spaced intervals the high tide is observed to be 6 feet above the average sea level after six hours passed a low tide occurs at 6 feet below the average sea level in this task you will model this occurrence using a trigonometric function by using x as a measurement of time assume the first high tide occurs at x=0. a. what are the independent and dependent variables? b. determine these key features of the function that models the tide: 1.amplitude 2.period 3.frequency 4.midline 5.vertical shift 6.phase shift c. create a trigonometric function that models the ocean tide for a period of 12 hours. d.what is the height of the tide after 93 hours?