Applicants for the University of Statland take two tests, one for writing ability and the other on critical thinking, and normalized scores are recorded on each between 0 and 1. For a given applicant, let X be the score on the writing test and YY the score on the critical thinking test. A model for the joint probability density function for the two test scores can be taken as:

f(x, y) = { x+y for 0 < x < 1, 0 < y < 1

{ 0 elsewhere.

(a) Find the marginal density of the writing test score, and evaluate it at the point X = 1/2.

(b) Find the marginal density of the critical thinking test score, and evaluate it at the point Y = 1/3.

Asilkworm winds its cocoon out of one long silk fiber. to make silk thread, 3 to 10 of these silk fibers are unwound from their cocoons and combined into aa single thread with a typical length of 300 yards. choose a reasonable number of silk fibers in a thread write an equation to find the total length of the silk fibersused in 300 yards of the thread

Someone answer this asap rn for ! a discount store’s prices are 25% lower than department store prices. the function c(x) = 0.75x can be used to determine the cost c, in dollars, of an item, where x is the department store price, in dollars. if the item has not sold in one month, the discount store takes an additional 20% off the discounted price and an additional $5 off the total purchase. the function d(y) = 0.80y - 5 can be used to find d, the cost, in dollars, of an item that has not been sold for a month, where y is the discount store price, in dollars. create a function d(c(x)) that represents the final price of an item when a costumer buys an item that has been in the discount store for a month. d(c(x)) =

On a cm grid, point p has coordinates (3,-1) and point q has coordinates (-5,6) calculate the shortest distance between p and q give your answer to 1 decimal place