Consider three independent random variables X, W1, and W2. Construct two new random variables Y1 and Y2 from simple algebraic combinations of X, W1, and W2 such that Y1 and Y2 are not independent, but are conditionally independent given X.

Aretha wanted to gather data about the cost of local bowling leagues in her area. she plotted the data and determined that the average bowling league costs consist of a one-time registration fee and a monthly fee modeled by the equation y = 15x + 20. identify and interpret the y-intercept in this model. the y-intercept is 20. this is the cost per month. the y-intercept is 20. this is the cost of registration. the y-intercept is 15. this is the cost of registration. the y-intercept is 15. this is the cost per month.

You had $235 in your savings account nine weeks ago. you withdrew the same amount each week for 8 straight weeks. your balence was then $75. solve the equation 235 - 8m=75 to find how much money m you withdrew from your account each week. 2 points

More challenges: 1) factor out the indicated quantity.8mn² + 7mn - m : factor out the quantity -m2) factor the polynomial by grouping.2vw + 7cv + 14cw + 49c²3) factor completely using the difference of squares along with factoring by grouping.25v³ - 25v² - 4v + 44) factor the sum of cubes. 125x³ + 645) q³ + 27r³6) factor completely. use difference of squares.729p^6 - 6^67) solve the equation(7x + 4)(9x - 1) = 08) a. find the values of x for which f (x) = 0b. find f (0)f (x) = x² + 2x - 489) find the x and y-intercepts for the function defined by y = f (x)f (x) = (x + 3)(x + 4)(x - 1)²10) factor the trinomial completely by using any method. remember to look for a common factor first. 3v² - 2v - 16