An ecologist wishes to select a point inside a circular sampling region according to a uniform distribution (in practice this could be done by first selecting a direction and then a distance from the center in that direction). Let X the x coordinate of the point selected and Y the y coordinate of the point selected. If the circle is centered at (0, 0) and has radius R, then the joint pdf of X and Y is given below: f(x, y) = {1/piR^2 x2+y2+ otherwise
a) What is the probability that the selected point is within R/6 of the center of the circular region?
b) What is the probability that both X and Y differ from 0 by at R/3?
c) What is the probability that both X and Y differ from 0 by at R/underroot3?

Which of the following represents a number squared is equal to twenty more than nine times that number ? a) x squared = 9x + 20 b) x squared = 20x + 9 c) x squared > 9 + 20x d) x squared = 9 + x + 20

7.(03.01 lc)which set represents the range of the function shown? {(-1, 5), (2,8), (5, 3), 13, -4)} (5 points){-1, 2, 5, 13){(5, -1), (8, 2), (3,5), (-4, 13)){-4, 3, 5, 8}{-4, -1, 2, 3, 5, 5, 8, 13}

Write the contrapositive of the conditional statement. determine whether the contrapositive is true or false. if it is false, find a counterexample. a converse statement is formed by exchanging the hypothesis and conclusion of the conditional. a) a non-converse statement is not formed by exchanging the hypothesis and conclusion of the conditional. true b) a statement not formed by exchanging the hypothesis and conclusion of the conditional is a converse statement. false; an inverse statement is not formed by exchanging the hypothesis and conclusion of the conditional. c) a non-converse statement is formed by exchanging the hypothesis and conclusion of the conditional. false; an inverse statement is formed by negating both the hypothesis and conclusion of the conditional. d) a statement not formed by exchanging the hypothesis and conclusion of the conditional is not a converse statement. true