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?

Hye ryung is the president of the local chapter of the american medical students association (amsa). she is organizing local outreach and informational meetings. at her first meeting there are five people present (including herself). every month after that her group grows by 5 people. a. how many members are in the group after 6 months? b. the logistics of hosting and feeding her group at meetings was more complicated than expected. the cost of feeding 5 people at her first meeting was $30, for 10 people it was $35, for 15 it was $45, and after 6 months all of the costs had added up to $100. write a function to model the cost with the number of people attending meetings. c. what connections can you make between the linear growth of the group’s membership and the increasing costs of running meetings?

Factor x2 – 8x + 15. which pair of numbers has a product of ac and a sum of what is the factored form of the

Solve 2x2 + 8 = 0 by graphing the related function. there are two solutions: . there are no real number solutions. there are two solutions: 2 and -2