A group of nn Ghostbusters is battling n ghosts. Each Ghostbuster carries a proton pack, which shoots a stream at a ghost, eradicating it. A stream goes in a straight line and terminates when it hits the ghost. The Ghostbusters decide upon the following strategy. They will pair off with the ghosts, forming nn Ghostbuster-ghost pairs, and then simultaneously each Ghostbuster will shoot a stream at his chosen ghost. As we all know, it is very dangerous to let streams cross, and so the Ghostbusters must choose pairings for which no streams will cross. Assume that the position of each Ghostbuster and each ghost is a fixed point in the plane and that no three positions are colinear. a. Argue that there exists a line passing through one Ghostbuster and one ghost such that the number of Ghostbusters on one side of the line equals the number of ghosts on the same side. Describe how to find such a line in O(n\lg n)O(nlgn) time. b. Give an O(n^2\lg n)O(n 2 lgn)-time algorithm to pair Ghostbusters with ghosts in such a way that no streams cross.

Ms. garcia and ms. ming are both sixth-grade english teachers. ms. garcia, a new teacher at the school, has additional certification in gifted education. ms. ming has been a certified english teacher for a number of years. ms. ming has been overheard in the faculty lounge making negative comments about ms. garcia's professional abilities and personal character. mr. daniels, the sixth-grade history teacher, has heard ms. ming making negative comments about ms. garcia on more than one occasion and he knows that these comments are false. he also knows that ms. ming has been angry that ms. garcia was asked to teach the advanced english class. this is a class ms. ming had expressed a desire to teach. he believes this contributes to her negativity toward ms. garcia. what should he do? * a. mr. daniels should do nothing because he is not directly involved in the disagreement. b. mr. daniels should discuss the situation with the principal because ms. ming is in direct violation of the code of ethics. c. mr. daniels should speak ms. ming and ask her to stop talking about ms. garcia. d. mr. daniels should talk to ms. garcia about letting ms. ming teach the class since she has seniority.