According to the journal of irreproducible results, any obtuse angle is a right angle! c d b p here is their argument. given the obtuse angle x, we make a quadrilateral abcd with \dab = x, and \abc = 90 , and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = p

d. so the triangles p ad and p bc have equal sides and are congruent. thus \pad = \pbc. but pab is isosceles, hence \pab = \pba. subtracting, gives x = \pad \pab = \pbc \pba = 90 . this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?

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?

Carl's candies has determined that a candy bar measuring 3 inches long has a z-score of +1 and a candy bar measuring 3.75 inches long has a z-score of +2. what is the standard deviation of the length of candy bars produced at carl's candies?

Consider circle c with angle acb measuring 3/4 radians.if minor arc ab measures 9 inches, what is the length of the radius of circle c? if necessary, round your answer to the nearest inch.