The diagram below models the layout at a carnival where g, r, p, c, b, and e are various locations on the grounds. grpc is a parallelogram.

part a: identify a pair of similar triangles.

part b: explain how you know the triangles from part a are similar.

part c: find the distance from b to e and from p to e. show your work.

Radii ok and nl are perpendicular to om because of the radius-tangent theorem. by definition of perpendicular, angles kom and lnm are right angles. this means that triangles kom and lnm are right triangles. angle lmn is common to both right triangles, so by the triangles kom and lnm are similar.

Need now max recorded the heights of 500 male humans. he found that the heights were normally distributed around a mean of 177 centimeters. which statements about max’s data must be true? a) the median of max’s data is 250 b) more than half of the data points max recorded were 177 centimeters. c) a data point chosen at random is as likely to be above the mean as it is to be below the mean. d) every height within three standard deviations of the mean is equally likely to be chosen if a data point is selected at random.

About 9% of th population is hopelessly romantic. if 2 people are randomly selected from the population, what is the probability that at least 1 person is hopelessly romantic?