An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously. The equation
2000.081 - 350 represents the situation, where t is the number of years the money has been invested. About how long has the
money been invested? Use a calculator and round your answer to the nearest whole number.

Me 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.

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

Meghan has created a diagram of her city with her house, school, store, and gym identified. a. how far is it from the gym to the store? b. meghan also wants to walk to get some exercise, rather than going to the gym. she decides to walk along arc ab. how far will she walk? round to 3 decimal places.