What are the values of a and b in the figure below?

1. there are 25 students who started computer programming in elementary school and 25 students who started computer programming in middle school. the first group had a mean final project grade of 95% and the second group had a mean final project grade of 92%. the line plot shows the differences after 10 rerandomizations. determine whether the difference in the means of the two groups is significant based on the line plot. explain your answer.

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) = .

Questions 7-8. use the following table to answer. year 2006 2007 2008 2009 2010 2011 2012 2013 cpi 201.6 207.342 215.303 214.537 218.056 224.939 229.594 232.957 7. suppose you bought a house in 2006 for $120,000. use the table above to calculate the 2013 value adjusted for inflation. (round to the nearest whole number) 8. suppose you bought a house in 2013 for $90,000. use the table above to calculate the 2006 value adjusted for inflation. (round to the nearest whole number)