Below are four different advertisements at four different stores for the same jeans. JL Fashion Mart Tops, Bottoms, and More Boy's Jeans Regular Price: $16 Sale Price: 20% off each Boy's Jeans Regular Price: $27 Coupon: Buy 2, get 1 free Clothing Outlet We Sell Everything Boy's Jeans Regular Price: $20 Coupon: Buy 1, get 1 for $1 Boy's Jeans Regular Price: $25.99 Sale Price: Rebate of $5 each

Afactory makes propeller drive shafts for ships. a quality assurance engineer at the factory needs to estimate the true mean length of the shafts. she randomly selects four drive shafts made at the factory, measures their lengths, and finds their sample mean to be 1000 mm. the lengths are known to follow a normal distribution whose standard deviation is 2 mm. calculate a 95% confidence interval for the true mean length of the shafts. input your answers for the margin of error, lower bound, and upper bound.

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) = .

The table shows the number of students who signed up for different after school activities. activity students cooking 9 chess 4 photography 8 robotics 11 select the true statements about the information in the table.