Johanna’s parents give her $10 per week for lunch money. She cannot decide whether she wants to buy or pack her lunch. If a hot lunch at school cost $2, write and solve an inequality to finding the maximum number of times per week Johanna can buy her lunch.
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Ajar contains a mixture of 20 black marbles, 16 red marbles, and 4 white marbles, all the same size. find the probability of drawing a white or red marble on the first draw. 125 12 01 next question ask for turn it in

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) = .

Use sigma notation to represent the following series for 9 terms.