Aprofessor must randomly select 4 students to participate in a mock debate. there are 15 students in his class. in how many different ways can these students be selected, if the order of selection does not matter?

Adifferent website gives the cost for the first train as £56.88 and the second train as £20.11 with a £9.50 charge for cycle storage for the whole trip. how much would the journey cost you?

Parks is wearing several rubber bracelets one third of the bracelets are tie dye 1/6 are blue and 1/3 of the remainder are camouflage if park swears to camouflage bracelets how many bracelets does he have on

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) = .