12. A chemist has 40 mL of a solution that is 50% acid. How much water should he add to make a solution that is 10% acid?
Total Amount x % Acid = Amount of Acid
Total Amount
% Acid
Amount of Acid
Original Solution
Water
New Solution

Mercury poisoning is dangerous overload of mercury within the body. a major source of mercury within the body, a major source of mercury poisoning is consuming fish that contain mercury. certain fish are more prone to having higher levels of mercury than others. the pie chart shows the distribution of four breeds of fish at a hatchery. the hatchery has approximately 6,000 fish. a biologist from the centers for disease control and prevention randomly test 5% of each breed of fish for mercury content. her findings are shown in the following table. based on the biologist's findings, if a single salmon is randomly selected from those that were tested, what is the probability that this particular fish would have a dangerous mercury level? a) 0.001 b) 0.004 c) 0.02 d) 0.08

Which expression is equivalent to the expression shown?

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) = .