One fifth of a number is 12. what is one third of a number?

Achemist has 200 ml of a 10% sucrose solution. she adds x ml of a 40% sucrose solution. the percent concentration, y, of the final mixture is given by the rational function: the chemist needs the concentration of the final mixture to be 30%. how many milliliters of the 40% solution should she add to the 10% solution to get this concentration?

If cos(2x) = tan^2(y), show that cos(2y) = tan^2(x).

Find the condition that the zeros of the polynomial f(x) = x^3+3px^2+3px+r may be in a.p.