Let X be a topological space and let Y be a subset of X . Check that the so-called subspace topology is indeed a topology on Y .

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?

Aman is 6 feet 3 inches tall. the top of his shadow touches a fire hydrant that is 13 feet 6 inches away. what is the angle of elevation from the base of the fire hydrant to the top of the man's head?

Florence price's brownies and more sells all types of cookies and pastries. on tuesdays, they markdown all brownies 75% to a sale of $1.50 a dozen. find the selling price and the markdown of a dozen brownies.