Element X is a radioactive isotope such that every 21 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 1800 grams, how much of the element would remain after 28 years, to the nearest whole number?

Factor completely. x^8 - 1/81 a) (x^4 + 1/9)(x^2 + 1/3)(x^2 - 1/3) b) (x^4 - 1/9)(x^2 + 1/3)(x^2 - 1/3) c) (x^4 + 1/9)(x^2 - 1/3)2

The volume of gas a balloon can hold varies directly as the cube of its radius. imagine a balloon with a radius of 3 inches can hold 81 cubic inches of gas. how many cubic inches of gas must be released to reduce the radius down to 2 inches?

Adecorative window is made up of a rectangle with semicircles at either end. the ratio of ad to ab is 3: 2 and ab is 30 inches. what is the ratio of the area of the rectangle to the combined area of the semicircles? possible answers: a. 2: 3 b. 3: 2 c. 6: π d. 9: π e. 30: π