A decorative​ tile, like the one shown​ (which is not to​ scale) features an image meant to resemble a butterfly. The wings are two​ semicircles, each with radius 6.3 inches. The head is a quarter circle with radius 3.3 inches. What is the total area of the butterfly image on the​ tile?

Acircular hot tub located near the middle of a rectangular patio has a diameter of 48 inches. the patio measures 11 feet by 6 feet. what is the area of the patio that is not covered by the hot tub?

Afurniture manufacturer produces chairs and sofas. each chair requires 10 yards of fabric, and each sofa requires 20 yards of fabric. the manufacturer has 300 yards of fabric available. to fulfill orders, the number of sofas must be at least twice the number of chairs. let x be the number of chairs and y the number of sofas. which inequalities are described in the problem? check all of the boxes that apply

Identify the initial amount a and the growth factor b in the exponential function. a(x)=680*4.3^x