In a triangle abc, with angles a, b, and c and sides ab, bc, and ac, angle b is a right (90°) angle. if the sin of angle a is 0.5 and side bc is 8 inches long, what is the length of side ac?

The weekly revenue for a company is r = 3p^2 + 60p + 1060, where p is the price of the company's product. what price will result in a revenue of $1200.

Liz is shipping a package to her friend. the maximum weight of a medium flat-rate box is 20 pounds, including the box which weighs 6 ounces. write and solve an inequality to describe the possible weight in pounds, w, of the contents that liz will ship to her friend if she must use a medium flat-rate box. use the drop-down menus to explain your answer.

White shapes and black shapes are used in a game. some of the shapes are circles. while the rest are squares. the ratio of the number of white shapes to the number of black shapes is 5: 11. the ratio of the number of white cicrles to the number of white squares is 3: 7. the ratio of the number of black circles to the number of black squres is 3: 8. work out what fraction of all the shapes are circles.