You have two parents, four grandparents, eight great-grandparents, and so forth.(a)If all your ancestors were distinct, what would be the total number of your ancestors for the past 42 generations (counting your parents' generation as number one)? (Hint: Use the formula for the sum of a geometric sequence.)(b)Assuming that each generation represents 25 years, how long (in years) is 42 generations?

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

The sum of two numbers is 86, and their difference is 20. find the two numbers

Atriangle has an area of 72 square inches. if the base of the triangle has a length of 18 inches, what is the height of the triangle? use the formula for the area of a triangle: area = (base)(height) type a numerical answer in the space provided. do not include the units or spaces in your answer.