A land owner is planning to build a fenced-in, rectangular patio behind his garage, using his garage as one of the "walls." He wants to maximize the area using 80 feet of fencing. The quadratic function A(x)=x(80−2x) gives the area of the patio, where x is the width of one side. Find the maximum area of the patio.

Acoin bank containing only dimes and quarters has 12 more dimes than quarters. the total value of the coins is $11. how many quarters and dimes are in the coin bank?

The fraction of defective integrated circuits produced in a photolithography process is being studied. a random sample of 300 circuits is tested, revealing 17 defectives. (a) calculate a 95% two-sided confidence interval on the fraction of defective circuits produced by this particular tool. round the answers to 4 decimal places. less-than-or-equal-to p less-than-or-equal-to (b) calculate a 95% upper confidence bound on the fraction of defective circuits. round the answer to 4 decimal places. p less-than-or-equal-to

What effect would doubling all the dimensions of a triangular pyramid have on the volume of the pyramid? explain your reasoning.