An elliptical riding path is to be built on a rectangular piece of property as shown below.

a vertical ellipse is shown centered on the coordinate plane, surrounded by a rectangle of equal length and width.

the rectangular piece of property measures 10 miles by 8 miles. find an equation for the ellipse if the path is to touch the center of the property line on all 4 sides

The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. the expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $95 and a standard deviation of $20. if the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift?