There are 40 people at Drake's sweet sixteen party. Drake's only rule is that everyone in the party must meet and shake each others hand. If all 40 guest shake each other's hand once and only once. (1) How many handshakes are there altogether? (50 pts)
(2) How did you get your solution? (30 pts)
(3) What's the quickest way to figure this out if Drake invited 1000 people? (20 pts)
PLEASE EXPLAIN 3.

Atoy company is considering a cube or sphere-shaped container for packaging a new product. the height of the cube would equal the diameter of the sphere . compare the volume to surface area ratios of the containers. which packaging will be more efficient? for a sphere, sa =4πr²

In a sample of 200 residents of georgetown county, 120 reported they believed the county real estate taxes were too high. develop a 95 percent confidence interval for the proportion of residents who believe the tax rate is too high. (round your answers to 3 decimal places.) confidence interval for the proportion of residents is up to . would it be reasonable to conclude that the majority of the taxpayers feel that the taxes are too high?

Sara can take no more than 22 pounds of luggage on a trip. her suitcase weighs 112 ounces. how many more pounds can she pack without going over the limit?