find the average Value of the function. 2 f(x) = x²-11 on [0,3]

The research department at a manufacturing company has developed a new process that it believes will result in an improved product. Management must decide whether to go ahead and market the new product. The new product may or may not be better than the old one. If the new product is better and the company decides to market it, sales should increase by $70,000. If it is not better and they replace the old product with the new product on the market, they will lose $25,000 to competitors. If they decide not to market the new product, they will lose a total of $60,000 if it is better and just research costs of $20,000 if it is not. Complete parts (a) and (b) below. (a) Prepare a payoff matrix. □ (Type an integer or decimal for each matrix element. Do not include the $ symbol in your answer.)

USA. Benjamin Banneker (1731-1806) is one of the great American heroes of all time. The son and grandson of Africans captured and enslaved, he was fortunate to have been born free. He inherited the family farm where he worked hard all of his life. As a child he had a few months of schooling. Everything else he had to do on his own. He loved mathematics and science but did not get a chance to learn astronomy until he was in his fifties. Then he performed a near miracle, learning it all in less than a year. In his hand-written journal, he recorded two right triangle examples that interested him. You can solve them here and remember the great man who enjoyed geometry. On the page in his journal next to the August 1775 astronomy calculations, Banneker wrote, in the style of that time: Suppose a ladder 60 feet long be placed in a Street so as to reach a window on the one Side 37 feet high, and without moving it at bottom, will reach another window on the other side of teh Street which is 23…

After running a mile a day over a period of two weeks, the average amount of weight loss is 2.5 pounds. A dietitian, who publishes health articles in a newspaper, states their new diet program helps with additional weight loss when combining their special diet with running a mile a day over a period of two weeks. Interested in studying the dietitian's article further, you ask friends who have tried the dietitian's new program and you determine their weight loss to be 3.0 pounds in a two-week period, on average. As you set up a hypothesis test to determine if the dietitian's article is correct, what is the dietitian's claim?