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- 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…The owl population in a year n can be divided into juveniles, subadults andadults. Adults produce, on average, 0.4 juveniles each year. Approximately53% of juveniles survive to be subadults the next year, while 73% of subadultssurvive to become adults. Approximately 89% of the adult population survivesfrom one year to the next.1. Write down the equations for juveniles, subadults and adults in the year n+1 as functions of the juvenile,subadult and adult populations at year n. Explain all terms.2. Carefully explaining your notation and the terms, write down a matrix equation of the form pn+1 = Apn. 3. If there are 21 juveniles, 17 subadults and 53 adults this year, how many of each would we expect nextyear? 4. What is the equation that would describe the population in 5 years? (Do not calculate it!)The table on the right shows the calories, sodium, and protein in one cup of various kinds of soup, How many cups of each kind of soup should be mixed together to produce 10 servings of soup, each of which provides 186 calories, 954 milligrams of sodium, and 13.2 grams of protein? What is the serving size (in cups)? Calories Sodium (mg) Protein (g) Chicken NoodleChicken & RiceChicken Rotini 100 130 520 730 7 9 110 530 8 To produce 10 servings of soup, each of which provides 186 calories, 954 milligrams of sodium, and 13.2 grams of protein, mix cups of Chicken Noodle, cups of Chicken & Rice, and cups of Chicken Rotini.
- 2х — у %3D 4 11 %3D у — 2х +5 -For the remainder of this question, we will consider one of the world's most popular video games, Minecraft (adapted from Mills & Mills, 2016). In this game, the character (you) can attempt to tame a wolf with a bone. Assume that you get 9 tries to tame the wolf, i.e. there are 9 bones. Each time you tame the wolf, the wolf becomes a dog and a new wolf appears which you can then attempt to also tame. This continues until you have used up all 9 bones, and the goal is to end up with as many dogs as possible at the end of the game. The probability of taming the wolf with each attempt is fixed at 0.54. Let X denote the number of dogs at the end of the game so that X BIN (9,0.54). Assume you are about to play the game. 12. What is the probability you will tame less than 4 dogs?(c) In 1997, the U.S. population was approximately 266,570,000 people. At the rate of 440 prisoners per 100,000 population, about how many prisoners were in the system? (Round answer to whole number.) prisoners The projected U.S. population for the year 2020 is 323,738,000. If the rate of prisoners per 100,000 stays the same as in 1997, about how many prisoners do you expect will be in the system in 2020? (Round answer to whole number.) prisoners
- Every February, Francine's Flowers packages bouquet for Valentine's The smaller bouquets consist of two Stargazs Liles, three Gardenia and five Alstroemerias and sells for $15.75 The larger bouquet has 6 Alstroernerias, 4 Gardenia and 8 Stargazer Lilies and sells for $34 The cost of producing the bouquets is $6.25 for the small bouquet and $16 for the large bouquet a Formulate a linear programming model that will help Francine decide on the number of bouquets or each size to package to minimize her costs. Do Not Solve. b Formutate a linear progranming model that will help Francine decide on the number of bouquets of each size to package to maxirmize her profits Do Not SolveYou are designing a poster which has a border around the printed portion. The border is 2 inches wide on the left and right sides, and 3 inches wide on the top and bottom. The entire poster will be a total of 300 square inches, including the borders and printed portion combined.For the remainder of this question, we will consider one of the world's most popular video games, Minecraft (adapted from Mills & Mills, 2016). In this game, the character (you) can attempt to tame a wolf with a bone. Assume that you get 9 tries to tame the wolf, i.e. there are 9 bones. Each time you tame the wolf, the wolf becomes a dog and a new wolf appears which you can then attempt to also tame. This continues until you have used up all 9 bones, and the goal is to end up with as many dogs as possible at the end of the game. The probability of taming the wolf with each attempt is fixed at 0.54. Let X denote the number of dogs at the end of the game so that X~ BIN (9,0.54). Assume you are about to play the game. 15. The probability that you will tame some number a or less dogs is 0.66144. What must be (round to the nearest whole number)?