2) (20 points) Lynn has a utility function U(W) = W/2, where W is the amount...

Transcribed Image Text:

2) (20 points) Lynn has a utility function U(W) = W/2, where W is the amount of wealth that she has. Lynn has two assets. She has $90,000 in a bank account, and she has a house worth $160,000, so her total wealth is initially $250,000. There is a 2% chance that her house is destroyed by a fire. a) (4 points) Considering the probability that there is a fire, what is Lynn's Expected Wealth, E(W)? E(W) = b) (4 points) What is Lynn's Expected Utility, E(U)? E(U) = = c) (4 points) What is Lynn's Certainty Equivalent? 2) market for Watches; market for jewelry The following was reported in the WSJ (Jan 22, 2014) :" Sales in luxury watches is slowing down among 25-35 year olds, so disillusioned Switzerland's watch companies decided to switch instead to the higher profit margins of the jewelry business" If so, use supply and demand to make a prediction about prices and quantities in the markets for watches and then in the market for jewelry. For any graphical changes you show, you must specify which real-life example and variable caused the change. : Graph of watches market Graph of jewelry market PLUMBING Find the surface area (exterior and interior) of the pipe shown. Round to the nearest tenth of a square inch. 10 m Find the surface area of each figure. Round to the nearest tenth. 14. 10 6in 15. 10cm 20 cm 7cm +15 cm 15 cm 16. MONEY A penny's mass is exactly half the mass of a nickel. Using the information in the table, determine the ratio between their surface areas. Round to the nearest tenth. Write as a fraction in simplest form 60cm Coin Mass Diameter Thickness Penny 2.50 Nickel 500 19.05 mm 21.21 mm 1.55 mm 1.95 mm 17. FINANCIAL LITERACY The Student Council is planning a movie night. They will sell popcorn in one of the open-top containers shown. The cost depends on the amount of cardboard used to make each container. Which container should they buy? Use volume and surface area measurements to explain your choice. 10 in. pon CORN 9.7 in. 6 in. 5.5 in. 5 in 18. Find the height of a cylinder if the surface area is 402 square centimeters and the radius is 4 centimeters. Round to the nearest tenth. H.O.T. Problems Use Higher-Order Thinking Skills 19. OPEN ENDED Create a prism that has approximately the same surface area as the cylinder shown at the right. 20. CHALLENGE A cylinder has a radius of 10 centimeters and a height of 6 centimeters. Without calculating, explain whether multiplying the radius or the height by a scale factor of 0.5 would have a greater effect on the surface area of the cylinder. 21. EWRITING IN MATH Both ice cubes have a volume of about 22.5 cubic centimeters. Which ice cube would you expect to melt faster? Find the total surface areas to explain your reasoning. 5 cm 3 cm 1.7 cm 2.5 cm 3 cm 742 Lesson 12-6 Surface Area of Cylinders 10.2 14.6 2) (20 points) Lynn has a utility function U(W) = W/2, where W is the amount of wealth that she has. Lynn has two assets. She has $90,000 in a bank account, and she has a house worth $160,000, so her total wealth is initially $250,000. There is a 2% chance that her house is destroyed by a fire. a) (4 points) Considering the probability that there is a fire, what is Lynn's Expected Wealth, E(W)? E(W) = b) (4 points) What is Lynn's Expected Utility, E(U)? E(U) = = c) (4 points) What is Lynn's Certainty Equivalent? 2) market for Watches; market for jewelry The following was reported in the WSJ (Jan 22, 2014) :" Sales in luxury watches is slowing down among 25-35 year olds, so disillusioned Switzerland's watch companies decided to switch instead to the higher profit margins of the jewelry business" If so, use supply and demand to make a prediction about prices and quantities in the markets for watches and then in the market for jewelry. For any graphical changes you show, you must specify which real-life example and variable caused the change. : Graph of watches market Graph of jewelry market PLUMBING Find the surface area (exterior and interior) of the pipe shown. Round to the nearest tenth of a square inch. 10 m Find the surface area of each figure. Round to the nearest tenth. 14. 10 6in 15. 10cm 20 cm 7cm +15 cm 15 cm 16. MONEY A penny's mass is exactly half the mass of a nickel. Using the information in the table, determine the ratio between their surface areas. Round to the nearest tenth. Write as a fraction in simplest form 60cm Coin Mass Diameter Thickness Penny 2.50 Nickel 500 19.05 mm 21.21 mm 1.55 mm 1.95 mm 17. FINANCIAL LITERACY The Student Council is planning a movie night. They will sell popcorn in one of the open-top containers shown. The cost depends on the amount of cardboard used to make each container. Which container should they buy? Use volume and surface area measurements to explain your choice. 10 in. pon CORN 9.7 in. 6 in. 5.5 in. 5 in 18. Find the height of a cylinder if the surface area is 402 square centimeters and the radius is 4 centimeters. Round to the nearest tenth. H.O.T. Problems Use Higher-Order Thinking Skills 19. OPEN ENDED Create a prism that has approximately the same surface area as the cylinder shown at the right. 20. CHALLENGE A cylinder has a radius of 10 centimeters and a height of 6 centimeters. Without calculating, explain whether multiplying the radius or the height by a scale factor of 0.5 would have a greater effect on the surface area of the cylinder. 21. EWRITING IN MATH Both ice cubes have a volume of about 22.5 cubic centimeters. Which ice cube would you expect to melt faster? Find the total surface areas to explain your reasoning. 5 cm 3 cm 1.7 cm 2.5 cm 3 cm 742 Lesson 12-6 Surface Area of Cylinders 10.2 14.6