MGF2106 Survey of Mathematics: Project 2
Directions: This project contains multiple parts. Each part of the project contains several questions.
Answer each question to the best of your ability and record your answer in a separate document (do not enter the answers on the project itself) and upload your work, in the proper format, to the appropriate “Assignment” within Falcon Online by the posted due date. You may work individually on this project or you may work in a group. If you choose to work within a group, each member of the group must upload the group’s submission. Submission Format Instructions:
1. Your submission must be a single, typed document saved as a Word document (.doc or .docx), Rich Text Format (.rtf), or a Portable Document Format (.pdf).
2. Your name must be on the top of your submission. If you worked in a group the names of every group member must be included on the top of your submission.
3. Do not type the questions from the project into your submission. You should submit only your answers to the questions along with any calculations used to obtain the answer.
4. Follow the numbering system used in the project when typing your answers. Failure to follow the directions or submission format instructions will result in loss of points. If you do not submit your work by the due date it will not be accepted for grading. Speak with your instructor as they may have additional requirements for your submission. 1 Part 1 – Measurement Conversion You have been hired as the new Lab Manager for your local hospital. As manager you must ensure that the doctors have all the medications they require and in the correct dosages. You are in charge of the following drugs/medications: Losartan, Atenolol, Metformin, Hydrochlorothiazide, Protocol A, and Protocol B. On the first day at your new job you are given the supply list for the medications that you will work with. On this list is the quantity of the supplies on hand. Your new supervisor wants to convert the amounts of each drug into different units as listed on the table below. Part 1 Exercises: Problems 1 – 6 are in the table below. Convert the quantity and units in column 2 to the new units listed in column 3. Your answers do not need to be given in a table. The answer should be the new quantity and unit, with the necessary work. Drug Original Quantity and Units New Units Losartan 7,000 centigrams 1. kilograms Atenolol 31,000 milligrams 2. dekagrams Metformin 6,900 kilograms 3. decigrams Hydrochlorothiazide 42,500 decigrams 4. dekagrams Protocol A 11,700 deciliters 5. centiliters Protocol B 930 kiloliters 6. milliliters Follow up Questions:
7. The range of doses for Losartan per day is 50 – 100 milligrams. What would be the corresponding range for doses in micrograms?
8. The hospital wants to prepare for an emergency by keeping track of how many 68 milligram doses of Losartan are available. Use the amount of Losartan given in the table above to find the number of doses the hospital currently has available.
9. If an epidemic hits the town would the hospital have enough Losartan on hand to give 1,800 people a dose of 68 milligrams each? Explain your answer. 2 Part 2 – Applications of Linear Equations In 1960 the United States generated 87.1 million tons of municipal solid waste and recovered (or recycled) 3.78 million tons (U.S. EPA, www.epa.gov). This means that only 4.3% of it was recovered (because 3.78/87.1 = 0.043 = 4.3%). The amount of municipal solid waste generated in the United States can be modeled by the formula g = 3.14n+87.1 while the amount recovered can be modeled by the formula r = 0.576n+3.78 where g and r are in millions of tons and n is the number of years since 1960. Use either the given equations or the given graph to answer the following questions. 10 20 30 40 50 100 150 200 Years Since 1960 Solid Waste Hin millions of tonsL H0, 87.1L H0, 3.78L Generated Recovered H12, 124.8L H37, 203.3L H12, 10.7L H37, 25.1L 3 Part 2 Exercises: Use the graph to answer questions 1 and 2. 1. Use the graph to answer the question. a. Find the amount of waste generated in 1972. b. Find the amount of waste recovered in 1972. c. Find the percent of waste recovered in 1972 2. Use the graph to answer the question. a. Find the amount of waste generated in 1997. b. Find the amount of waste recovered in 1997. c. Find the percent of waste recovered in 1997 Use the formulas to answer questions 3 and 4. 3. Use the formulas to answer the question. a. Find the amount of waste generated in 1986. b. Find the amount of waste recovered in 1986. c. Find the percent of waste recovered in 1986. 4. Use the formulas to answer the question. a. Find the amount of waste generated in 2005. b. Find the amount of waste recovered in 2005. c. Find the percent of waste recovered in 2005. 5. What is increasing faster, the amount of waste generated or the amount of waste recycled? Explain your reasoning based on the graph and the concept of slope. 4 Part 3 – Theoretical and Experimental Probability Theoretical probability can be used to predict the likelihood of an event. If a single, 6-sided die is rolled there are six possible outcomes. That is, after rolling the die, the side facing up will show one of six possibilities: 1, 2, 3, 4, 5, or 6. Part 3 Exercises: 1. If a single 6-sided die is rolled once, what is the theoretical probability that the die would show a 3? Express your answer as a reduced fraction and a decimal rounded to three decimal places. 2. Three experiments are conducted in which a single 6-sided die is rolled 15, 30, and 45 times. The outcomes of the experiments are shown here. For each result calculate the experimental probability of rolling a 3. Express your answer as a reduced fraction and a decimal rounded to three decimal places. a) Experiment 1: 15 rolls b) Experiment 2: 30 rolls c) Experiment 3: 45 rolls 3. How do the experimental probabilities found in #2 compare to each other? Which one is closer to the theoretical probability? 5