Final Exam - Quantitative Skills and Reason with Answer Key | MATH 1001, Exams of Quantitative Techniques

Download Final Exam - Quantitative Skills and Reason with Answer Key | MATH 1001 and more Exams Quantitative Techniques in PDF only on Docsity! FINAL EXAM REVIEW MATH 1001 1. Identify the fallacy in the given arguments. (a) You should brush your teeth every day because brushing your teeth is very important. (b) Buy this television—it’s the most popular brand! (c) Dad: “If you want to do well in life, you should do well in school” Son: “Oh yeah? Well, Mom tells me your grades weren’t very good either.” (d) Bob is not a Republican, so he must be a Democrat. 2. Draw a Venn diagram representing each of the categorical propositions below. (a) No birds are four-legged creatures. (b) Some mammals are four-legged creatures. (c) All pigs are four-legged creatures. (d) Some mammals are not four-legged creatures. 3. Rephrase the following statements in the form “if p, then q.” (a) Attending practice is necessary for staying on the team. (b) I am in California if I am in Los Angeles. (c) Showing up at the party is sufficient to get a door prize. 4. Describe how you would structure a key word search to find the information given. (a) Articles about tornadoes in Idaho (b) Articles that mention either wars or natural disasters (or both) that involved Belgium (c) Articles about George Bush’s inauguration (d) Articles about how World War II affected feminism in either the United States or Japan (or both) 5. Identify the simplest set of numbers that describes the given number. (a) 11 (b) −11 (c) 2/11 (d) 11.3 (e) 11 6. Complete the probability distribution below and use it to answer the questions. Number of Girls Probability 4 0.0625 3 0.2500 2 ? 1 0.2500 0 0.0625 (a) What is the probability of exactly two girls? (b) What is the probability of getting 0, 1, or 2 girls? 7. Suppose $3,500 is deposited in the bank at an APR of 4.3% for 7 years. (a) Find the accumulated balance if the interest is compounded annually. (b) Find the accumulated balance if the interest is compounded quarterly. (c) Find the accumulated balance if the interest is compounded monthly. (d) Find the accumulated balance if the interest is compounded daily. (e) Find the accumulated balance if the interest is compounded continuously. 16. The doubling time of a city's population is 11 years. How long does it take for the population to quadruple? 17. The following table gives the birth and death rates for four towns in three different years. Find Littleton’s net growth rate due to births and deaths in 1980, 1990, and 2000. Birth Rate (per 100) Death Rate (per 100) Town 1980 1990 2000 1980 1990 2000 Simpleton 1.9 1.5 0.9 1.2 1.2 0.8 Normalton 2.8 2.4 2.1 0.7 0.6 0.5 Ruralton 1.3 1.2 1.2 1.1 1.0 0.9 Littleton 1.4 1.6 1.5 0.9 0.8 0.7 18. In the town of Oak Forest, a 2% local sales tax and a 4% state sales tax are charged on all retail sales. Let p be the before-tax amount of a purchase in dollars. Let T be the after-tax amount of the purchase. Find a linear equation that describes how T varies with p. What is the total price of an item that costs $63 before taxes? 19. Use the Venn diagram, which describes the types of cookies in a bakery, to answer the following questions. Cookies Chocolate Chip 15 10 Walnut 13 7 (a) How many of the chocolate chip cookies do not also have walnuts? (b) How many cookies have neither chocolate chips nor walnuts? (c) How many cookies do not have walnuts? 5 20. The following table gives the per capita value of money in circulation in the United States in selected years. Year 1985 1990 1994 1996 1997 Dollars 779 1029 1428 1573 1665 (a) Find the best-fit quadratic model for this data. (Let t be the years since 1985.) (b) Use your model to predict the per capita value of money in 2000. Round your answer to the nearest whole dollar. (c) Find the SSE and average error for the model. ANSWERS 1. (a) circular reasoning (b) appeal to popularity (c) personal attack (ad hominem) (d) limited choice. 3. (a) If you stay on the team, then you must attend practice. (b) If you are in Los Angeles, then you are in California. (c) If you show up at the party, then you will get a door prize. 4. (a) tornado AND Idaho (b) (wars OR natural disasters) AND Belgium (c) George Bush AND inauguration (d) World War II AND feminism AND (United States OR Japan) 5. (a) whole number (b) integer (c) rational number (d) rational number (e) irrational number 6. (a) 0.375 0.6875 $4,699.57 $4,721.64 $4,726.69 $4,729.15 $4,729.23 observational study Experiment without blinding. Experiment with double blinding Observational study stratified sampling systematic sampling random sampling convenience sampling 1995 1990 60% 30% strong negative correlation no correlation weak positive correlation 6 (d) strong positive correlation (e) weak negative correlation 12. (a) 16 students (b) 24 students (c) 8 students (d) 16 students (e) 8 students 13. 8 7 14. (a) 1 to 7 (b) 1 to 11 linear; 1539 people exponential; 27,225 people exponential; $6476.21 linear; $1.95 22 years 0.5 people per 100 0.8 people per 100 0.8 people per 100 = 1.06p; $66.78 15 cookies 7 cookies 22 cookies = 2.532t2 + 45.431t + 770.727 $2022 SSE = 3234.3995 average error = 25.4338 7