MATH 106 Finite Mathematics 2152-US1-4010-V1 MATH 106 Finite .docx
- 1. MATH 106 Finite Mathematics 2152-US1-4010-V1 MATH 106 Finite Mathematics 2152-US1-4010-V1 MULTIPLE CHOICE 1. Which of the corner points for the system of linear inequalities graphed below maximizes the objective function P = 5x + 4y ? 1. _______ A. (0, 4) C. (1, 2) B. (3, 0) D. (2, 0) 2. Find the equation of the line passing through (1, – 7) and (4, 1): 2. _______ A. 8x + 3y = – 13 B. 2x + y = – 5 C. 2x – y = 9 D. 8x – 3y = 29 3. A survey of 15 randomly selected students responded to the question “How many hours a day do you work on MATH 106?” as follows: 3, 2, 2, 4, 6, 5, 2, 5, 1, 4, 2, 3, 2, 3, 4 . Which histogram below accurately reflects the frequency distribution of the 15 students’ responses? 3. ______ HISTOGRAM A HISTOGRAM C
- 3. 6 4 2 0 1 2 3 4 5 6
- 4. 6 4 2 0 1 2 3 4 5 6 HISTOGRAM B HISTOGRAM D
- 5. 8 6 4 2 0 1 2 3 4 5 6
- 7. 8 6 4 2 0 1 2 3 4 5 6 4. Identify the single row operation that transforms the matrix as shown: 4. ________ A. 0.5�1 → �1 C. �2 + �1 → �1 B. �2 ↔ �1 D. 3�2 + �1 → �1 5. The amount of money you should deposit in an account paying 8% compounded quarterly in order to receive quarterly payments of $1000 for the next 4 years can be determined using formula for: 5. _______ A. Single-payment, simple interest B. Single-payment, compound interest C. Sequence of payments: present value of an ordinary annuity D. Sequence of payments: future value of an ordinary annuity 6. – 7. The Black Entertainment Television Company (BET) employs copy coordinators and programming analysts. According to company data, a copy coordinator reviews 5 scripts and 3 show schedules per day, whereas a programming
- 8. analyst reviews 2 scripts and 7 show schedules per day. The company needs enough staff on hand to review at least 12 scripts per day and at least 17 show schedules per day. A copy coordinator makes $230 per day and a programming analyst makes $190 per day. The company wants to minimize daily labor costs. Let x represent number of copy coordinators and y represent number of programming analysts. 6. Identify the daily production constraint for scripts: 6. _______ A. 5� + 2� ≤ 12 C. 5� + 2� ≥ 12 B. 5� + 2� ≤ 17 D. 5� + 2� ≥ 17 7. State the objective function. 7. _______ A. � = 190� + 230� C. � = 12� + 17� B. � = 230� + 190� D. � = 17� + 12� 8. In the dice game “Yahtzee”, five-of-a-kind gives the maximum score for a single turn. What is the probability of getting 5 “5”s in a single roll of 5 six-sided dice? 8. ________ A. 1⁄7776 (0.000129) C. 1⁄1296 (0.000772) B. 1⁄30 (0.033333) D. 5⁄36 (0.138889) 9. Maria purchases a new home for $320,000. She makes a down payment of 20%, and finances the rest with a 30-year fixed loan at an annual interest rate of 3.75% compounded monthly. What is the amount of her monthly loan payment to amortize the loan?
- 9. 9. _______ A. $1481.97 C. $1511.11 B. $1888.89 D. $1185.58 10. The mean time from prescription drop-off to medicine pickup for a customer served at Heisenberg’s Pharmacy is 51 minutes, with a standard deviation of 17 minutes. Assuming a normal distribution, what is the probability that a randomly chosen customer experiences service done between 34 and 68 minutes? 10. ______ A. 0.6826 C. 0.3413 B. 0.4772 D. 0.5000 11. If K = {3, 7, 11, 15} and M = {7, 12, 15, 18}, list {�|� ∈ � ��� � ∈ �} 11. _________ A. {Ø} C. { 7, 15 } B. {3, 7, 11, 12, 15, 18} D. {3, 7, 11, 15, 7, 12, 15, 18} 12. Determine which region defines the solution region of the following system of linear inequalities graphed below: 12. ________ 2� − 5� ≤ −3 −3� + � ≥ −2 I II III IV
- 10. A. Region I C. Region III B. Region II D. Region IV SHORT ANSWER (work NOT required to be shown) 13. For the linear equation 8� + 3� = 72: a. Determine the slope: _______________________ b. Determine x – intercept if it exists: _______________________ c. Determine y – intercept if it exists: _______________________ d. Express equation in slope-intercept form: _______________________ 14. 1000 randomly-selected respondents to a TV marketing survey were asked their age in years (18 to 39 or 40+) and the kind of TV show most often watched. Following table was obtained. Show Most Watched on TV Viewer Age 18 - 39 Viewer Age 40 + Total Comedy 208
- 11. 88 296 Drama 150 74 224 News 32 140 172 Sports 228 80 308 Total 618 382 1000 (Report your answers as fractions or as decimal values rounded to the nearest hundredth.) Find the probability that a randomly-selected respondent most often watches: (a) drama shows and is age 18 – 39. Answer: ______________ (b) drama shows or is age 18 – 39. Answer: ______________ (c) drama shows given that viewer is age 18 – 39. Answer: ______________ 15. Let (�) = 60, �(�) = 75, �(� ∪ �) = 113, and �(�) =
- 12. 150. a. Determine �(�′) : ___________________________________ b. Determine �(� ∩ �) : ___________________________________ c. Determine �(�′ ∩ �′): ___________________________________ SHORT ANSWER, with work required to be shown, as indicated. 16. Eighteen people are summoned to jury duty. 10 are women and 8 are men. (a) In how many ways can 12 jurists be randomly selected out of the 18 people? Show work. (b) In how many ways can 12 jurists be chosen, if 8 must be women and 4 must be men? Show work. (c) If 12 jurists are randomly selected from the 18 people, what is the probability that 4 are men and 8 are women? Round answer to nearest ten-thousandth (4 places after decimal). Show work. _____________________________________________________ _________________________
- 13. 17. Cara needs $9,000 in 11 years. What amount can she deposit at the end of each quarter at 8% annual interest compounded quarterly so she will have her $9,000? Show work. A. $125.19 C. $134.01 B. $129.49 D. $540.69 18. Solve the system of equations using substitution, elimination by addition, or augmented matrix methods (your choice). Show work. 3� − 2� = −2 −4� + 3� = 1 _____________________________________________________ _________________________ 19. According to the US Census Bureau, "United States Census 2010", 33 million Americans were age 65 or older in 1995; an amount which climbed to 40 million in 2010. (a) Which of the following linear equations could be used to predict number of Americans age 65 or older (in millions) “y” in a given year “x”, where x = 0 represents the year 1995? Explain/show work. (b) Use the equation from part (a) to predict the number of Americans age 65 or older (in millions) in the year 2040. Round answer to nearest tenth of a million people. Show work.
- 14. (c) Fill in the blanks to interpret the slope of the equation: The rate of change of number of Americans age 65 or older with respect to time is ______________________ per ________________. (Include units of measurement.) 20. A local car rental agency charted daily demand as shown in the following table: Number of customers 8 10 12 14 16 Probability 0.3 0.2 0.3 0.1 0.1 Find the expected number of customers. Show work _____________________________________________________ _________________________ 21. According to a recent report, 0.10 is the probability that a randomly-selected American citizen knows that Janet Yellen is the Chair of the Federal Reserve Board of the US Government. Nine Americans are randomly selected. Find the probability that exactly 3 of the 9 Americans selected identifies Ms Yellen as the Chair of the Federal Reserve Board. Round answer to the
- 15. nearest thousandth (three places after decimal).Show work. _____________________________________________________ _________________________ 22. The feasible region shown below is bounded by lines x + y = 2, 5x – y = 3, and y = 0. Find the coordinates of corner point A. Show work. 23. A network security specialist records the number of incoming e-mails containing links that six randomly-selected network users receive in a day. Numbers are 27, 23, 19, 38, 27, and 22. (a) State the mode (if one exists). (b) Find the median. Show work/explanation. (c) Determine the sample mean. Show work (d) Using the sample mean found in part (c), and given that the sample standard deviation of the data set above is 6.6, what percentage of the data set falls within one standard deviation of the mean? Show work/explanation. (d) _______ A. 34.2% C. 66.7% B. 83.3% D. 68.3%
- 16. 24. You have $5000 to invest in a single payment. Which is the better investment: 8.7% compounded annually or 8.4% compounded monthly? Show work 25. A dietitian surveyed her group of 100 patients and found that most of them ate fast food yesterday. 45 patients said they ate at “Greasies” yesterday. 55 patients said they ate at “Pluckies” yesterday. 15 patients said they ate at both “Greasies” and “Pluckies” yesterday. (a) What is the probability that a single randomly-selected patient either ate at “Greasies” or at “Pluckies” (but not both) yesterday? Show work. (b) Let G = {patients who ate at “Greasies”} and P = {patients who ate at “Pluckies”}. Determine the number of attendees belonging to each of the regions I, II, III, IV.
- 17. U P G II IV III I Region I: ________ Region II: __________ Region III: _________ Region IV: __________ _____________________________________________________ _________________________ Page 1 of 9 Page 10 of 11
- 18. Page 11 of 11 Darkened Windows In recent weeks, New Yorkers have been watching a family drama unfold among an angry patriarch, the mayor, Bill de Blasio; his petulant charges in the Police Department, apparently as huffy as 12-year-olds told to stop texting; and a mother, Police Commissioner William J. Bratton, who, like mothers everywhere hoping to get Daddy to understand and the children to listen, has been trying to broker peace. What risks getting obscured in a story whose other central characters include irritable union leader babysitters and their incitements to misbehavior is that the significant rift here isn't political. It is civic, spurred by the continued friction between an underclass with ample reason to feel alienated from the modern culture of law enforcement and a police department that can seem intolerant of any challenge to its methods and methodologies. Just how wide that gulf remains was evident this week, when New York City advocates for police reform delivered testimony to President Obama's Task Force on 21st-Century Policing that condemned the practice of "broken windows" policing, which postulates that summonses issued and arrests made for minor offenses preclude the eruption of major crimes. Writing on behalf of the group, Communities United for Police Reform, Monifa Bandele, a native of Crown Heights, Brooklyn, who now lives in Bedford-Stuyvesant, called for an end to the approach, arguing that its casualties include the black and Hispanic men who end up stigmatized, burdened with fines and arrest records that make it harder to find jobs, secure loans or obtain housing. At the spectrum's far end are unnecessary civilian deaths.
- 19. A few weeks before, writing in City Journal, a periodical publication of the conservative Manhattan Institute, Commissioner Bratton put forth a lengthy defense of the policy he has passionately advocated and implemented for decades, arguing essentially that minorities love "broken windows"; that critics who don't see this "have never been to a police/community meeting in a poorer, mostly minority neighborhood"; that those who attribute historic decreases in crime to broader social trends are lost in academic mumbo- jumbo; and that anyone else standing in opposition to the practice must be too young to know that New York was once Detroit. Both Mr. Bratton and his critics on the left understand that the way forward is for police officers to vastly improve their relationship with the communities they serve and for community members to be more deeply involved in the maintenance of the social order. This notion of community or neighborhood policing, as Michael Jenkins, a professor of criminal justice at the University of Scranton and author of the new book "Police Leaders in the New Community Problem Solving Era," pointed out, arose in tandem with "broken windows," both in the literature and in practice. But the approaches have come to be regarded as antagonistic to each other, or at the very least have taken on the veneer of incompatibility, in large part because of the discriminatory tactics of stop-and-frisk, which "broken windows" engendered -- a relationship that Mr. Bratton refuses to acknowledge. "Different neighborhoods have different ideas about the problems they'll want police responding to, and varying capacities to manage disorder," Mr. Jenkins said. "If police are viewed as intervening across the board everywhere or viewed as carpet-bombing an area, that's usually not going to be helpful to community relationships. If you add a layer of disrespectful or unnecessary interactions with citizens, broken windows can be denigrated."
- 20. Additional testimony before the president's task force this week included a report from Dolores Jones-Brown, a former prosecutor and director of the John Jay College Center on Race, Crime and Justice, who argued that San Diego, a model for alternative techniques, had experienced a greater long-term reduction in violent crime than New York had without resorting to broken-windows tactics. From 1991 to 1998, she wrote, New York's homicide rate declined by 70.6 percent but San Diego's dropped by more than 76 percent. From 2002 to 2012, while violent crime in New York fell by 19 percent, violent crime in San Diego fell by 27 percent. How was this accomplished? In the '90s, for example, when a spate of robberies occurred around a particular bus stop, the San Diego police, rather than flooding the area with officers or making mass arrests, simply relocated the bus stop to a spot in front of a convenience store, which provided more light. The thought, which turned out to be correct, was that the robberies were largely crimes of opportunity, committed by impulsive young people who would not bother to set up shop elsewhere. Underpinning the execution of "broken windows" is the conviction that someone doing something stupid -- committing a minor act of vandalism, for instance -- is on the path to becoming someone bad. As Ms. Bandele said, her neighbors are all too aware that while they may be given a summons for drinking beer on their stoop, residents of more affluent quarters of the city can do those sorts of things and go unnoticed and ignored. If Mr. Bratton believes that "broken windows" is indispensable to keeping the city safe -- and perhaps it is -- then he must retool and reframe it, a process that might begin not with the arrogant dismissal of its critics, but with an admission and some attention to where it has gone wrong, or at least real recognition that, like any system, it is imperfec
- 21. Procrastination: Time Travel approach To End Procrastination, Look to the Science of Mood Repair Author: Shellenbarger, Sue Procrastinators, take note: If you've tried building self- discipline and you're still putting things off, maybe you need to try something different. One new approach: Check your mood. Often, procrastinators attempt to avoid the anxiety or worry aroused by a tough task with activities aimed at repairing their mood, such as checking Facebook or taking a nap. But the pattern, which researchers call "giving in to feel good," makes procrastinators feel worse later, when they face the consequences of missing a deadline or making a hasty, last- minute effort, says Timothy Pychyl (rhymes with Mitchell), an associate professor of psychology at Carleton University in Ottawa, Canada, and a researcher on the topic. Increasingly, psychologists and time-management consultants are focusing on a new strategy: helping procrastinators see how attempts at mood repair are sabotaging their efforts and learn to regulate their emotions in more productive ways. The new approach is based on several studies in the past two years showing that negative emotions can derail attempts at self-control. It fills a gap among established time-management methods, which stress behavioral changes such as adopting a new organizing system or doing exercises to build willpower. Gisela Chodos had a habit of procrastinating on cleaning the interior of her car until it became so littered with toys, snack wrappers, fast-food bags, pencils and other stuff that she was embarrassed to park it in a public lot or offer anyone a ride, says Ms. Chodos, a Salt Lake City mother of two school-age children and part-time computer-science student. She came across podcasts by Dr. Pychyl in 2012 and realized she was just trying to make herself feel better when she told herself she would feel more like tackling a task later. She says, "I am trying to run away from the feelings and avoid the discomfort" -- the anxiety she often feels that her work won't be good enough or that someone will disapprove.
- 22. "Emotion is at the core," Ms. Chodos says. "Just knowing that gives me a little bit of fight, to say, 'Fine, I'm feeling discomfort, but I'm going to feel more discomfort later' " if the job is left undone. The insight has helped her get around to cleaning her car more often, she says; "it's been a long time since my car was so bad that I freaked out at the thought someone might look inside." Researchers have come up with a playbook of strategies to help procrastinators turn mood repair to their advantage. Some are tried-and-true classics: Dr. Pychyl advises procrastinators to "just get started, and make the threshold for getting started quite low." Procrastinators are more likely to put the technique to use when they understand how mood repair works, says Dr. Pychyl, author of a 2013 book, "Solving the Procrastination Puzzle." He adds, "A real mood boost comes from doing what we intend to do -- the things that are important to us." He also advises procrastinators to practice "time travel" -- projecting themselves into the future to imagine the good feelings they will have after finishing a task, or the bad ones they will have if they don't. This remedies procrastinators' tendency to get so bogged down in present anxieties and worries that they fail to think about the future, says Fuschia Sirois, a psychology professor at Bishop's University in Sherbrooke, Quebec, and author of a forthcoming 4,000-person study on the topic. Sean Gilbertson read an earlier book by Dr. Pychyl in 2012 after trying other time-management techniques such as keeping a daily log of his attitudes. The Minneapolis software engineer says the techniques didn't go deep enough to help him see how his emotions were blocking action and shift them in a more positive direction. Using the time-travel technique, he asks himself, "What negative things will happen if I procrastinate? Will it come up in my review? How will it affect my reputation? Will it affect my raise and bonuses?" He used the technique recently when programming a prototype of a medical device to help doctors prevent pressure sores in
- 23. wheelchair-bound patients. He imagined the good feelings he would have after completing the project well and pleasing his client and his employer. He envisioned patients "living happily and feeling better." The resulting positive feelings gave him the energy to de-bug the device faster and finish the three-month project on time. The client was so pleased that "just talking to them is a pleasure," he says. About 20% of adults claim to be chronic procrastinators, based on research by Joseph Ferrari, a psychology professor at DePaul University, Chicago, and others. Other studies suggest the rate among college students may be as high as 70%. The habit predicts lower salaries and a higher likelihood of unemployment, according to a recent study of 22,053 people co- authored by Dr. Ferrari. Procrastination also predicts such long-term problems as failing to save for retirement and neglecting preventive health care. Studies show men are worse procrastinators than women, and researchers suspect the habit plays a role in men's tendency to complete fewer years of education. Most procrastinators beat up on themselves even as they put things off, repeating negative thoughts such as, "Why can't I do what I should be doing?" or, "I should be more responsible," says Gordon Flett, a psychology professor at York University in Toronto. "That negative internal dialogue reflects concerns and doubts about themselves," Dr. Flett says. One mood-repair strategy, self-forgiveness, is aimed at dispelling the guilt and self-blame. University freshmen who forgave themselves for procrastinating on studying for the first exam in a course procrastinated less on the next exam, according to a 2010 study led by Michael Wohl, an associate professor of psychology at Carleton. Thomas Flint learned about the technique by reading research on self-regulation, including studies by Dr. Sirois and Dr. Pychyl. He put it to use after his family moved recently to a new house in Sewell, N.J. Instead of beating himself up for failing to unpack all the boxes stacked in his garage right away,
- 24. Mr. Flint decided to forgive himself and start with a single step. "I'd say, 'OK, I'm going to take an hour, with a goal of getting the TV set up, and that's it,'" he says; then he watched a TV show as a reward. Allowing himself to do the task in stages, he says, is "a victory."