MATH106 2019 January All Weeks Discussions Latest

MATH 106 6383 Finite Mathematics (2192)

Week 1 Discussion

LEO Participation Discussion Topics

SIMPLE INTEREST AND DISCOUNT

1.            You borrow $4,500 for six months at a simple interest rate of 8%. How much is the interest?

2.            Jessica takes a loan of $800 for 4 months at 12% simple interest. How much does she owe at the end of the 4-month period?

3.            Jamie just paid off a loan of $2,544, the principal and simple interest. If he took out the loan six months ago at 12% simple interest, what was the amount borrowed?

4.            A credit card company charges 18% interest on the unpaid balance. If you owed $2000 three months ago and have been delinquent since, how much do you owe?

5.            Nancy borrowed $1,800 and paid back $1,920, four months later. What was the simple interest rate?

6.            Tasha signs a note for a discounted loan agreeing to pay $1200 in 8 months at an 18% discount rate. Determine the amount of the discount and the proceeds to her.

7.            An amount of $4,000 is borrowed at a discount rate of 10%, find the proceeds if the length of the loan is 180 days.

8.            Mary owes June $750, and wants to pay her off. She decides to borrow the amount from her bank at a discount rate of 16%. If she borrows the money for 10 months, find the amount of the loan she should ask for so that her proceeds are $750?

COMPOUND INTEREST

9.            How much should be invested at 10.3% for it to amount to $10,000 in 6 years?

10.          Thuy needs $1,850 in eight months for her college tuition. How much money should she deposit lump sum in an account paying 8.2% compounded monthly to achieve that goal?

 

MATH 106 6383 Finite Mathematics (2192)

Week 2 Discussion

LINEAR EQUATIONS AND INEQUALITIES  (Basic Mathematics Review, Chapter 5, Sections 5.5 – 5.8, and Chapter 7, Sections 7.2 – 7.7)

Solve for the variable:

1. 1. (c/2) – 8 = 0
   2. 5(m – 3) + 4 = -1
   3. 3r + 25 = – 1
2. 1. 3x/4 + 2 = 14
   2. -7(2a-1) = 63
   3. 3x + 7 = 5x - 21
3. 1. 4x – 36 + 2 = -6
   2. 3y/4 + 16 = 10
   3. 4(x+2) = 20

 

1. 1. -2(a-3) = 16
   2. 6x – 17 = 3
   3. x/7 – 15 = -11
2. 1. -(8r+1) = 33
   2. 4y + 5 = -3
   3. 2(3x+1) -5x = 4(x-6) + 17

 

1. 1. Solve P =R – C  for R. Find the value of R when P =480 and C =210.
   2. Solve y =5x +8 for x.

 

1. 1. Solve 3y −6x =12 for y.
   2. Solve 4y +2x +8=0 for y.

 

Solve: 

1. Twenty percent of a number is 6 What is the number?

 

1. This year an item costs $106, an increase of 10% over last year’s price. What was last year’s price?

 

 

MATH 106 6383 Finite Mathematics (2192)

Week 3 Discussion

AUGMENTED MATRIX METHOD TO SOLVE SYSTEM OF LINEAR EQUATIONS  (Precalculus, Section 9.7)

For the following exercises, write the augmented matrix for the linear system.

1. 8x−37y=8       2x+12y=3
2. 2x−3y=−95x+4y=58
3. 6x+2y=−43x+4y=−17
4. 2x+3y=12  4x+y=14

For the following exercises, solve the system by Gaussian elimination.

1. 100030
2. 124536
3. -20   0211
4. 6234-4-17
5. -4-33-5-2-13
6.     3   4-6-8   12-24

 

 

MATH 106 6383 Finite Mathematics (2192)

Week 4 Discussion

LINEAR PROGRAMMING   (Applied Finite Mathematics, “Linear Programming: A Geometric Approach”)

For the following exercises, solve using the graphical method.  Choose your variables, write the objective function and the constraints, graph the constraints, shade the feasibility region, label all corner points, and determine the solution that optimizes the objective function.

1. A farmer has 100 acres of land on which she plans to grow wheat and corn. Each acre of wheat requires 4 hours of labor and $20 of capital, and each acre of corn requires 16 hours of labor and $40 of capital. The farmer has at most 800 hours of labor and $2400 of capital available. If the profit from an acre of wheat is $80 and from an acre of corn is $100, how many acres of each crop should she plant to maximize her profit?

 

1. Mr. Tran has $24,000 to invest, some in bonds and the rest in stocks. He has decided that the money invested in bonds must be at least twice as much as that in stocks. But the money invested in bonds must not be greater than $18,000. If the bonds earn 6%, and the stocks earn 8%, how much money should he invest in each to maximize profit?

 

1. A computer store sells two types of computers, desktops and laptops. The supplier demands that at least 150 computers be sold a month. In order to keep profits up, the number of desktops sold must be at least twice of laptops. The store pays its sales staff a $75 commission for each desk top, and a $50 commission for each lap top. How many of each type of computers must be sold to minimize commission to its sales people? What is the minimum commission?

 

1. Mr. Shoemacher has $20,000 to invest in two types of mutual funds, Coleman High-yield Fund, and Coleman Equity Fund. The High-yield fund gives an annual yield of 12%, while the Equity fund earns 8%. Mr. Shoemacher would like to invest at least $3000 in the High-yield fund and at least $4000 in the Equity fund. How much money should he invest in each to maximize his annual yield, and what is the maximum yield?

 

1. Dr. Lum teaches part-time at two different community colleges, Hilltop College and Serra College. Dr. Lum can teach up to 5 classes per semester. For every class taught by him at Hilltop College, he needs to spend 3 hours per week preparing lessons and grading papers, and for each class at Serra College, he must do 4 hours of work per week. He has determined that he cannot spend more than 18 hours per week preparing lessons and grading papers. If he earns $4,000 per class at Hilltop College and $5,000 per class at Serra College, how many classes should he teach at each college to maximize his income, and what will be his income?

 

1. Mr. Shamir employs two part-time typists, Inna and Jim for his typing needs. Inna charges $10 an hour and can type 6 pages an hour, while Jim charges $12 an hour and can type 8 pages per hour. Each typist must be employed at least 8 hours per week to keep them on the payroll. If Mr. Shamir has at least 208 pages to be typed, how many hours per week should he employ each student to minimize his typing costs, and what will be the total cost?

 

1. Mr. Boutros wants to invest up to $20,000 in two stocks, Cal Computers and Texas Tools. The Cal Computers stock is expected to yield a 16% annual return, while the Texas Tools stock promises a 12% yield. Mr. Boutros would like to earn at least $2,880 this year. According to Value Line Magazine's safety index (1 highest to 5 lowest), Cal Computers has a safety number of 3 and Texas Tools has a safety number of 2. How much money should he invest in each to minimize the safety number? Note: A lower safety number means less risk.

 

1. A department store sells two types of televisions: Regular and Big Screen. The store can sell up to 90 sets a month. A Regular television requires 6 cubic feet of storage space, and a Big Screen television requires 18 cubic feet of space, and a maximum of 1080 cubic feet of storage space is available. The Regular and Big Screen televisions take up, respectively, 2 and 3 sales hours of labor, and a maximum of 198 hours of labor is available. If the profit made from each of these types is $60 and $80, respectively, how many of each type of television should be sold to maximize profit, and what is the maximum profit?

 

1. A small company manufactures two types of radios- regular and short-wave. The manufacturing of each radio requires two operations: Assembly and Finishing. The regular radios require 1 hour of Assembly and 3 hours of Finishing. The short-wave radios require 3 hours of Assembly and 1 hour of Finishing. The total work-hours available per week in the Assembly division is 60, and in the Finishing division, 60. If a profit of $50 is realized for every regular radio, and $75 for every short-wave radio,

 

1. 1. how many of each should be manufactured to maximize profit, and
   2. what is the maximum profit?

 

1. A company produces two types of shoes - casual, and athletic - at its two factories, Factory I and Factory II. Daily production of each factory for each type of shoe is listed below.

	Factory I	Factory II
Casual	100	200
Athletic	300	100

The company must produce at least 8000 pairs of casual shoes, and 9000 pairs of athletic shoes. If the cost of operating Factory I is $1500 per day and the cost of operating Factory II is $2000,

1. how many days should each factory operate to complete the order at a minimum cost, and
2. what is the minimum cost?

 

 

 

 

MATH 106 6383 Finite Mathematics (2192)

Week 5 Discussion

PROBABILITY (Applied Finite Mathematics, “Probability”)

1. A card is selected from a deck. Find the following probabilities.

 

1. 1. P(a red card)
   2. P(a face card)
   3. P(a jack and a spade)

 

1. A jar contains 6 red, 7 white, and 7 blue marbles. If a marble is chosen at random, find the following probabilities.

 

1. 1. P(red)
   2. P(white)
   3. P(red or blue)
   4. P(red and blue)

 

1. Consider a family of three children. Find the following probabilities.

 

1. 1. P(two boys and a girl)
   2. P(at least one boy)
   3. P(children of both sexes)
   4. P(at most one girl)

 

1. Two dice are rolled. Find the following probabilities.

 

1. 1. P(the sum of the dice is 5)
   2. P(the sum of the dice is 8)
   3. P(the sum is 3 or 6)
   4. P(the sum is more than 10)

 

1. A jar contains four marbles numbered 1, 2, 3, and 4. If two marbles are drawn, find the following probabilities.

 

1. 1. P(the sum of the number is 5)
   2. P(the sum of the numbers is odd)
   3. P(the sum of the numbers is 9)
   4. P(one of the numbers is 3)

 

MUTUALLY EXCLUSIVE EVENTS AND THE ADDITION RULE

Determine whether the following pair of events are mutually exclusive.

1.  

1. A={A person earns more than $25,000}B={A person earns less than $20,000}

 

1. A card is drawn from a deck:   C={It is a King}D={It is a heart}

 

1. A single, fair, 6-sided die is rolled:    E= {An even number shows}   F={A number greater than 3 shows}

 

1.  

1. Two fair 6-sided dice are rolled:   G={The sum of dice is 8}     H={One die shows a 6}

 

1. Three fair coins are tossed:    I= {Two heads come up}    J={At least one tail comes up}

 

1. A family has three children:    K= {First born is a boy}    L={The family has children of both sexes}

 

Use the addition rule to find the following probabilities.

1. A card is drawn from a 52-card deck, and the events C and D are as follows:   C= {It is a king}    D={It is a heart}.  Find “the probability of event C  OR  event D occurring”,  P(C  U  D).

 

1. A single fair 6-sided die is rolled, and the events E and F are as follows:  E={An even number shows}   F={A number greater than 3 shows}.  Find “the probability of event E  OR  event F occurring”, P(E  U  F).

 

1. At De Anza College, 20% of the students take Finite Mathematics, 30% take Statistics and 10% take both. What percentage of the students take Finite Mathematics or Statistics?

 

 

 

 

MATH 106 6383 Finite Mathematics (2192)

Week 6 Discussion

INTRODUCTION TO STATISTICS 

(Online Statistics Education:  A Multimedia Course of Study, Chapter 1: “Distributions” ; Chapter 2 “Histograms” ; Chapter 3 “Measures of Central Tendency” and “Measures of Variability”; Chapter 5 “Binomial Distribution”)

CHARTS, FREQUENCY TABLES, HISTOGRAMS

1. The students in Ms. Ramirez’s math class have birthdays in each of the four seasons.  The following table shows the four seasons,the number of students who have birthdays in each season, and the percentage (%) of students in each group. Construct abar graph showing the number of students.

Seasons	Number of students	Proportion of Population
Spring	8	24%
Summer	9	26%
Fall	11	32%
Winter	6	18%

 

1. A student has decided to display the results of his project on the number of hours people in various countries slept per night. He compared the sleeping patterns of people from the US, Brazil, France, Turkey, China, Egypt, Canada, Norway, and Spain. He was planning on using a line graph to display

this data. Is a line graph appropriate? What might be a better choice for a graph?

 

1. For the data in the table below from the 1977 University of New Hampshire Stat. and Biom. 200 class for eye color, construct a pie graph:

 

Eye Color	Brown	Blue	Green	Gray
Number of Students	11	10	4	1

(Question submitted by J. Warren, UNH)

 

1. For the data in the table below from the 1977 University of New Hampshire Stat. and Biom. 200 class for eye color, construct a horizontal bar graph:

Eye Color	Brown	Blue	Green	Gray
Number of Students	11	10	4	1

(Question submitted by J. Warren, UNH)

 

 

 

1. For the data in the table below from the 1977 University of New Hampshire Stat. and Biom. 200 class for eye color, construct a vertical bar graph:

 

Eye Color	Brown	Blue	Green	Gray
Number of Students	11	10	4	1

(Question submitted by J. Warren, UNH)

 

1. Using the data below, complete the frequency table.

DATA: 30, 32, 11, 14, 40, 37, 16, 26, 12, 33, 13, 19, 38, 12, 28, 15, 39, 11, 37, 17, 27, 14, 36

Interval	Frequency
11 – 15
16 – 20
21 – 25
26 – 30
31 – 35
36 – 40

 

 

1. Twenty five applicants to the Peace Corps are given a blood test to determine their blood type. The data set is:

 

A             B             B             AB          O

O             O             B             AB          B

B             B             O             A             O

A             O             O             O             AB

AB          A             O             B             A

 

Complete the following frequency distribution and construct a bar chart for this data.

 

Blood Types	Frequency
A
B
O
AB
Total

 

 

 

 

1. The test scores for 10 students in Ms. Sampson'shomeroom were 61, 67, 81, 83, 87, 88, 89, 90,98, and 100.  Complete the frequency table.

Interval	Frequency
61 – 70
71 - 80
81 - 90
91 - 100

 

1. The scores on a mathematics test were 70, 55, 61, 80, 85, 72, 65, 40, 74, 68, and 84. Completethe accompanying table, and use the table to construct a frequency histogram for these scores.

Interval	Frequency
40 – 49
50 – 59
60 – 69
70 – 79
80 – 89

 

 

1. Create a frequency table and histogram using the given information.

 

Number of crimes committed in 1984 in Metropolisburg:

January	124	February	96	March	89
April	113	May	107	June	102
July	85	August	87	September	91
October	119	November	122	December	115

 

 

Interval	Frequency
80 – 89
90 – 99
100 - 109
110 - 119
120 - 129

 

 

 

 

MATH 106 6383 Finite Mathematics (2192)

Week 7 Discussion

NORMAL DISTRIBUTION  (Online Statistics Education:  A Multimedia Course of Study:  Chapter 7, Sections:  “Areas of Normal Distribution” ;  “Standard Normal” ; “Normal Approximation to Binomial”)

AREAS OF NORMAL DISTRIBUTION

1. For a normal distribution with mean of 100 and a standard deviation of 12, find the number of standard deviations the raw score 76 is from the mean (Give answer as a positive value rounded to nearest hundredth). 

 

1. For a normal distribution with mean of 120 and a standard deviation of 15, find the number of standard deviations the raw score 144 is from the mean (Give answer as a positive value rounded to nearest hundredth). 

 

1. For a normal distribution with mean of 80 and a standard deviation of 8, find the number of standard deviations the raw score 67 is from the mean (Give answer as a positive value rounded to nearest hundredth). 

 

1. For a normal distribution with mean of 62 and a standard deviation of 6, find the number of standard deviations the raw score 47 is from the mean (Give answer as a positive value rounded to nearest hundredth). 

 

1. A normal distribution has a mean of 40 and a standard deviation of 68% of the distribution can be found between what two numbers?

 

1. A normal distribution has a mean of 20 and a standard deviation of 3. Approximately 95% of the distribution can be found between what two numbers?

 

1. A normal distribution has a mean of 5 and a standard deviation of 2. What proportion of the distribution is above 3?  Use either the Area Under Normal Distribution Calculatoror Z - tablelink (round answer to nearest thousandth).

 

1. A normal distribution has a mean of 12 and a standard deviation of 3. What proportion of the distribution is below 7?Use either the Area Under Normal Distribution Calculatoror  Z - tablelink (round answer to nearest thousandth).

 

1. A normal distribution has a mean of 120 and a variance of 100. 35% of the area is below what number?  Use either the Inverse Normal Distribution Area Calculator or orZ - tablelink (round answer to nearest thousandth).

 

1. A normal distribution of test scores has a mean of 38 and a standard deviation of 6. Everyone scoring at or above the 80th percentile gets placed in an advanced class. What is the cutoff score to get into the class?Use either the Inverse Normal Distribution Area Calculator or orZ - tablelink (round answer to nearest thousandth).

 

 

MATH 106 6383 Finite Mathematics (2192)

Week 8 Discussion

Linear Programming

 

1.        Graphically solve the following:

            Maximize , subject to:

 

2.        Solve the given linear programming problem graphically:

            Nutrition:  A dietitian is to prepare two foods to meet certain requirements.  Each pound of Food Icontains 100 units of vitamin C, 40 units of vitamin D, and 10 units of vitamin E and costs 20 cents.  Each pound of Food II contains 10 units of vitamin C, 80 units of vitamin D, and 5 units of vitamin E and costs 15 cents.  The mixture of the two foods is to contain at least 260 units of vitamin C, at least 320 units of vitamin D, and at least 50 units of vitamin E.  How many pounds of each type of food should be used to minimize the cost?

 

3.        Solve the given linear programming problem graphically:

            Maximize              Subject to: 

 

4.        Solve the given linear programming problem graphically:

 

            Maximize   Subject to: 

 

5.        Solve the given linear programming problem graphically:

 

            Advertising:  An advertising agency has developed radio newspaper, and television ads for a particular business.  Each radio ad costs $200, each newspaper ad costs $100, and each television ad costs $500 to run.   The business does not want the television ad to run more than 20 times, and the sum of the numbers of times the radio and newspaper ads can be run is to be no more than 110.             The agency estimates that each airing of the radio ad will reach 1000 people, each printing of the newspaper ad will reach 800 people, and each airing of the television ad will reach 1500 people.  If        the total amount to be spent on ads is not to exceed $15,000, how many times should each type of ad be run so that the total number of people reached is a maximum?

 

6.  Solve the following linear programming problem graphically:

            Maximize          Subject to: 

7.        Solve the following linear programming problem graphically:

 

            Minimize     subject to: 

 

8.        Solve the following linear programming problem graphically:

 

            The InfoAge Communication Store stocks fax machines, computers, and portable CD players.  Space restrictions dictate that it stock no more than a total of 100 of these three machines.  Past sales patterns indicate that it should stock an equal number of fax machines and computers and at least 20 CD players.  If each fax machine sells for $500, each computer for $1800, and each CD player for $1000, how many of each should be stocked and sold for maximum revenues?

 

Mathematics of Finance

9.        Find the amount that aprincipal of $800will accumulate in 12 years for each given account:

a.        7% simple interest

b.        7% compounded quarterly

c.         7% compounded monthly

 

10.      Find the principal P required to achieve a future amount A=$5000 with an interest rate of 6% compounded quarterly for 5 years.