Module far Middle and High School Mathematics Teachers of the Deaf

Career Exploration for Deaf and Hard-of-Hearing Students

Using Math Word Probtems (Reat Life Applications)

Alvin C. Boyd, Sr.

Rochester Institute of Technology

National Technical Institute for the Deaf

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Rochester Institute of Technology National Technical Institute for the deaf Business Studies Department 52 Lomb Memorial Drive Rochester, NY 14623-5604 Email: Alvin.Boyd@rit.edu albee429me@yahoo.com . Voice/TTY: 585-475-4307 VP: 585-286-3461

Disclaimer:

As a form of professional courtesy for the free use of this material, the author welcomes comments and suggestions for the evaluation and modifications. Please provide the author with feedback in regards to the application of this module with your students, whether positive or negative. Also, if you make any modifications which may have proven beneficial to students, please provide the author with your modifications (in content, mathematical wording or problems, and deaf professionals).

Table of Contents

I. Deaf Restaurant Owner and Manager ................................................. 5 • Pre-Algebra - Number Sense, Operations, and Business Math

II. Deaf Adventure Guide .................................................................. 7 • Pre-Algebra -Number Sense and Operations

III. Deaf Statistician .......................................................................... 9 • Pre-Algebra - Fractions, Decimals, and Percents • Statistics - Average, Data Analysis • Algebra

IV. Deaf Bank President ................................................................... 13 • Algebra and Business Math

V. Deaf Photographer ..................................................................... 16 • Algebra - Proportion, Perimeter, and Area

VI. Deaf Office Administrator ........................................................... 18 • Algebra, Business Math, and Currency Conversion

VII. DeafBaker .............................................................................. 21 • Algebra - Inequalities and Number Sense

VIII. Deaf Inspector ......................................................................... 23 • Statistics - Probability, Sampling to Predict

IX. Deaf Climatologist .................................................................... 26 • Statistics - Average • Pre-Algebra - Number Sense, Inequalities, and Temperature Conversion

X. Deaf Animator ........................................................................ 29 • Geometry - Transformation

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XI. Appendix ............................................................................ 31

XII. Math Interview ..................................................................... 3 3

XIII. Solutions ............................................................................ 35

1. Deaf Restaurant Owner and Manager ....................................... 3 5

2. Deaf Adventure Guide ......................................................... 36

3. Deaf Statistician ................................................................ 37

4. Deaf Bank President ........................................................... 39

5. Deaf Photographer ............................................................. 40

6. Deaf Office Administrator ..................................................... 40

7. Deaf Baker ...................................................................... 41

8. Deafinspector .................................................................. 42

9. Deaf Climatologist ............................................................. 44

10. Deaf Animator ................................................................ 45

www.rit.edu/ntid/businesstech

Please note that the information (exact measurements, amounts, volumes, and estimates) in each lesson has been created to model true problems. The information is not the exact information that the deaf persons use in their actual careers.

4

Deaf Restaurant Owner and Manager - Danny Delcambre

Danny Delcambre is the first Deaf-Blind founder and operator of a Seattle restaurant. Having grown up in Louisiana, prime Cajun country, Danny appropriately named his restaurant Ragin Cajun. Danny has Usher's Syndrome- tunnel vision, difficulty seeing in poor light, poor balance, congenital deafness. A student of world renowned chef Paul Prudhomme, Danny is experienced in the fine art of cooking. Named the Small Business Employer of the Year by President of the United States William Jefferson Clinton and subsequently followed by the Small Businessman of the Year awards by the City of Seattle and the State of Washington, his path to success was not easy though. Delcambre's Ragin Cajun Restaurant employed three deaf employees, three hearing employees who knew sign language of which 2 persons worked full-time and four persons worked part time.

One of Danny's responsibilities as a restaurant manager is handling reservations. Before the restaurant opens for the day, the he inspects the reservation list. Then the wait staff groups the tables according to the size of the parties the restaurant is expecting. The staff combines tables to seat a range of group sizes from the smallest to the largest.

Solve.

1. The hourly pay rates of the six employees are: $9, $7.50, $5 .50, $5.50, $7, $8.50. Help Danny make a frequency table of the data. What are the highest and lowest pay rates? What is the range of pay rates?

2. On a typical day, the deaf employee whose hourly rate is $9 works for 8 hours. The deaf employee whose hourly rate is $8.50 works for 10 hours. Two hearing employers whose hourly rate is $5 .50 works for 12 hours and 10 hours, respectfully. The deaf employee whose hourly rate is $7 works for 9 hours. The last employee works for 10.5 hours at an hourly rate of $6.50. How much does Danny pay to his employees, in total, on a typical day?

3. Danny expects the size of the parties on one evening to be: 6, 2, 6, 2, 8, 10, 4, 2, 15, 8. On average, 20% of the parties order Danny's special, Stuffed Flounder with Craw.fish Etouffee.

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a. How many of the owner's specials does Danny estimate he will have to cook for that evening? Round up to the nearest whole number.

b. If the special entree costs $16.99 each, how much does Danny estimate he will earn that evening?

4. One of the restaurant's famous entrees is Shrimp Creole. Danny has to buy shrimp for this entree. Shrimp is sold by size. Shrimp sizes are expressed in counts per pound. Danny orders the large size Wild American shrimp which are counted 31 to 35 shrimp per pound, with the average count per pound of 33 shrimp. Danny orders two 5-pound boxes of shrimp, weekly. An average of 8 shrimp is used in a 10 oz serving of Shrimp Creole.

a. What's the average count of shrimp in a 5 pound box?

b. How many shrimp does Danny receive each week if he orders three 5-pound boxes each week?

c. How many servings of Shrimp Creole can be prepared in one week (based on the original order of shrimp)?

5. The accounting department of the Delcambre's Ragin Cajun Restaurant is checking to see whether the actual expenses of a department differ from the budgeted expenses by more than $500 or by more than 5%. Fill in the missing information, and determine whether each actual expense passes the "budget variance test."

Budgeted Expense, b Actual Expense, a I a-b I 5% of the budgeted

exTJenses (b) ·Wages $112,700 $113,356 Utilities $9,400 $9,772 Taxes $37,640 $37,335 Insurance $2,575 $2,613

6. Danny purchases a new stainless steel stove top oven for $125,000. The depreciated value y after t years is

y = 125,000- 10,000t,

a. Sketch the graph of the equation. b. What is the value of the stove top oven after 3 years? c. What will happen to the value of the stove top oven after 6 years? Explain

(For more information about Danny Delcambre refer to the Appendix)

6

Christy Smith received a Bachelor of Arts degree in sociology/criminology from Gallaudet University. She most recently worked as a children's adventure guide for the Aspen Camp School for the Deaf. Christy is called the Deaf Survivor from the reality television show, "Survivor." Her favorite hobbies are socializing, doing anything outdoors and writing letters. She has traveled to Costa Rica and spent 50 days on a wilderness adventure trip in Alaska with Outward Bound. She describes herself as independent and goal-oriented.

As an adventure guide, Christy leads groups of people on outdoor adventure trips. The trips may involve activities such as hiking, camping, mountain climbing, white-water rafting, and cross-country skiing. Christy is athletic, a good leader, and relates will with others. The best guides know the climate of the region and a little of its history and geography. They should also be familiar with the region's plants and animals, and they should know first aid and CPR.

For overnight hiking, or camping trips, and Christy will recommend different kinds of sleeping bags. Sleeping bags have temperature ratings that list the lowest temperature for which the bags are suitable . The temperature in Celsius degrees 'C' can be changed to Fahrenheit degrees 'F' by the formula F = (115) • (9C + 160).

Solve. 1. Christy has four sleeping bags with temperature ratings of+ 10°C, +5°C, -5°C and

-15°C. Which sleeping bag should Christy recommend hikers take if she expects the temperature to drop below 32°F? Explain.

2. Christy has five sleeping bags with temperature ratings of 20°C, l 5°C, 10°C, 5° C and 0°C. Which sleeping bag should Christy recommend hikers take if she expects the temperature to be no less than 59°F? Explain.

3. Rearrange the temperature formula that will allow you to find the temperature in Celsius degrees 'C' based on given Fahrenheit degrees 'F'.

C=

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4. Order the temperature ratings -20°F, -5°C, 0°F, -l0°C, and !5°F from greatest to least (for both Fahrenheit and Celsius).

5. Every day Christy receives a signal in her GPS weather device that she carries with her when she partakes in a hiking trip twice, once in the noon and another in the late evening. One day in her hiking trip in the Appalachian Mountains she received two signals with information on weather. At noon, the temperature was 87°F. Late in the evening, the temperature was 68°C. Use the formula to find the corresponding temperature at noon in Celsius. Round to the nearest hundredth. What is the range of the temperature (in Celsius) during that day?"

6. Draw a graph depicting the relationship between the Celsius degrees and Fahrenheit degrees.

(For more information about Christy Smith refer to the Appendix)

8

Deaf Statistician - H. Latham Breunig

H. Latham Breunig, Ph.D., resided in Arlington, Virginia. He retired from Eli Lilly and Company, Indianapolis, Indiana. Dr. Breunig was born hard-of-hearing; then he lost more hearing after scarlet fever at the age of five, and became deaf at age seven as the result of a skull fracture. He attended Wabash College, Indiana; earned his Ph.D. in Chemistry from Johns Hopkins University; and also studied at Purdue University, Indiana, in the field of Statistics and Quality Control.

Among the many organizations where Dr. Breunig has been active are the President's Committee on Employment of the Handicapped; the American Statistical Association; the Clarke School for the Deaf; and the Alexander Graham Bell Association for the Deaf, where he has served on the Board of Directors for the past twenty-four years, two of them as President. He founded the nonprofit organization, Telecommunications for the Deaf in 1968, and was Chief Executive Officer until 1978. He has been active in the development of oral interpreters for deaf people.

Special awards presented to Dr. Breunig have included the President's Committee on Employment of the Handicapped Commendation by President Johnson in 1967. In 1977, Teletypewriters for the Deaf, Inc. made him the first recipient of its H. Latham Breunig Award. Dr. Breunig was honored by Wabash College in 1984 with its Alumni Award of Merit. Latham Breunig, a former member of the presidential commission on deafness.

Other Statisticians, like Breunig, would help to design surveys and experiments. They also collect, analyze, and interpret numerical data. Some work for businesses and some work in government.

Statisticians often use samples to collect information. A sample provides information about a small group within a much larger group. They can then take what they learned about the small group and apply it to the larger group.

Statisticians decide where and how to gather the data. They choose the sample size. They decide about the type of survey. They tell workers who gather the data how to do their job. They process the collected data and reach conclusions about the data. They do this with the help of computer software.

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SOL VE. Write each answer as a whole number, a fraction, a decimal and a percent. Round decimals to the nearest hundredths place if necessary.

For problems 1 and 2, use the following survey results:

The Benson School District superintendent asked the cafeteria managers at the two schools in her district to determine what kind of food the students like. A group of students at each school was asked if they liked thin crust veggie pizza, wheat pasta with ground turkey and tomato sauce, taco salad with fresh beans and salsa, and turkey subs with lettuce and tomato. The superintendent received these results of the survey:

Middle School:

High School

5 of every 6 students said they like thin crust veggie pizza. 4 of every 5 students said they like wheat pasta with ground turkey and tomato sauce. 1 of every 3 students said they like taco salad with fresh beans and salsa. 1 of every 9 students said they like turkey subs with lettuce and tomato.

2 of every 3 students said they like thin crust veggie pizza. 7 of every 12 students said they like wheat pasta with ground turkey and tomato sauce. 3 of every 10 students said they like taco salad with fresh beans and salsa. 2 of every 9 students said they like turkey subs with lettuce and tomato.

1. There were 90 students surveyed at the middle school. How many middle school students liked:

a. taco salad with fresh beans and salsa? b. turkey subs with lettuce and tomato?

2. There are 180 students surveyed at the high school. How many high school students liked:

a. wheat pasta with ground turkey and tomato sauce? b. thin crust veggie pizza?

3. Viola is a pitcher for the Littleville softball team. During a recent practice she measured her pitch velocity using a radar gun. She pitched 5 balls a distance of 40 feet. The speeds measured were 43, 36, 37, 41, and 44 miles per hour, respectively.

a. What is the average miles per hour for Viola's pitches?

b. Use this information, 1 mile= 5280 feet, to find the average time it took for the balls to travel the 40 feet?"

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x y

4. Use the table below, which shows the mathematics entrance test scores x and the final examination scores y in an algebra course for a sample of I 0 high school students.

Connie Marie Tim Alvin Chris Josh Erin Mitch Dionne Charles 22 29 35 40 44 48 53 58 65 76 53 74 57 66 79 90 76 93 83 99

a. Sketch a scatter plot of the data shown in the table. b. Find the entrance exam score of any student with a final exam score in the 80s. c. Does a higher entrance exam score imply a higher final exam score? Explain.

5. The table shows the life expectancy of a child (at birth) in the United States for selected years from 1920 to 2000. (Source: U.S. National center for Health Statistics, U.S. Census Bureau)

Year, t Life expectancy, y 1920 54.1 1930 59.7 1940 62.9 1950 68.2 1960 69.7 1970 70.8 1980 73.7 1990 75.4 2000 77.1

A model for the life expectancy during this period is

y = -0.0025t' + 0.572t + 44.31

where y represents the life expectancy and t is the time in years, with t = 20 corresponding to 1920.

a. Sketch a scatter plot of the data.

b. Graph the model for the data and compare the scatter plot and the graph. (What is the relationship between the data and the graph? Does the data match the graph?)

c. Use the equation of the model to estimate the life expectancy of a child for the years 2005 and 2010.

d. Do you think this model can be used to predict the life expectancy of a child 50 years from now? Explain.

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6. The number of married women y (in millions) in the civilian work force in the United states from 1990 to 1999 can be approximated by the model

y = 0.41t + 30.9

where t = 0 represents 1990.

a. Create a bar graph that represents the years 1990 to 1999.

b. According to this model, during which year did the number reach 33 million?

c. Explain how to answer this question graphically and algebraically.

(Source: U.S. Bureau of Labor Statistics)

(For more information about H. Latham Breunig refer to the Appendix)

12

Deaf Bank President/CEO - James Meisser

James "Jim" Meisser of Kohler is striving for a couple of firsts - to be the first profoundly deaf bank president in the nation and to run the first financial institution to use modem technology to cater to customers with disabilities.

Meisser, 48, who has been profoundly deaf since he was born. Meisser and his wife, Jeanene, are in the process of getting state and federal regulatory approvals as well as raising $20 million in capital to open Lake Shore Bank in Sheboygan in November.

Jim will be the very first profoundly deaf president and CEO of a bank.

James and deaf and hard of hearing bank customers will be able to use voice recognition and text screen technology to be clearly understood by others. Text messaging and instant messaging through the Internet and through wireless are other modes of communication. Also, bank tellers will be trained to communicate with the deaf and hard of hearing.

Some of Jim's responsibilities as a bank president are processing data to produce accurate facts, figures and reports; evaluating new and renewal lending proposals, negotiating terms with customers and, current account transactions, unsecured loans, credit cards and personal loans.

1. A man pays loan payments equaling 58.6% of his annual income to Jim's bank, Lake Shore Bank in Sheboygan. During the year, his payments total $13,077.75.

a. What is his average monthly payment? (Assume that the family uses a pay schedule and pays the same amount each month)

b. What is his annual income?

c. The man has refinanced his loan to save money. He wants to pay 47.3% of his annual income. How much would his annual payments total after he has refinanced his loan?

d. What is his average monthly payment after refinancing his loan? (Assume that the man uses a pay schedule and pays the same amount each month)

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2. One of the bank's senior managers receives a monthly salary of $3250 plus commission of 5% of Certificate of Deposit (CD), new account openings (NA), and small business loan (SBL) sales.

a. Write a linear equation for the senior manager's monthly wage Win terms of monthly sales S. (S detonates the total monthly sales from CD, NA and SBL)

b. What would be the senior manager's monthly wage if she sold $5,300 worth of CDs, new accounts, and small business loans?

3. If the Lake Shore Bank earns $1.6 million in 2008 and $2.1 million in 2010,

a. What would be the estimated earnings for the 2009? Use the midpoint formula. (Assume Lake Shore Bank's earnings have followed a linear pattern.)

b. Plot the coordinate points and draw a line through the three points.

c. Estimate how much will the Lake Shore Bank earn in 2013.

4. Jim has a customer that invested $5000 in a high risk-high yielding CD which is compounded annually at an interest rate r, after 2 years, will yield an amount of 5000(1 + r)2.

a. Write the polynomial in standard form.

b. Jim's customer would like to know the potential earnings of his investment at various interest rates. Evaluate the polynomial for the values of r shown in the table.

I ~000(1 + r)' 2 Yi% 3% 4% 5%

5. A person gets a loan for a new car at Lake Shore Bank. Jim has to use the formula that approximates the annual interest rate r of a monthly installment loan is given by

r = [24(N:- P)l

(P+~~)

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where N is the total number of payments, Mis the monthly payment, and P is the amount financed.

a. Approximate the annual interest rate for a four-year car loan of $16,000 that has monthly payments of $400.

b. Approximate the annual interest rate ifthe person wanted to extend the car loan to a five-year car loan of $16,000 with lower monthly payments of $300.

6. Jim invests $25,000 of the bank's profits in two funds paying 3% and 4Yz % simple interest. (There is more risk in the 4Yz % fund.) His goal is to obtain a total annual interest income of $1000 from the investments. What is the smallest amount he can invest in the 4Yz % fund and still meet his objective?

(For more information about James Meisser refer to the Appendix)

15

Deaf Photographer - Michael Pimentel

Michael Pimentel is a well-known Deaf professional photographer. He has covered different professional and college sports, such as the 2004 Olympics in Athens, Greece, 2003 FIFA Women's World Cup, NBA, MLB, NFL, just to name a few. In 2003, Michael was a Team Photographer for USA Deaf Team Deaflympics at Sundsvall, Sweden. His photos have been published in many magazines and newspapers around the world, including, but not limited to: Sports Illustrated, ESPN, Sports Illustrated for Kids, and many more.

After Michael is finished taking his pictures he has to develop them. He has to process the film. Depending on the where the picture will be shown and for what reason the size of the picture will vary. He has to keep the length and width of an enlargement proportional to the original photo, the measurements for the enlargement must be computed mathematically.

SOLVE

1. Suppose Michael wants to enlarge a photo of the WIBA and the IWBF Super Middleweight Boxing Champion, Laila Ali that is 4 inches long and 6 inches wide. The enlarged photo must have the same proportions as the original, but be 12 inches long. What size will the enlargement be?

2. Michael has an enlargement photo of New Orleans Saints Running Back, Reggie Bush that is 16 inches long and 20 inches wide. The original has the same proportions as the enlargement, but is only 4 inches long. How wide is the original?

3. Michael takes a photo of All Star NBA basketball player, Tim Duncan that is 30 inches long and 18 inches wide.

a. What is the perimeter of the photo?

b. What is the area of the photo?

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4. The perimeter of an original photo, shot by Michael, of the first deaf student government president at the Rochester Institute of Technology and Gold Medal team winner of the 2005 U.S. Deaf Women's Olympic Soccer team, Elizabeth "Lizzie" Sorkin, is 9.6 inches. The original photo has a width of3.4 inches. The enlarged photo is the same proportion as the original, but has a width of 17 inches. What is the perimeter of the enlarged photo?

5. The area of an enlarged photo of San Francisco Giants player, Barry Bonds, taken by Michael when Barry broke the all-time career home run record with his 7561

h

home run, is 864 square inches. The length of the photo is 24 inches long. The original has the same proportions as the enlargement, but is only 7 inches long. What is the area of the original?

6. Michael has to enlarge a photo of a deaf mixed martial arts fighter, Matthew "The Hammer" Hamill that is 3 inches wide. The area of the photo is 24 square inches. The enlarged photo must have the same proportions as the original, but will be 11.25 inches long. What is the area of the enlarged photo?

(For more information about Michael Pimentel refer to the Appendix)

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CSD (Communication Service for the Deaf, Inc.) and USA Deaf Sports Federation (USADSF) appointed Melody Tsai as USADSF home office administrator at its new home office location in Sioux Falls, S.D. Born in Hong Kong, Tsai began her education at the Philippines Association of the Deaf in Manila, later transferring to the Canossian School for the Deaf in Singapore. She later moved to California, where she graduated from the California School for the Deaf-Fremont (CSDF) in 1992.

After attending the National Technical Institute for the Deaf at the Rochester (N.Y.) Institute of Technology and Gallaudet University in Washington, D.C., Tsai earned a Bachelor of Science degree in hospitality management from San Francisco State University in San Francisco, Calif.

Melody is a multi-talented worker responsible for many office tasks. Some of her responsibilities include supervising employees, maintaining databases, receiving and sending bills, ordering supplies, scheduling appointments, organizing meetings and working with the company's budge (Accounts Receivable bookkeeping, Accounts Payable, and payroll).

Solve.

1. Suppose the company's marketing manager needs to hire a printer to make some advertising packets. The printer quotes $3 for each packet and a one-time fee of $2,000 to design the materials. The budget for these materials is $8,000.

a. How many packets can Melody order with a budget of $8,000?

b. Calculate how many packets Melody can order for $5,000 if each packet costs $5 and the design fee is $1,000.

2. Referring to problem #1, suppose each advertising packet costs $7 and the design fee is $3,000. The marketing manager wants 1,000 packets but Melody has only $8,000 to spend.

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a. Does the she have enough money in the budget to purchase the 1,000 packets plus the cost of the design fee? Explain.

b. How much would Melody's budget need to be in order for her to purchase 1,000 packets?

3. Melody's supervisor often travels from the United States to Japan to attend business conferences. As such, she needs to convert US dollars to Japanese Yen for her supervisor to conduct any business transaction.

If a certain item cost 150,000 yen r, how much would it be in US dollars? Today, the exchange rate for 1 dollar is 115 yens. Round the amount to the nearest hundredth. (Research the internet for a more current exchange rate.)

4. Occasionally, Melody has to use her personal car to conduct business transactions for her company and attend professional development workshops. She receives $120 per day for lodging and meals plus $0.35 per mile driven.

a. Write a linear equation giving the daily cost C to the company in terms of x, the number of miles driven.

b. What would be the company's total cost for Melody's 5 day, 432 mile round trip drive to Santa Monica, CA?

5. Melody's department sends its copying to the photocopy center of her company. The center bills her department $0.10 per page. Melody has investigated the possibility of buying a departmental copier for $3000. With department's own copier, the cost per page would be $0.03. The expected life of the copier is 4 years. How many copies must you make in the four-year period to justify buying the copier? Explain.

6. Melody's company has a 40l(K) Profit Sharing Plan for employees. Employees may defer up to 15% of their salary to the profit sharing plan. This is a great benefit to employees. Not only is the deferral "pre-tax", the company offers a "match" on the deferral.

The 401 (K) amount is deducted from the gross payroll before Federal and State taxes are deducted. The company matches $.50 on the dollar up to 3% of salary. Payment for the deferrals and company match must be sent to the Trust each pay period. Their names of six employees, their monthly salary, and their chosen deferral percentage are listed below.

What is the total check amount to the Trust each pay period?

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Complete the table to find the total investment to the Trust each pay period for each employee:

I Employee I Salary I % Deferral I Amount I Match* I Total

I Charles I $1,ooo 1 15%

I Karl I 1,200 1 10%

I Joycelyn I 2,000 1 3% I I Maria I 900 1 5% I F~~lll I Allen I 1,750 1 7%

(For more information about Melody Tsai refer to the Appendix)

20

Deaf Baker - Jimmy Libman

Jimmy Libman, who is deaf, received the Our Way Achievement Award as the co­founder of the highly successful "Gimmee Jimmy's Cookies." Jimmy launched his cookie company 22 years ago from his childhood home in West Orange, N.J. with his mother's cookie recipe. Gimmee Jimmy's produces at least 20 varieties of handmade home-style cookies. Among the top sellers are chocolate chip, chocolate chip M&M™ (different colors of the candy reflect the seasons and holidays) and chocolate chip walnut. Jimmy plans to expand the menu to include muffins, brownies and other bakery items as well as coffee and cappuccino drinks.

Jimmy runs his own business. As well as knowing how to bake, he must know about nutrition, business administration, marketing, and health and safety regulations.

Jimmy must adapt recipes to bake smaller or bigger cakes, cookies, and brownies. When the recipe contains fractions, bakers must multiply and divide fractions.

Solve.

1. A recipe for a two-pound cake includes Yi teaspoon of vanilla flavoring. The Jimmy wants to make a ten-pound cake, but only has two teaspoons of vanilla flavoring left. Does the Jimmy have enough vanilla flavoring to make the ten­pound cake? Explain.

2. How much time does he spend baking in 3 weeks, assuming he works for 10 hours a day, 7 days a week?

3. Jimmy is baking and needs 4 cups of sugar for a cake recipe. His problem is that he has misplaced all of his measuring cups except for the 112 cup measure and 3/4 cup measure. What is the least number of scoops that he could make in order to get 4 cups? Explain your answer.

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4. Jimmy has a recipe that will make 18 dozen chocolate chip cookies. But the chocolate chip cookie has not been selling as well as it did in the previous month. Change the recipe so that Jimmy only makes 9 dozen chocolate chip cookies.

Chocolate Chip Cookies

7 Y, cups all-purpose flour 3 teaspoons baking soda 3 pinches of salt 1 Yi cups light brown sugar, firmly packed 3 cups granulated sugar 6 eggs 6 teaspoons vanilla extract 3 cups butter or margarine, room temperature 3 packages (36 ounces or 6 cups) semisweet chocolate chips

5. Wheat flour and sugar are two basic ingredients necessary to bake two items: a loaf of bread and a muffin. Jimmy has 25 pounds of wheat flour and 5 pounds of sugar. To bake each loaf of bread, Jimmy needs to use 2 pounds of wheat flour and 1 pound of sugar. To bake each muffin, Jimmy needs 1 pound of wheat flour and 0.5 pound of sugar.

a. Set up the inequalities representing the baker's possible choices for baking the number ofloaves of bread and muffins to use up his available resources (wheat flour and sugar). Bread= x and Muffins = y

b. Solve inequalities for y

c. Graph the inequalities

d. Find the possible solutions and make a table ofx and y that satisfies the two inequalities.

e. If Jimmy makes 2 loaves of bread would he be able to make 7 muffins, given the resources he has? Why or why not?

6. Jimmy has a secret ingredient that makes his cakes moist and tasty. The secret ingredient is butterfat. Milk that has 5% butterfat mixed with milk that has 2% butterfat. Jimmy wants to know how much of each is needed to obtain 60 gallons of milk that has 3% butterfat. 3% butterfat milk is a mixture of 5% butterfat milk and 2% butterfat milk. Find how much of each milk is needed to obtain 60 gallons of milk that has 3% butterfat.

(For more information about Jimmy Libman refer to the Appendix)

22

Deaf Inspector - Kathy Wigley

Kathy Wigley is a machine parts inspector, is the first deaf inspector at Raytheon. Raytheon is a technology leader specializing in defense, homeland security, and other government markets throughout the world. Kathy is a fourth-generation deaf family member. "I've never been afraid because I'm deaf. It is a challenge; but I take and accept that challenge," said Kathy.

Kathy is a machine parts inspector but there are other kinds of inspectors such as a Consumer Safety Inspector. A Consumer Safety Inspector inspects items such as food, animal feeds, pesticides, cosmetics, and pharmaceuticals. Inspectors visit manufacturing facilities that produce manufacturing facilities that produce, handle, store, or market consumer products. Part of their job is to ensure that products are labeled correctly and that weights and contents are accurate. They also check for contamination that could have resulted from unsterilized processing equipment or unsanitary food handling.

Solve.

1. Sup pose a law states that only . 7 5 % of a sample of metal panels may be discolored. Calculate what the percent of a sample is discolored if the Kathy finds that 3 metal panels out of a sample of 500 are discolored. Would the metal panels pass inspection based on the sample? Explain.

2. Suppose a health law states that only .5% of a sample of chocolate may be contaminated. Calculate what percent of a sample is contaminated if 4.5 gallons of chocolate milk out of a sample of 800 gallons are contaminated. Based on the sample, would the chocolate milk pass inspection? Explain.

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3. Kathy collected I 0 samples of 500 mechanical parts and found that each sample has x defective mechanical parts.

SAMPLES Number of Defective Mechanical Parts

Sample I IO Sample 2 7 Sample 3 11 Sample 4 2 Sample 5 4 Sample 6 14 Sample 7 9 Sample 8 8 Sample 9 17

Sample IO 6

a. Find the average percentage of mechanical parts that is defective.

b. If the company's policy states that an average I% of the mechanical parts is allowable, did the inspection with the ten samples pass the policy's requirement? Explain.

4. Radars for shipment at the Raytheon owned factory come down a ramp in single file. Kathy checks every third radar, beginning with the third. Her partner checks every fifth. If 98 radars came down the ramp while both inspectors were working on Monday, how many of these radars were not checked by either of these two inspectors.

5. Suppose Kathy oversees a team of six inspectors. Kathy decides that she needs a three-person group to check mechanical parts at a Raytheon-owned factory. The team members are Alvin, Chris, Erin, Gerry, Mitchell, and Thomastine (A, C, E, G, M, and T, for short). How many groups could be formed from the six team members?

a. Count the possible groups by listing them all.

b. Use this formula, "C' = n! , to find the number of possible (n- r)!xr!

combinations if we make r selections from a group of n items.

c. Does your answer for b match your answer for a?

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6. Kathy obtained several readings of the range between the center of a wafer and various points on the edge of a wafer this process is called Center to Edge (CTE). She then logs the readings in a table (See below). She then calculates the CTE and compares it with a critical value to determine ifthe process is accurate. The critical value is I 000.

Determine whether Process A and Process B are accurate (absolute value is less than 1000).

[ X1 +Xi+ X4 + Xs J

CTE= 4 -X2

x,

(For more information about Kathy Wigley refer to the Appendix)

25

Deaf Climatologist-Vincent "Bim" Wood

Vincent "Bim" Wood, a research meteorologist, has been deaf since infancy. Bim conducted a nine-month survey, after tornadoes struck Oklahoma on May 3, 1999, that revealed 81 percent of deaf and hard-of-hearing people in the state of Oklahoma have experienced fear about being unprepared for weather emergencies. He also found they have relatively limited ways of knowing severe weather is imminent. Bim has helped initiate a new program with the Hazardous Weather Pager Program that sends life-saving weather messages via pagers to deaf and hard of hearing subscribers. Bim received the "Public Personnel Employee Award" from the Oklahoma City mayor's Committee on Disability Concerns for his work.

A research meteorologist is very similar to a climatologist who studies the climate and weather patterns and makes summaries from these patterns. The formation in these summaries can be used in the design of heating and cooling systems, and sometimes in the design of entire buildings. Bim can use terms such as mean, median, and mode in his climate summaries.

Solve: 1. Suppose a building in an area with lots of sunlight and heat needs a more

powerful air conditioning system than a building in an area with much less sunlight and heat. Bim wants to find the mean, median, and mode for this set of temperatures in his climate summaries. Once Bim has found the mean, median, or mode, which method/s of finding the average would provide him the best information to make a decision about the air conditioning system needed?

100°, 93°, 85°, 75°, 89°, 92°, 81°, 96°, 88°, 93°

2. Suppose a building in an area with lots of snow needs to have a more powerful heating system than a building in an area with no snow. Bim wants to find the mean, median, and mode for this set of temperatures in his climate summaries. Once Bim has found the mean, median, or mode, which method of finding the average would provide him the best information to make a decision about the heating system needed?

14°, 0°, 17°, 5°, 13°, 9°, 12°, 16°, 8°, 12°

26

3. After calculating the mean, median, and mode for this set of temperatures in his climate summaries, Bim accidentally deleted one temperature from the set. Find the missing temperature.

1 o, 1 o, -80, 90, 00, _30, 50, -2o, Io, -60, -

Mean: -1° Median: 0° Mode: 1°

4. After calculating the mean, median, and mode for this set of temperatures in his climate summaries, Bim accidentally deleted two temperatures from the set. Find the two missing temperatures.

45°, 61°, 52°, 42°, 43°, 53°, 53°, 46°, 62°, 47°, ' --

Mean: 49.75° Median: 46°, 47° Mode: 42°, 53°

5. Bim has an electronic device that is to be operated in an environment with relative humidity h in the interval defined by jh - SOI :'S 30. What are the minimum and maximum relative humidities for the operation of this device?

6. Citizens of the United States primarily use the Fahrenheit scale, the rest of the world uses the Celsius scale, and Bim also uses the Celsius and Kelvin scale. Since there are three different scales used to measure temperature, it seems reasonable to have formulas for changing or converting from one scale to another. The Kelvin scale is a scale that measures temperatures beginning with absolute zero, the lowest possible temperature at which matter can exist. The Kelvin is often used in the measure of the color temperature of light sources. For the problems below, round to the nearest whole number.

F0 = (1/5) • (9C0 + J 60).

K= C0 +273

27

a. If the temperature is 75° Fahrenheit, what are the equivalent readings on the Celsius and Kelvin scales?

b. If the temperature is 26° Celsius, what are the equivalent readings on the Fahrenheit and Kelvin scales?

c. If the temperature is 288 Kelvin, what are the equivalent readings on the Celsius and Fahrenheit scales?

d. Create a formula to determine the Kelvin temperature given the degrees in Fahrenheit.

(For more information about Bim Wood refer to the Appendix)

28

Deaf Animator - Mark Fisher

Born Deaf, Mark Fisher attended the Archbishop Ryan Memorial Institute in Philadelphia and later the Marie Katzenbach School for the Deafin New Jersey. He holds a Bachelors of Fine Arts from Gallaudet University. He is recognized as the first successful Deaf animator, working on several well-known films such as: Universal's Land Before Time, Disney's The Little Mermaid and Prince and the Pauper, Nest Entertainment's The Swan Princess, Morgan Creek's Stayed Tuned and Warner Bros' Thumbelina and The King and I, in addition to having worked on several TV cartoons series for Universal, Warner Bros. and others as a storyboarder/revisionist. Fisher's Elves and the Bat Beast was chosen Best Animation at the Atlantic City Film Festival, held August 4, 2001 in New Jersey.

Although Mark is skilled at drawing by hand, most animators draw using computer software. He must not only be a good artist, but he must also know how to use computer graphics and animation software. As computer software improves, Mark must master it to help him create better animation sequences efficiently.

Solve.

I . Mark draws a magic treasure chest that can disappear and reappear in another place. The magic treasure chest's points are (-4, 5), (-2, 5), (-1, 4), (-1, 2), (-5 , 2), and (-5, 4) and Mark wants to have the chest disappear and then reappear in another place. Use transformation, shifting or translating upwards 6 units (0, +6) to find where the magic treasure chest will reappear.

2. In the movie, Land Before Time, a Quetzalcoatlus moves so that its left wing has the coordinates (-2, 1), (2, 1), (-2, 12), (2, 12) and (0, 16). Calculate the coordinates of the Quetzalcoatl us' left wing reflection in the lake (across the x­axis).

3. Mark draws furniture that can move around and rearrange themselves. The triangular shaped table is has the coordinates of (1, 0), (2, 1 ), and (-1, 3 ). Mark draws the table walking to another area in the room. What are the new coordinates of the table if Mark used 270° rotation to move the table (rotate at origin)?

29

4. Based on the previous question #1 the magic chest is never in one place very long, Mark wants to move the chest again.

a. After the treasure chest moved upwards 6 units in the first problem, it is then shifted or translated 1 unit right and 7 units down(+ 1, -7). Find its coordinated points.

b. Find where the magic treasure chest will reappear next after it appeared rotated 180° (rotate at origin). What are the new coordinates of the chest?

5. In one of Mark's cartoons, a van moves so that its corners are at (-6, 1), (-3, 1), (-3, 6), (-5, 6) and (-6, 4).

a. Calculate the coordinates of the van's reflection in the window of a near by building (across the y-axis).

b. To show the van's reflection moving in the window, Mark will shift or translate 5 units up (0, 5).

6. The corners of king's throne in the cartoon movie, The King and I, are at (8, 7), (12, 7), (8, 18) and (12, 18).

a. Calculate the coordinates of the king's throne reflection on the shiny golden floor (across the x-axis).

b. Calculate the coordinates of the king's throne ifthe reflection is then shifted or translated 14 units left and 2 units up (-14, 2)?

c. Calculate the coordinates of the king's throne if the translation is rotated about the origin 90°.

(For more information about Mark Fisher refer to the Appendix)

30

Appendix

Deaf Restaurant Owner and Manager - Danny Delcambre http://ww\\.\\ashington.edu/doi t/Nev. s letters/ Dec97 /06.html http://www.tvworldwide.com/globe shO\\ /alpha entrepreneur/danm delcambre/ http://w\\ W.deafbayou.com/content/blogsecti on/ 16/66/ VIDEO

Other Deaf chefs http://www. ntid .rit.edu/media/fu ll text. php?artic le id=38 I http://www.as lsilentchef.com/ http://www.gazette.net/stori es/05062009/chevne\\200033 3252 1.shtml http://netac.rit.edu/goa ls/menu.html?vid=5&clip=mbakerrm VIDEO

Deaf Adventure Guide - Christy Smith http ://W\\\\,.cbs.com/pri metirne/survi vor/bio/christ) 6/bio.php http://en.\\ ikipedia.org/wiki/Christ\ Smith

Deaf Statistician - H. Latham Breunig http://sci.ga llaudet.edu/DS/deafsci F .html http://www. tdi-onl.ine.org/tdi/TD I A wards.asp Lang, H. G., & Meath-Lang, B. (1995). Deaf persons in the arts and sciences,­A biographical dictionary. Westport, Connecticut & London: Greenwood Press.

Deaf Bank President - James Meisser http://IS\\ isc.com/index.html http:/fow\\ .biztimes.com/money/2008/3/ 11/shebo) gan-bank-will-serve-deaf-customers http://w\\\\.4hearingloss.com/archi \es/2007/07/kohler man a ims.html

Deaf Photographer - Michael Pimentel http://wwv.. michaelpimentel.com/biography/ index.html http://dea fnation.com/blog/news/deaf-sports-Rhotographer-has-large-cl ientele

Other Deaf photographers http://w'v\ \\. ri t.edu/ntid/dccs/dada/dada. htm

Deaf Office Administrator - Melody Tsai Stein http://\\ ' ' \\ .c-s-d.org/default.aspx?pageid=295

31

Deaf Baker - Jimmy Libman http://modernbaking.bakery-net.com/artic lc/6533 http://w·ww.deafweekly.com/backissues/020905.htm http://vv\vw.pen.ntid.rit.edu/newdownloads/events/exchanges/2006/summer­institute/schedule english/Jimmy.pdf http://netac. rit.edu/goa ls/menu.htm I ?v icl=2&cl ip= I ibmanrm VIDEO

Deaf Inspector - Kathy Wigley http://www.kansas2 I I .com/success stories/2000 success stories/success story fe b2000 .htm

Other Deaf Inspector http://netac.rit.edu/goals/menu.htm l?vid=S&cl ip= jsilvarm VIDEO

Deaf Climatologist- Bim Wood http ://vV'vV\.Y. nssl. noaa. gov/briefi ngs/vo 14 1102/pagers. html http://www.accessnoaa. noaa .gov/mar0602/ index.html

Deaf Animator - Mark Fisher http://www. rit.edu/ntid/dccs/dada/dada.htm (click Artists, Animation, Mark Fisher) http://www.trudysuggs.com/200 1/08/0 l/fisher-wi ns%e2%80%88grand%e2%80%88 prize-at-festival/

Other Deaf Animators http://www.rit.edu/ntid/dccs/dada/dada.htm (click Artists, Animation)

32

Mathematics Career Interview

I would like you to interview people in various jobs to see the importance mathematics plays in their careers. Please record the answers to the following questions and then to write a well-constructed paragraph on what you learned.

1. Where do you work?

2. What is your job title?

3. Briefly explain your job.

4. Why did you decide to become a/an _____ ?

5. When did you decide to become a/an ____ ?

6. What is your educational background?

7. Who do you work with on your job? Do you work alone or in a team?

33

8. What skills in mathematics are important to your job?

9. Please give examples of when you use these skills on your job.

I 0. On a scale of 1 to I 0 (I being low and I 0 being high), how important is mathematics to your job? Why?

11. Problem solving is a life-skill. When do you problem solve in your job?

12. Why is the study of mathematics important in school?

13. What are your suggestions for me, as a student, to study mathematics?

14. Is there anything else you would like to add?

34

Solutions

Deaf Restaurant Owner and Manager I. $9; $5.50; $3.50

2. $409.25

3. a. about 12-13 of the specials b. $203.88 or $220.87

4. a. about 165 shrimp b. about 495 shrimp

c. about 41 servings of the 10 oz. serving

5. Wages ll 13,356-112,7001 = $656 $656 > $500 0.05($112,700) = $5635

Because the actual expenses differ from the budget by more than $500, there is failure to meet the "budget variance test."

Utilities 1$9' 772 - $9 ,4001 = $3 72 0.05($9,400) = $470

$372 < $500

Because the difference between the actual expenses and the budget is less than $500 and less than 5% of the budgeted amount, there is compliance with the "budget variance test."

Taxes 137,335 - $37,6401 = $305 0.05($37,640) = $1882

$305 < $500

Because the difference between the actual expenses and the budget is less than $500 and less than 5% of the budgeted amount, there is compliance with the "budget variance test."

Insurance 1$2,613 - $2,5751 = $38 < $500 0.05(2,575) = $128.75

Because the difference between the actual expenses and the budget is less than $500 and less than 5% of the budgeted amount, there is compliance with the "budget variance test."

35

6. a. -

Function

v= 125.000 - 1 O.OOOt 140000 t v 120000 1 115000 100000

---.. 2 105000 80000

......___ 3 95000 >- ---60000 4 85000 40000 . 5 75000 20000 6 65000 O·

0 2 4 ti 8

t

b. $95,000 c. Depreciation will increase rapidly

Deaf Adventure Guide 1. Christy could recommend either sleeping bag with the temperature rating of -5° C

or-15°C.

Christy expects the temperature to drop below 32° F. 32° F equal to 0° C. Only sleeping bags with a temperature rating of below freezing or 0° C will keep the hikers warm. The only sleeping bags that will keep the hikers warm below freezing are the sleeping bag with the temperature rating of -5° C and -15° C.

2. Christy should recommend the sleeping bag with the temperature rating of 15° C.

Christy expects the temperature to be no less than 15° C. 15° C is equal to 59° F. The sleeping bag with the temperature rating of 15° C would keep the hikers comfortably warm.

3. C = (5F - 160)/9

4. 23° F, 15° F, 14° F, 0° F, -20° F

-5° C, -9° C, -10° C, -18° C, -29° C

5. The corresponding temperature of 87° Fin Celsius is 30.56° C. The range of the temperature in that day is 3 7.44 °C.

36

1---v l

6.

0 32 15 59 .... -5 23 ·;;

.s::.

-10 14 c: ~

5 41 "' u.

-15 5

-20 -15 -10 -5

Deaf Statistician 1.

a. 30; 113 , .333 (repeating), 33.33%

b. 10; 1/9, .111 (repeating), 11.11 %

2.

70

0

Celsius

a. 105, 7/12, .583 (repeating 3), 58.33%

b. 120, 2/3, .67, 66.67%

3. a. 40.20 miles/hour b. 0.678 seconds

4. a.

C'ourur: M,uu:: Tun Alv111 Cl111s , 'I(,' 22 29 35 40 y 53 74 57 66

1 120

5 10 15 20

Josh Eun MJtcli Du:mne Cli.u les 44 48 53 58 65 76 79 90 76 93 83 99

100 • Josh • Mitch

• Ch.ules

i E 80 ~ x

LU 60 (ij c: 40 -u::

~ 20

0 0 20

1 ~

• Mari e • Chris • Erin

• Alv in

• Conni e • Ti111

37

40

Entrance Exam

• Oio 1111 e

60 80

5.

6.

b. Dionne

c. Yes, it seems that a higher entrance exam implies a higher final exam score, but note that Josh has a low entrance exam score of 48 with a high final exam score of 90. (What about Erin and Chris?)

a. Ytar. Lift

f n11rrta11ry,

.I' 1920 5-11 1930 59 -

90 I 80 ________.

~ 70 ~ 60

,._,.,..-....--

~ 50 I-+- Life expectancy, vi ~ 40 19-10 62 9

1950 68 1 ~ 30 ::; 20

1960 69 - 10 0

i9-o -o 8 1900 1920 1940 1960 1980 2000 2020 1980 -3 -

Year (t) 1990 -5 -l

2000 -- 1

b. The curve seems to be a good fit for the data

c. 2005: 76.8 years; 2010: 77.0 years (Would it be better to use the given equation to solve this problem?)

d. Answers will vary.

a.

Function ---= 0 .41t + 30.9

t _y_ 0 30.9 -

35

1 31.31 2 31.72 3 32.13 4 32.54

I• Senes1 I

5 32.95 ~

G 33.36 7 33 .77

~ 30 z 29 .......-._ ____ .__. ________________ ___

8 34 .18 3 4 5 6 8 9

9 34.59 ts o 1ep1 esents 1990

b. 5 = t -71995

38

Deaf Bank President 1.

2.

3.

Year

2008

I 2009

2010

2013

4.

5.

6.

a. about $1089.81

b. $22, 316.98

c. $10,555.93

d. about $879.66

a. $3250 + .05(S) = W

b. $3515

a. (2009, 1.85)

b. & c.

Earnings In millions of $'s

1.6

1.85

2.1

2.85

3 .. ;.. 2.5

~ "O 2 c: ..., ·- c: 1 5 E o ~ § 1

E §. 0 5

a. 5000r2 + 1 O,OOOr + 5000

Deaf Bank President

Year

b. $5253 .13, $5304.50, $5408, $5512.50

a. about 9%

b. about 4.5%

$16,666.67

39

201 3, 2 85

Deaf Photographer 1. 12 inches long by 18 inches wide

2. The original width is 5 inches

3. a. Perimeter is 96 inches b. Area is 540 in2•

4. Perimeter of the enlarged photograph is 48 inches.

5. The area of the original photograph is 73.5 in2•

6. The area of the enlarged photograph is 47.47 in2•

Deaf Office Administrator I.

a. 2,000 b. 800

2. a. Melody would not be able to purchase 1,000 packets with a budget of

$8,000. She would only be able to purchase about 714 packets.

b. Melody would need a budget of $10,000 in order to purchase the 1,000 packets.

3. $1,304.35

4. a. C = .35x + 120 b. $751.20

5. Melody's dept. has to make more than 42,858 copies to justify buying the copier.

6. Deferral Amount= Salary x % Deferral

Match* s 3% (salary).

Example: Charles receives $1,000 each pay period. He invests $150/month. The company matches $.50 on the dollar up to .03($1000) or $30. $30 (.50) equals $15. The company will add $15/month to Charles' investment.

Total = Deferral amount plus match amount.

40

I Employee I Payroll I % Deferral I Amount I Match* I Total

I Charles r $1,ooo I 15% $150.00 1 $15.00 I $165.00

I Karl I 1,200 1 10% 120.00 I 18.00 I 138.00

I Joycelyn I 2,000 1 3% 60.00 I 30.00 I 90.00

I Maria I 900 I 5% 45.00 I 13.50 I 58.50

I Marcus I 1,500 I 3% 45.00 I 22.50 I 67.50

I Allen I 1,750 1 7% 122.50 I 26.25 I 148.75

I Total check to trust: I $667.75

Deaf Baker

I. No, Jimmy would not have enough vanilla to make a 10 pound cake. Jimmy needs 2 Yz teaspoons of vanilla to make a 10 pound cake.

2. 210hours

3. 6 scoops ( 4 scoops with the% cup and 2 scoops with the Yz cup)

4. Chocolate Chip Cookies (9 dozen) 3 % cups all-purpose flour

5.

1 Yz teaspoons baking soda 1 Yz pinches of salt % cups of light brown sugar, firmly packed 1 Yz cups of granulated sugar 3 eggs 3 teaspoons vanilla extract 1 Yz cups butter or margarine, room temperature 1 Y2 packages (13 ounces or 3 cups) of semisweet chocolate

a. 2x + y::; 25 x + .5 y::; 5

b. y:S-2x+25 y:S-2x+10

41

c&d

t -gar -2x + 10 x v 0 10 1 8 2 6 3 4 4 2 5 0 6 0 7 0 8 0 9 0

Flour IV - -2x + 25

x v 0 25 1 23 2 21 3 19 4 17 5 15 6 13 7 11 8 9 9 7

0 2 6 8

-+-Y

: 10

• y

1 12

10 0 10 5 -2· + 10 _ -2x + 25 11 0 11 3 12 0 12 1

e. No, Jimmy would not be able to make 2 loaves of bread and 7 muffins. Jimmy would only have enough sugar to make 6 muffins when he makes 2 loaves of bread.

6. 20 gallons of the 5% butterfat milk and 40 gallons of 2% butterfat milk

Deaf Inspector I. Yes, the metal panels would pass inspection based on the sample because 3 metal

panels out of a sample of 500 are discolored. 3 out of 500 equals .6% which is less than the allowable .75% discolored.

2. No, the chocolate milk would not pass inspection based on the sample, because 4.5 gallons of a sample of 800 gallons was contaminated. 4.5 gallons out of 800 gallons equals .5625% which exceeds the .5% allowable contaminated chocolate milk.

3. a. The average percentage of mechanical parts that is defective is 1. 76%.

b. No, the inspection with 10 samples did not pass the policy 's requirement, because the average percentage of mechanical parts that is defective equals 1.76% which exceeds the allowable average of I% defective mechanical parts.

4. Kathy checks 32, her partner checks 19. Of these, 6 are common. 32 + 19 - 6 = 45

98 - 45 = 53 radars were not checked by either.

42

14

5. a. ACE, ACG, ACM, ACT, AEG, AEM, AET, AGM, AGT, AMT, CEO, CEM, CET, COM, COT, CMT, EGM, EGT, EMT, GMT Total Count: 20 possible groups

6! 6 • 5 • 4 • 3 • 2 • 1 6. 5 • 4 120 20 b c = = = = - = - = 20

• 6 3

( 6 - 3) ! x 3! 3 • 2 • 1 x 3 • 2 • 1 3 • 2 • 1 60 1

c. Yes

6. The CTE range is calculated by finding the difference between the average or mean of the readings taken on the edge of the wafer with the reading taken in the center.

[ X1 +Xi+ X4 + Xs J

CTE= 4 -X2

I rx;-~~~ Xs !Process A 122000123500121000 l-24_0_0_0_r------2-1_5_00-----I

I Process B 117000 j 19000 i 20000 j 21000 I 19700

[ 22000 + 21000 + 24000 + 21500

CTEA = 4 - 23500 = -1375

[ 17000+20000+21000+ 19700 J

CTEs = 4 - 19000 = 425

Process B is accurate because it has a CTE range less than the critical value of I 000.

_,.' -~ -

'\ x

/ I j;. X. Xj

\ I \ // ' ~ ;:.__

43

Deaf Climatologist I. Mean - 89.2°

Median - 90.5° * Mode-93°

(*Best Method-there is no extreme number that can pull the average (median) or the number is not categorical (mode).)

2. Mean 10.6° Median 12° * Mode 12°

(*Best Method-there is no extreme number that can pull the average (median) or the number is not categorical (mode).)

3. -9

4. 42°' 51°

5. 20::; h::; 80

6. a. about 24° C; about 297 Kelvin

b. about 78.8° F; about 299 Kelvin

c. about 15° C; about 58.7° F

d. K = (5F - 160)/9 + 273

44

Deaf Animator

1.

Deaf Animator ·12

D' E '

After Translation c· F ' 10

A ' ( 1 8) D (-4 11 )

B '. ( ·5 . 8) E '· ( -2 1 1) 8

B' T2 A'

C" (-5. 10) F '. ( · 1 . 10)

" D E

O r iginal c F

"' A : (-1 . 2) D : (-4. 5)

B : (-5. 2) E : ( -2 , 5) 2

B T1

A C : (-5.4) F : (-1 , 4)

· 1 0 ·5

2. D REFLECTION

Original c E

A: (2. 1}

B: (-2. 1) 10

W1 C: (-2, 12)

D: (0. 16) 5

E: (2. 12) 8 A

)(

1 0 8 ' A' 10

After Refle ction

·5 A': fl. -1)

B': (-2. -1) W2

-'10 C': (-2. -12)

c D': (0. -16)

E ': (2 -12)

o·

45

3.

ROTATION 6

4 Original After Rotation

Coordinates A':(0,1) A: (1. 0)

B': (·1, 2) B: ( 2. 1 t B

C': (·3, ·1) C: (·1. 3)

.5 5

C'

·2

46

4.

1"1

A: (-4, 11 t 12

B:(-2, 11t A 8

C:(-1.10t Original F c 10 D: (-1, St

T1 E: (-5. St

E 8 F: (·5, 1 Ot

6 A': (-3. 4t B ' : (-1. 4)

A' 8 ' C' : (0. 3) Translation 4 •

F' c· D': (0. 1)

T2 2 E': (-4. 11 F': (-4. 3)

E'

·10 .5 D' E" 5

A": p, -4) D": {O. -1) Rotation ·2

B": {1. -41 E": (4. -1 t T3 C": (0. -3) F": (4. -3t C" F"

.4 8" A"

5.

E" A": (3.6)

A: (·3. 1) 10 B": (6. 6)

Original B: (-6. 1)

C" C": (6, 9) Translation

C: (·6. 4) D": (5.11) D : (· 5, 6) e E": (3, 11) E: (-3. 6) VJ

E D' 9"

V1

c 4 c· A': (3. 1)

B ': (6. 1) Reflection C': f6. 4)

V2 D': j5. 6)

E': p . 6}

9 A A' 9 '

.5 10

47

6. 20

Coordinates after 8 c Original

Rotation Coordinates 15

A"': (-3. 6) A: (8. n B"': (-14. 6) B: (8. 18) C"': (·14. 2) 10 C: (12.181 D'": (·3. 2) 0:(12.n

B'" ...

D 0 ft."' A D

5

C"' O "O oo•

·20 ·10 10 20

P.." D"

.5 .A.' D'

Coordinates after Coordinates after Translation Reflection

·10 A': (8, ·7) A": (·6. -3)

B": ( -6. -14) B': (8, -18)

C": (-2. -14) B" C" -'15 C': (12, -18)

D": (-2. -3) D': (12, -7) 8 ' c·

·20

48