Basic Math Questions and Answers

Determine the coefficients p and q and exponents m and n when the following expression is simplified 2x y 3xy5 3 px qyn

Simplify the following expression and choose the correct answer 4x 4 y 2 x 4y I 4 O 4

A rectangular garden has an area of 310 m and its length is 25 m longer than the width What are the width and length of the garden and how much fencing would be required to enclose the garden Width mE Round to two decimal places Length m

Simplify the expression and answer the following What is the resulting coefficient of b b What is the resulting coefficient of a b 6a a b 116 5a b 4a 36 10a

Factor fully 4x 12 o x 4 x 3 o x 9 x 5 x 6 x 2 1 x 6 x 2

Alice and Luisa run on circular track every morning The time difference between when they finish one lap is t 2 r V1 2 r V2 where v and v are their speeds Factored the right side of this equation gives

Given the fraction x 5x6 x 6x which of the following represents the fraction reduced to its lowest terms

DACK L USE YOUR MATH SKILLS TO FIND THE VALUE OF EACH ICON AND THE 36 X 4 28

2 Individual and market demand Suppose that Alex and Becky are the only consumers of ice cream cones in a particular market The following table shows their monthly demand schedules PRICE Dollars per cone Price Dollars per cone 4 SEN 3 4 Alex s Quantity Demanded Cones 8 53 HO 0 Becky s Quantity Demanded Cones 14 10 6 3 On the following graph plot Alex s demand for ice cream cones using the green points triangle symbol Next plot Becky s demand for ice cream cones using the purple points diamond symbol Finally plot the market demand for ice cream cones using the blue points circle symbol 1 Alex s Demand Becky s Demand Market Demand

3 The following truss system is planned to be designed The material of the structure is assumed to be st 52 L 2m 5t 10 t 2m 20 t 11 2 m 10 t 11 5t a Design the marked elements with section of double angle 5 Draw the selected section 2m 4 1m 1 m

Solve the system using either Gaussian elimination with back substitution or Gauss Jordan elimination If there is no solution enter NO SOLUTION If there are an infinite number of solutions set x3 t and solve for x and X X1 3x3 1 3X X 2x3 7 2x1 2x2 x3 4 X1 X2 X3 13 4 3 2 4 12 X

Identify the elementary row operation s being performed to obtain the new row equivalent matrix Select all that app New Row Equivalent Matrix 1 2 1 2 Original Matrix 1 2 1 2 2 4 1 5 5 5 4 7 Multiply Row 2 by two Add 5 times Row 1 to Row 2 Add 2 times Row to Row 2 Add 5 times Row 1 to Row 3 Multiply Row 2 by five 0 83 9 0 51 3

nd the reduced row echelon matrix that is row equivalent to the given matrix 15 45 1 5

Identify the elementary row operation s being performed to obtain the new row equivalent matrix Select all that app New Row Equivalent Matrix 1 2 1 2 0 8 3 9 0 5 1 3 Original Matrix 1 2 1 2 2 4 1 5 5 5 4 7 O Multiply Row 2 by two Add 5 times Row 1 to Row 2 Add 2 times Row 1 to Row 2 Add 5 times Row 1 to Row 3 Multiply Row 2 by five W

Use back substitution to solve the system Enter your answers as a comma separated list If there is no solution enter NO SOLUTION If the system has an infinite number of solutions set z t and solve for x and y in terms of t X x y z y 3y Z 0 Z 2 0

Which of the following is not a major approach used to deal with breakdowns Multiple Choice O O O O spare parts cost of repairs repair technicians operators backup equipment

Required 1 What amount of total liabilities does Apple report for each of the fiscal years ended a September 28 2019 and b Septe 29 2018 2 What amount of total assets does it report for each of the fiscal years ended a September 28 2019 and b September 2 2018 3 Compute its debt ratio for each of the fiscal years ended a September 28 2019 and b September 29 2018 4 In which fiscal year did it employ more financial leverage September 28 2019 or September 29 2018 Complete this question by entering your answers in the tabs below Required 1 Required 2 Required 3 What amount of total assets does it report for each of the fiscal years ended a September 28 2019 and b September 29 2018 Note Enter your answers in millions of dollars a September 28 2019 Total Assets Required 4

Assign trucks to delivery routes so that total costs are minimized given the cost data shown What is the total cost Leave no cells blank be certain to enter 0 wherever required Truck 1 2 3 4 5 A 4 6 7 5 6 ROUTE B C 5 9 4 8 10 3 2 5 5 3 Click here for the Excel Data File D 8 3 4 5 4 E 7 5 6 8 9

The following information applies to the questions displayed below Gabi Gram started The Gram Company a new business that began operations on May 1 The Gram Company completed the following transactions during its first month of operations May 20 May 22 May 25 May 26 May 27 May 28 May 30 May 30 May 31 May 1 Gabi Gram invested 40 000 cash in the company May 1 The company rented a furnished office and paid 2 200 cash for May s rent May 3 The company purchased 1 890 of equipment on credit May 5 The company paid 750 cash for this month s cleaning services May 8 The company provided consulting services for a client and immediately collected 5 400 cash May 12 The company provided 2 500 of consulting services for a client on credit May 15 The company paid 750 cash for an assistant s salary for the first half of this month May 20 The company received 2 500 cash payment for the services provided on May 12 May 22 The company provided 3 200 of consulting services on credit May 25 The company received 3 200 cash payment for the services provided on May 22 May 26 The company paid 1 890 cash for the equipment purchased on May 3 May 27 The company purchased 80 of equipment on credit May 28 The company paid 750 cash for an assistant s salary for the second half of this month May 1 May 1 May 3 May 5 May 8 May 12 May 15 May 30 The company paid 300 cash for this month s telephone bill May 30 The company paid 280 cash for this month s utilities May 31 Gabi Gram withdrew 1 400 cash from the company for personal use Required 1 Enter the amount of each transaction on individual items of the accounting equation Note Enter the transactions in the given order Enter reductions to account balances with a minus sign Select NA for account titles if the transaction does not include an expense Date Cash 0 Assets Accounts Receivable Equipment 0 1 11 In 0 Liabilities Accounts Payable Gabi Gram Capital 0 IIIIIII TE 1 1 TI Equity Gabi Gram Withdrawals 0 Revenues ITHIIHIILIHULIHI Expenses Account Titles for Expenses NA Rent Salary Telephone Utilities

2 Use the expanded accounting equation to compute the missing financial statement amounts Complete this question by entering your answers in the tabs below Required 1 Required 2 Use the accounting equation to compute the missing financial statement amounts Company Assets 1 2 3 75 000 CA 11 Liabilities 25 000 85 000 SA Equity 40 000 70 000 20 000 4

listed upgrade tiffes Minutes are being evaluated Samples of five observations each have been taken and the results are as 2 4 3 79 6 78 9 79 4 1 79 2 80 5 78 8 78 7 79 6 80 0 81 0 80 4 78 4 80 4 80 3 79 4 1 0 80 1 80 8 80 6 79 7 Number of Observations in Subgroup n 5 6 7 9 10 11 12 13 14 15 Click here for the Excel Data File Factors for three sigma control limits for and R charts SAMPLE 16 17 18 20 Factor for X Chart A2 1 88 1 02 0 73 0 58 0 48 0 42 0 37 0 34 0 31 0 29 0 27 0 25 0 24 5 80 5 79 6 6 79 7 80 6 80 4 80 5 80 8 80 0 78 8 81 1 0 22 0 21 0 20 0 19 0 19 0 18 FACTORS FOR R CHARTS Lower Control Limit D3 0 0 0 0 0 0 08 0 14 0 18 0 22 0 26 0 28 0 31 0 33 0 35 0 36 0 38 0 39 0 40 0 41 Upper Control Limit 04 3 27 2 57 2 28 2 11 2 00 1 92 1 86 1 82 1 78 1 74 1 72 1 69 1 67 1 65 1 64 1 62 1 61 1 60 1 59

Jane got a prepaid debit card with 25 on it For her first purchase with the card she bought some bulk ribbon at a craft store The price of the ribbon was 17 cents per yard If after that purchase there was 22 45 left on the card how many yards of ribbon did Jane buy yards V 6

The process specifications are 13 25 and 14 25 minutes Based on the data given does it appear that specifications are being met Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 13 3 13 5 13 6 13 8 13 4 13 3 13 3 14 3 13 8 14 4 13 9 13 6 13 4 Totals 53 9 Yes O No 13 4 54 6 13 5 54 1 13 3 55 0 13 4 13 3 14 0 13 5 54 3

The lower and upper specifications for a software upgrade are 77 minutes and 81 minutes Estimate the percentage of process output that can be expected to fall within the specifications Round your answer to 1 decimal place SAMPLE 3 4 1 2 5 6 79 7 79 2 81 9 79 6 78 9 82 1 82 6 78 7 79 6 80 2 79 6 80 6 80 0 81 0 79 8 79 7 80 4 78 5 78 4 80 4 80 3 79 4 79 7 80 0 81 0 80 1 80 8 80 6 78 8 81 1 stout OF

Each of the processes listed is non centered with respect to the specifications for that process Standard Deviation Lower Upper Spec 0 32 16 0 1 00 36 5 0 40 20 1 Process H K T Mean 15 0 33 0 18 5 Click here for the Excel Data File Process H Compute the appropriate capability index for each and decide if the process is capable Round your answers to 2 decimal places Spec 14 1 30 0 16 5 Cpk Capable

A process that produces computer chips has a mean of 04 defective chips and a standard deviation of 003 chips The allowable variation is from 038 to 042 defective a Compute the capability index Cp for the process Round your intermediate calculations to 3 decimal places and final answer to 2 decimal places Capability index b Is the process capable Hint Use 1 33 as the standard capabality index O No YOE

An electrical contractor s records during the last five weeks indicate the number of job requests Week 1 2 3 4 5 Requests 28 24 22 23 30 Click here for the Excel Data File Predict the number of requests for week 6 using each of these methods a Naive Number of requests b A four period moving average Round your answer to 2 decimal places Number of requests c Exponential smoothing with a 0 25 Use 27 for week 2 forecast Round your intermediate forecast values and final answers

C 3 2 B 3 2 10 An altitude of a triangle is a segment drawn from a vertex so that it is perpendicular to the non adjacent side of the triangle Based on the triangle above write the equation of the altitude from A to BC 4 points 11 A midsegment of a triangle is a segment that joins the midpoints of two sides of a triangle 4 points Based on the triangle above write the equation of the midsegment from AB to AC

b Apply for a home equity loan 1 Service rep forwards application to loan committee III Service rep asks for necessary documents and checks to see if customer qualifies II Loan committee meetings are scheduled Customer actions line of information Contact person s line of visibility Backstage contacts ne of internal interaction Alive and The IV Greets service rep and Service rep greets customer and leads to cubicle Loan committee evaluates application and makes a decision to approve or not approve loan Tislis service rep typa of loan wanted III Service rep fils out necessary paperwork Forms are ordered Customer sighs for Service rep indicates approval date 1 IV Loan rates are Customer is i of decisi

Construct a list of steps for making a cash withdrawal from an automated teller machine ATM Assume that the process begins at t TM with your bank card in hand Assume that the ATM asks for PIN number after selecting the transaction option 1 Touch screen to begin 2 3 4 5 Insert card magnetic strip should be facing down Enter information PIN amount of transaction etc Insert card magnetic strip should be facing down Lift the Withdrawal Door being careful to remove all cash Select transaction option Withdrawal

1 2 3 4 5 of payment a Self service comprises the following order of steps gas Customer selects station 1 2 3 4 5 into your car for full service and for seir service Assume that paying cash is the only means Customer pumps desired amount of gas and performs other services Customer selects station Pay cashier for gas and other products inside station Return to auto and drive off Select octane level b Full service comprises the following order of steps Attendant pumps desired amount of gas and performs other services Customer selects station Drive off Pay attendant for gas and other services

Which technique for gathering data observational study or experiment do you think was used in the following studies a The Colorado Division of Wildlife netted and released 774 fish at Quincy Reservoir There were 219 perch 315 blue gill 83 pike and 157 rainbow trout This is an experiment because observations and measurements of individuals are conducted in a way that doesn t change the response or the variable being measured This is an experiment because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured This is an observational study because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured This is an observational study because observations and measurements of individuals are conducted in a way that doesn t change the response or the variable being measured b The Colorado Division of Wildlife caught 41 bighorn sheep on Mt Evans and gave each one an injection to prevent heartworm A year later 38 of these sheep did not have heartworm while the other three did This is an experiment because observations and measurements of individuals are conducted in a way that doesn t change the response or the variable being measured This is an observational study because observations and measurements of individuals are conducted in a way that doesn t change the response or the variable being measured This is an observational study because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured This is an experiment because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured c The Colorado Division of Wildlife imposed special fishing regulations on the Deckers section of the South Platte River All trout under 15 inches had to be released A study of trout before and after the regulation went into effect showed that the average length of a trout increased by 4 2 inches after the new regulation This is an experiment because observations and measurements of individuals are conducted in a way that doesn t change the response or the variable being measured This is an observational study because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured This is an observational study because observations and measurements of individuals are conducted in a way that doesn t change the response or the variable being measured This is an experiment because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured d An ecology class used binoculars to watch 23 turtles at Lowell Ponds It was found that 18 were box turtles and 5 were snapping turtles This is an experiment because observations and measurements of individuals are conducted in a way that doesn t change the response or the variable being measured This is an observational study because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured This is an observational study because observations and measurements of individuals are conducted in a way that doesn t change the response or the variable being measured This is an experiment because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured

Which technique for gathering data observational study or experiment do you think was used in the following studies a The Colorado Division of Wildlife netted and released 774 fish at Quincy Reservoir There were 219 perch 315 blue gill 83 pike and 157 rainbow trout This is an experiment because observations and measurements of individuals are conducted in a way that doesn t change the response or the variable being measured This is an observational study because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured This is an observational study because observations and measurements of individuals are conducted in a way that doesn t change the response or the variable being measured This is an experiment because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured b The Colorado Division of Wildlife caught 41 bighorn sheep on Mt Evans and gave each one an injection to prevent heartworm A year later 38 of these sheep did not have heartworm while the other three did This is an experiment because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured This is an observational study because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured This is an experiment because observations and measurements of individuals are conducted in a way that doesn t change the response or the variable being measured This is an observational study because observations and measurements of individuals are conducted in a way that doesn t change the response or the variable being measured c The Colorado Division of Wildlife imposed special fishing regulations on the Deckers section of the South Platte River All trout under 15 inches had to be released A study of trout before and after the regulation went into effect showed that the average length of a trout increased by 4 2 inches after the new regulation This is an experiment because observations and measurements of individuals are conducted in a way that doesn t change the response or the variable being measured This is an observational study because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured This is an observational study because observations and measurements of individuals are conducted in a way that doesn t change the response or the variable being measured This is an experiment because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured d An ecology class used binoculars to watch 23 turtles at Lowell Ponds It was found that 18 were box turtles and 5 were snapping turtles O This is an observational study because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured This is an observational study because observations and measurements of individuals are conducted in a way that doesn t change the response or the variable being measured This is an experiment because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured This is an experiment because observations and measurements of individuals are conducted in a way that doesn t change the response or the variable being measured

The ogives shown are based on data collected on the U S and show the average annual personal income per capita for each of the 50 states The data are rounded to the nearest thousand dollars i Ogive Cumulative frequency 55 50 Percent of states 45 40 35 30 25 20 15 10 5 0 0 27 5 100 80 60 40 20 OE Personal Income per Capita by State 0 ii Ogive Showing Cumulative Percentage of Data Personal Income per Capita by State 96 17 27 5 32 5 36 37 5 Per capita Income 1 000 34 43 42 5 72 48 47 5 86 32 5 37 5 42 5 47 5 Per capita Income 1 000 50 52 5 100 52 5 a How were the percentages shown in graph ii computed O The percentages in graph ii were computed by dividing each of the cumulative frequencies in graph i by 100 and then converting those values into decimals The percentages in graph ii were computed by dividing each of the cumulative frequencies in graph i by 50 and then converting those values into percents O The percentages in graph ii were computed by multiplying each of the cumulative frequencies in graph i by 100 and then converting those values into decimals The percentages in graph ii were computed by multiplying each of the cumulative frequencies in graph i by 50 and then converting those values into percents O The percentages in graph ii were computed by dividing each of the cumulative frequencies in graph i by 50 and then converting those values into fractions b How many states have average per capita income less than 37 5 thousand dollars c How many states have average per capita income between 42 5 and 52 5 thousand dollars

e Categorize the basic distribution shape mound shaped symmetrical bimodal skewed left uniform skewed right

stem and leaf diagram shown below The study uses tree rings to accurately determine the year in which a tree was cut The figure gives the tree ring cutting dates for samples of timbers found in the architectural units at Sand Canyon Pueblo The text referring to the figure says The three digit numbers in the left column represent centuries and decades A D The numbers to the right represent individual years with each number derived from an individual sample Thus 124 2 2 2 represents three samples dated to A D 1242 Use the table below and the verbal description to answer the following questions leaf stem 119 56 120 120 121 2 121 55 122 122 589 123 012 334 123 5555555555555556889 124 12 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 344 124 5689999999999 125 0 0 1 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 125 000 0000000000001111111222 1190s 1200s O 1210s 1220s 1230s 1240s 1250s 1260s 1270s 0011112234444444 126 00012222222222222 4444444 126 555 667 127 0111144 a Which decade contained the most samples V b How many samples had a tree ring cutting date between 1200 A D and 1239 A D inclusive X samples c Find the longest interval during which no tree cutting samples occurred What is the first year that no tree cutting samples occurred in that interval X A D What is the final year that no tree cutting samples occurred in that interval A D d What might this indicate about new construction or renovation of the pueblo structures during this period O There was more renovations during those years than new construction There was no need for new construction or renovation of the pueblo structures There was more new construction during those years than renovations

Convert a speed of 105 mi h to units of feet per minute Also show the unit analysis by dragging components into the mit factor slots 105 mi 1h 60 h 1 min X 3 ft Answer Bank 60 s 12 in x f 1 5280 ft 1 ft 1h 11 ft mir

With the age of cellphones adults have relied on the use of text messages as a fast and efficient way to communicate This has le many researchers to believe that more adults spend their time sending text messages rather than talking on their phone A sample of 22 random adults was surveyed on the number of text messages they believe they send a day This gave the following counts 124 95 77 64 84 96 54 147 92 85 113 36 100 99 83 75 69 53 94 103 47 134 a Make a stem and leaf display for this data Enter numbers from smallest to largest separated by spaces Enter NONE for stems with no values stem 3 4 5 6 7 8 9 10 11 12 13 14 6 7 34 49 03 3 4 7 leaf X X X

Round each number to two significant figures 233 356 230

Arrange the values according to magnitude Greatest Least

A work sampling study is to be conducted on rush hour traffic 4 00 p m to 6 59 p m five days per week The study will encompass 40 days Determine the day hour and minute for 10 observations using the following procedure and table 1 2 1 6912 7264 2 3491 1192 3 4715 2486 3264 1918 4 5 8510 4237 2044 3957 1632 1546 1950 1844 7209 0938 2376 6 3950 1328 7343 6083 7 7871 7752 0521 8511 8 2716 9 2935 10 8533 11 8818 9912 3761 4028 9207 9585 1039 2159 2438 2768 4666 9530 3352 2951 0131 4359 3095 4421 3018 1396 7354 0249 8259 9957 0538 1640 12 3 4 2811 8921 0575 7547 2093 2776 2664 3856 1123 0120 2128 3956 7728 Observation 1 a Read two digit numbers going down the first two digits of column 1 e g 69 34 47 and then down the second two digits of that column e g 12 9115 for days b For hours read one digit numbers going from left to right across row 3 and then across row 4 Read only 4s 5s and 6s c For minutes read two digit numbers going down column 1 first using the last two digits e g 12 91 15 and after exhausting those numbers repeat using the first two digits of that column e g 69 34 47 16 2 3 4 Arrange your times chronologically by day then hour and then minute Enter hours as a single digit 4 5 or 6 without a leading zero Day 5 4627 Time 6 8387 4617 16 33 38 15

recent publication The data by state are shown in the table Average Length of Stay stem 5 7 8 9 State Alabama 456 Alaska 37 Arizona Arkansas California Colorado Connecticut Delaware D C Florida Georgia Hawaii Idaho Illinois Indiana 6 11356677889999 Iowa Kansas No of Hospitals leaf 0111111222223334445579 120 15 60 87 441 72 34 9 12 226 163 20 42 210 114 122 7 1 X 5 8 7 1 6 1 5 4 Maine 7 4 State 7 1 Kentucky 6 9 Michigan 7 1 Louisiana 7 5 Minnesota 6 7 Mississippi 7 2 Maryland Massachusetts 7 9 Missouri Montana 9 3 Nevada Nebraska New Hampshire 7 2 New Jersey 6 5 New Mexico 8 5 New York N Carolina No of Hospitals 106 135 39 50 102 176 147 101 132 54 91 22 26 95 36 232 118 Average Length of Stay 6 8 6 6 7 3 7 2 8 6 6 9 Oregon 7 3 6 9 Pennsylvania 7 3 State N Dakota 6 3 Ohio 7 1 Oklahoma 5 4 Rhode Island S Carolina 10 1 Texas S Dakota 9 7 Utah Tennessee Vermont Virginia 7 5 Washington W Virginia 10 0 Wisconsin No of Hospitals 48 194 114 65 237 13 69 51 121 420 43 16 97 91 60 128 26 Average Length of Stay 11 0 6 7 6 6 5 4 7 4 6 8 7 0 132 7 2 Wyoming Make a stem and leaf display of the data for the average length of stay in days Enter numbers from smallest to largest separated by spaces Enter NONE for stems with no values 10 2 6 9 6 1 5 3 7 7 7 1 5 7 7 2 7 4 8 4

Recently people have a tendency to check a movie s review online before deciding whether watching the movie is worth the time and money One of the most prominent web sites for movie reviews is Rotten Tomatoes which is well known for scoring movies by collecting information from several film critics A sample of 18 random movies from 2020 gave the following ratings on the web site a Make a stem and leaf display for these data Enter numbers from smallest to largest separated by spaces Enter NONE for stems with no values stem 2 3 4 5 6 7 00 8 66 94 92 97 61 54 79 70 59 59 71 70 76 73 89 81 42 29 9 leaf b What shape does the distribution appear to take on O uniform skewed left skewed right mound shaped symmetric

How long did real cowboys live One answer may be found in the book The Last Cowboys by Connie Brooks University of New Mexico Press This delightful book presents a thoughtful sociological study of cowboys in West Texas and Southeastern New Mexico around the year 1890 A sample of 32 cowboys gave the following years of longevity stem 4 a Make a stem and leaf display for these data Enter numbers from smallest to largest separated by spaces Enter NONE for stems with no values 5 6 7 8 72 60 69 74 71 72 86 83 89 58 76 9 77 85 94 57 leaf 46 b Consider the following quote from Baron von Richthofen in his Cattle Raising on the Plains of North America Cowboys are to be found among the sons of the best families The truth is probably that most were not a drunken gambling lot quick to draw and fire their pistols Does the data distribution of longevity lend credence to this quote No these cowboys did not live long lives as evidenced by the high frequency of leaves for stems 4 and 5 i e 40 year old and 50 year old Sort of these cowboys lived somewhat long lives as evidenced by the high frequency of leaves for stems 5 and 6 1 e 50 year old and 60 year old Yes these cowboys certainly lived long lives as evidenced by the high frequency of leaves for stems 7 8 and 9 i e

With the age of cellphones adults have relied on the use of text messages as a fast and efficient way to communicate This has le many researchers to believe that more adults spend their time sending text messages rather than talking on their phone A sampl of 22 random adults was surveyed on the number of text messages they believe they send a day This gave the following counts 124 95 77 64 84 96 54 147 92 85 113 36 100 99 83 75 69 53 94 103 47 134 a Make a stem and leaf display for this data Enter numbers from smallest to largest separated by spaces Enter NONE for stems with no values stem 3 4 5 6 7 8 00 9 10 11 12 13 14 leaf b Comment about the general shape of the distribution skewed right uniform O fairly symmetric

Wetlands offer a diversity of benefits They provide a habitat for wildlife spawning grounds for U S commercial fish and renewable timber resources In the last 200 years the United States has lost more than half its wetlands Environmental Almanac gives the percentage of wetlands lost in each state in the last 200 years For 30 of the lower 48 states the percentage loss of wetlands per state is as follows 26 49 54 50 38 46 46 72 67 56 24 81 50 39 35 35 50 35 91 48 56 86 52 36 Make a stem and leaf display of these data How are the percentages distributed Is the distribution skewed Are there any gaps Step 1 We are given the following data set and we are to make a stem and leaf display of this data 60 89 46 31 28 26 49 54 50 38 46 46 72 67 56 24 81 50 39 35 35 36 8 60 89 46 31 28 50 35 91 48 56 86 52 Recall that a stem and leaf display is a method of exploratory data analysis that is used to rank order and arrange data into groups The digits of each data value will be divided into two parts The leftmost part is called the stem and the rightmost part is called the leaf The largest number in this data set is a two digit number so we need to first write all the numbers in the data set as two digit numbers by adding leading zeros as needed 26 49 54 50 38 46 46 72 67 56 24 81 50 39 35 35 50 35 91 48 56 86 52 36 08 60 89 46 31 28 49 50 50 50 52 54 56 56 Since all the numbers for the data are now two digit numbers the stem will be the number in the tens place and the leaf will be the number in the ones 0 place Now organize the numbers in the data set from smallest to largest value 08 24 26 28 31 35 35 36 38 39 46 46 60 67 72 81 46 48 89 91

Suppose a research firm included data by state on the number of community hospitals and the average patient stay in days in a recent publication The data by state are shown in the table stem 5 6 7 8 9 10 State 11 Alabama Alaska Arizona Arkansas California Colorado Connecticut Delaware D C Florida Georgia Hawaii Idaho Illinois Indiana Iowa Kansas No of Hospitals leaf 120 15 60 87 441 72 34 9 12 226 163 20 42 210 114 122 132 Average Length of Stay 7 1 X 5 4 5 8 Louisiana 7 1 7 5 6 7 6 1 Massachusetts 7 4 6 9 Michigan 7 1 7 1 State Kentucky 7 2 7 2 Maine Maryland Minnesota Comment about the general shape of the distribution The dint Mississippi Missouri 9 3 Nevada Montanal Nebraska New Hampshire New Jersey 6 5 New Mexico 8 5 New York 7 9 N Carolina No of Hospitals 106 135 39 50 102 176 147 101 132 54 91 22 26 95 36 232 118 Average Length of Stay 6 8 N Dakota 6 6 Ohio 7 3 6 9 6 9 7 2 8 6 7 3 9 7 6 3 State 7 1 7 5 5 4 Oklahoma 7 3 Tennessee 10 0 Oregon 10 1 Texas Pennsylvania Rhode Island S Carolina S Dakota Utah Vermont Virginia Washington W Virginia Wisconsin 7 2 Wyoming No of Hospitals 48 194 114 65 237 13 69 51 121 420 43 16 97 91 60 N 128 26 Average Length of Stay 11 0 6 7 6 6 5 4 7 4 6 8 7 0 Make a stem and leaf display of the data for the average length of stay in days Enter numbers from smallest to largest separated by spaces Enter NONE for stems with no values 10 2 6 9 6 1 5 3 7 7 7 1 5 7 7 2 7 4 8 4

Recall that an ogive is a graph that displays cumulative frequencies where the cumulative frequency for a class is the sum of the frequencies for that class and all the previous classes We will use the class boundaries and the corresponding cumulative frequencies to create an ogive Class Limits Class Boundaries Cumulative Frequency 28 38 39 49 50 60 61 71 72 82 27 5 38 5 38 5 49 5 49 5 60 5 60 5 71 5 71 5 82 5 For the ogive we use the cumulative frequency on the vertical 5 30 47 49 50 axis There are five classes in the table so

We will now determine the midpoint of each class Recall that the midpoint is the average of each class Find the average by dividing the sum of the class boundaries by 2 Complete the table Class Boundaries 27 5 38 5 38 5 49 5 49 5 60 5 60 5 71 5 71 582 5 28 38 39 49 Complete the table 50 60 45 61 71 27 5 38 5 2 38 5 49 5 2 55 66 51 51 51 77 Step 6 Now determine the frequencies The class frequency is the total number of data values in that class Recall that each data value should fall into exactly one class Now examine the data set and determine how many data values fall into each class Note that with such a large number of values you may find it helpful to order the data first Midpoint Class Limits Class Boundaries 44 28 33 33 35 38 39 40 40 27 5 38 5 33 46 46 47 47 47 47 38 5 49 5 55 49 5 60 5 66 60 5 71 5 77 52 52 53 54 44 47 55 Frequency x x 41 41 41 42 43 43 44 44 45 48 49 50 51 51 51 57 60 65 69 47 48 48 55 55 56 81

Calculate the length of the line segment defined by each pair of endpoin a A 6 2 and B 4 3 b J 2 1 8 3 and K 4 5 4 7