Basic Math Questions and Answers

2 Express 1 414 1 414414414 as the ratio of two integers

21 Find x 7 45 201 60

Consider a cost function of the form Calculate MC 1 000 20 000 980x x for 0 x 1 000 for x 1 000 In an attempt to calculate the marginal cost at x 1 000 economists have devised the formula MC 1 000 lim C x lim C x 2 x 1 000 x 1 000 Provide your answer below C x 0

What was the overall increase in prices due to inflation as a percentage from 1995 to 2005 Assume that all prices have risen at the same rate as the CPI The inflation rate was about Round to one decimal place as needed Year 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 CPI 90 9 96 5 99 6 103 9 107 6 109 6 113 6 118 3 124 0 130 7 136 2 140 3 144 5 148 2 Average Annual Consumer Price Index CPI 1982 1984 100 Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 CPI 152 4 156 9 160 5 163 0 166 6 172 2 177 1 179 9 184 0 188 9 195 3 201 6 207 3 215 3 Year 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 CPI 214 5 218 224 229 233 236 237 240 245 251 255 258

Suppose a particular car cost 2300 in 1995 What was the price in 2010 dollars Assume that all prices have risen at the same rate as the CPL In 2010 dollars the price is Round to the nearest dollar as needed GIZA extre Year 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 CPI 90 9 96 5 99 6 103 9 107 6 109 6 113 6 118 3 124 0 130 7 136 2 140 3 144 5 148 2 Average Annual Consumer Price Index CPI 1982 1984 100 CPI Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 152 4 156 9 160 5 163 0 166 6 172 2 177 1 179 9 184 0 188 9 195 3 201 6 207 3 215 3 Year 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 UNNNN22222222 C 21 21 23 23 23 24 24 25 25 25

K Karla Tanner opens a web consulting business called Linkworks and completes the following transactions in its first month of operations Prepare journal entries for each transaction and identify the financial statement impact of each entry The financial statements are automatically generated based on the journal entries recorded April 1 Tanner invested 80 000 cash along with office equipment valued at 26 000 in the company in exchange for common stock April 2 The company prepaid 9 000 cash for 12 months rent for office space The company s policy is to record prepaid expenses in balance sheet accounts April 3 The company made credit purchases for 8 000 in office equipment and 3 600 in office supplies Payment is due within 10 days April 6 The company completed services for a client and immediately received 4 000 cash April 9 The company completed a 6 000 project for a client who must pay within 30 days April 13 The company paid 11 600 cash to settle the account payable created on April 3 April 19 The company paid 2 400 cash for the premium on a 12 month prepaid insurance policy The company s policy is to record prepaid expenses in balance sheet accounts April 22 The company received 4 400 cash as partial payment for the work completed on April 9 April 25 The company completed work for another client for 2 890 on credit April 28 The company paid 5 500 cash in dividends April 29 The company purchased 600 of additional office supplies on credit April 30 The company paid 435 cash for this month s utility bill Requirement General Journal General Ledger Trial Balance Income Statement St Retained Earnings Balance Sheet FS Impact Every journal entry must keep the accounting equation in balance Prepare the journal entries for each of the transactions of the Linkworks Company entering the debits before the credits Each transaction will automatically be posted to the General Ledger and the Trial Balance as soon as you click Record Entry Che

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Answer the following questions using the information given The length of a small ant is 3 10 meter and the length of a large ant is 3 5 10 2 meter a Find the difference in length in millimeters of the two ants Write your answer in scientific notation millimeters b If there is a trail of 2 small ants and 1 large ant in a straight line find the total length of the line Write your answer in scientific no meters

Writing Equations from Ratios each problem Ex Every quart is 2 pints Write an equation to express the total number of pints 2 in y quarts Name 1 Every pint is 2 cups Write an equation to express the total number of cups Z in y pints 2 For each kilogram there are 1 000 grams Write an equation to express the total number of grams Z in y kilograms 3 Every quarter is 25 pennies Write an equation to express the total number of pennies Z in y quarters 4 Every dollar is 4 quarters Write an equation to express the total number of quarters Z in y dollars 5 Every meter is 100 centimeters Write an equation to express the total number of centimeters Z in y meters 6 Every centimeter is 10 millimeters Write an equation to express the total number of millimeters Z in y centimeters 7 Every liter is 1 000 milliliters Write an equation to express the total number of milliliters Z in y liters 1 2 3 4 8 Every cup is 8 ounces Write an equation to express the total number of ounces Z in y cups 9 Every gallon is 4 quarts Write an equation to express the total number of quarts Z in y gallons 5 10 Every dollar is 10 dimes Write an equation to express the total number of dimes Z in y dollars 11 Every yard is 3 feet Write an equation to express the total number of feet Z in y yards 6 12 For each pound there are 16 ounces Write an equation to express the total number o ounces Z in y pounds mation to express the total number of

Custom Creations Furniture Company manufactures furniture at its Akron Ohio factory Some of its costs from the past year include Depreciation on sales office 9 100 Depreciation on factory equipment 16 700 Factory supervisor salary 50 100 Sales commissions 23 300 3 900 21 700 115 500 10 800 Lubricants used in factory equipment Insurance costs for factory Wages paid to maintenance workers Fabric used to upholster furniture Freight in on raw materials Costs of delivery to customers Wages paid to assembly line workers Lumber used to build product Utilities in factory Utilities in sales office Product costs for Custom Creations Furniture Company totaled A 474 100 B 374 000 OC 448 900 D 490 300 3 500 9 600 115 300 82 300 54 300 26 800

Bert s Bottles provided the following expense information for July Assembly line workers wages Depreciation on factory equipment Caps for bottles Plastic bottles Reconfiguring the assembly line Salaries of salespeople Customer support hotline Salaries of research scientists Delivery expenses Customer toll free order line OA 61 300 O B 12 700 OC 21 200 OD 76 400 56 000 35 400 3 000 52 300 123 100 63 700 12 700 65 500 40 100 8 500

Directions Using the map of Washington D C determine the coordinates for Each set of coordinates is worth 2 points otra 1 A 2 B 3 C dyow ega12 77 10 4 D B 5 E MARYLAND VIRGINIA Washington National Airport A 08 WEST LONGITUDE WASHINGTON White House 06 POTOMAC RIVER 04 02 of E D C A 39 U S CAPITOL 38 53 23 North Latitude 77 0 34 West Longitude 77 58 56 C 54 02 01 59 58 57 56 55 54 53 52 51 38 50 49 NORTH LATITUDE 48 47 CIE gibi sbarten a sih T

1 A highway study finds that on average there are five potholes per every 6 miles of a particular highway Using the Poisson equation from chapter 5 s PowerPoint show detail work to calculate the probability of four potholes in a 6 mile section of this highway 2 Show detail work calculating the probability of two potholes in a 3 mile section of the same highway from the above question 3 Customers arrive at a local credit union at the rate of four per half hour during the afternoon hours Using the Poisson equation from chapter 5 s PowerPoint show detail work to calculate the probability that five customers will arrive during the afternoon hours in a 30 minute interval 4 You are the manager of a local bank branch You have 6 tellers scheduled today but only 4 teller stations You decide to randomly select 4 tellers to be assigned at the 4 stations a How many different ways can you select the 4 tellers if order does not matter b How many different ways can you select 4 tellers if order matters

4 Elliott Credit Corp wants to earn an effective annual return on its consumer loans of 17 1 percent per year The bank uses daily compounding on its loans What interest rate is the bank required by law to report to potential borrowers Explain why this rate is misleading to an uninformed borrower

2 Find the APR or stated rate in each of the following cases Stated Rate APR Compounding Periods Semiannually Monthly Weekly Effective Rate EAR 11 1 19 6 10 50

1 Find the EAR in each of the following cases Stated Rate APR 9 16 12 Compounding Periods Quarterly Monthly Daily Effective Rate EAR

maceutical salesperson wants to schedule appointments with three doctors to introduce a new line of antibiotics Use a tree diagram to determine all possible schedules that would allow the salesperson to meet with each doctor List those schedules Select all possible schedules that would allow the salesperson to meet with each doctor A Dr Cook Thu at 10 00 Dr Garcia Mon at 11 00 Dr Baker Wed at 10 00 B Dr Cook Mon at 12 00 Dr Garcia Mon at 12 00 Dr Baker Mon at 12 00 C Dr Cook Thu at 10 00 Dr Garcia Mon at 11 00 Dr Baker Mon at 12 00 D Dr Cook Mon at 12 00 Dr Garcia Mon at 12 00 Dr Baker Wed at 10 00 E Dr Cook Wed at 10 00 Dr Garcia Mon at 12 00 Dr Baker Thu at 10 00 F Dr Cook Mon at 12 00 Dr Garcia Mon at 11 00 Dr Baker Mon at 12 00 G Dr Cook Thu at 10 00 Dr Garcia Mon at 12 00 Dr Baker Thu at 10 00 H Dr Cook Thu at 10 00 Dr Garcia Mon at 12 00 Dr Baker Mon at 12 00 1 Dr Cook Wed at 10 00 Dr Garcia Mon at 12 00 Dr Baker Mon at 12 00 J Dr Cook Mon at 12 00 Dr Garcia Mon at 11 00 Dr Baker Thu at 10 00 K Dr Cook Wed at 10 00 Dr Garcia Mon at 12 00 Dr Baker Wed at 10 00 L Dr Cook Thu at 10 00 Dr Garcia Mon at 12 00 Dr Baker Wed at 10 00 M Dr Cook Thu at 10 00 Dr Garcia Mon at 11 00 Dr Baker Thu at 10 00 N Dr Cook Wed at 10 00 Dr Garcia Mon at 11 00 Dr Baker Mon at 12 00 Dr Cook Wed at 10 00 Dr Garcia Mon at 11 00 Dr Baker Wed at 10 00 O P Dr Cook Mon at 12 00 Dr Garcia Mon at 12 00 Dr Baker Thu at 10 00 C Doctors Availability Dr Cook Monday at 12 00 Wednesday at 10 00 Thursday at 10 00 Dr Garcia Monday at 11 00 Monday at 12 00 Dr Baker Monday at 12 00 Wednesday at 10 00 Thursday at 10 00 Print Done x

At least one of the answers above is NOT correct 1 point Below are the steps of a proof by induction that 2n 1 2 for all integers n 3 Arrange the given steps in the correct order Step 2 Step 8 Step 3 Step 4 Step 1 Step 5 Step 6 Step 7 2k 1 2 2 2 by inductive hypothesis By the principle of mathematical induction we conclude that the statement is true for all integers n 3 Assume that 2k 1 2 for some integer k 3 2 k 1 1 2k 1 2 by algebra The statement is true for n 3 because 2 3 1 7 8 2 2k 2 2k 2k because k 3 2k 2 2 2k 2k 1 Therefore 2 k 1 1 2 1 which shows the statement is true for k 1 by algebra Motor in order to got orodit for this problem ell onowe must be cont

A rectangular box with a volume of 720 ft3 is to be constructed with a square base and top The cost per square foot for the bottom is 15 for the top is 10 and for the sides is 1 5 What dimensions will minimize the cost What are the dimensions of the box The length of one side of the base is The height of the box is Round to one decimal place as needed

n a proof by mathematical induction that a statement P n is true for all 0 what are you trying to prove in the induction step Select all that apply A That P k and P k 1 are true for all k 0 B That P k implies P k 1 for some k 20 C That P k implies P k 1 for all k 0 D That P k 1 implies P k for some k 0 E That assuming P k 1 is true for an arbitrary k 0 we can prove that P k is true

ing statements from the left column to the right column below give a proof by induction of the following statement ect proof will use 8 of the statements below Statements to choose from Let an be a sequence such that ap 0 and for all integers k 1 a 8a 1 3 Then for all integers n 0 1 8n 1 8 Your Proof Put chosen statements in order in this column and press the Submit Answers button Note that your proof should only contain of the statements on the left 1 gn Let P n be the statement an 3 1 8 Now assume that P k is true for an arbitrary integer k 0 This simplifies to 1 8 1 8 ak 1 3 8 a 3 3 3 8 8k 1 8 8 8 1 1 1 8 3 3 1 8811 0 Note that 1 80 1 1 3 3 1 8 1 8 1 8 as required for the truth of the base case 1 8 By the recurrence relation we have ak 1 8ax 3 8 3 1 3 Thus P k 1 is true Then a Therefore by the Principle of Mathematical Induction P n is true for all n 1 a 3

Answer the following questions for the function f x 4x12x 180x 14 C Enter f x f x and f x into your grapher to examine the table b The formula for the first derivative f x can be factored Set f x 0 to find the two critical numbers Hint You can factor out 12 from all terms in the formula for f x You can also scroll the table function on your calculator The critical values are x 5 3 Use a comma to separate answers as needed c Use your table to complete the following At the negative critical value listed in part b what does your table tell you about the value of the second derivative f 5 96 Type integers or simplified fractions Consequently what can be concluded about the graph of f Select the correct choice below and if necessary fill in the answer boxes within your choice OA The graph of f is concave down and f has a relative maximum at OB The graph of f is concave down and f has a relative minimum at OC The graph of f is concave up and f has a relative maximum at OD The graph of f is concave up and f has a relative minimum at OE No conclusion can be made

Opera Invest Finan Net C 2 Enter the Net In 3 Operatin Depre Loss 4 Operatin Accol Cu Pri Ch Invent Cu Pri Ch Prepa Cu Pri 3 Part 2 of 2 5 points oBook Print References 1 Deciaren and naIO CASA CIVienas A35 500 Required information Required Prepare a complete statement of cash flows using a spreadsheet using the indirect method Note Enter all amounts as positive values Balance sheet debit Cash Accounts receivable Inventory Prepaid expenses Equipment Saved Balance sheet credit Accumulated depreciation Equipment Accounts payable Long term neler pavable FORTEN COMPANY Spreadsheet for Statement of Cash Flows For Current Year Ended December 31 December 31 Prior Year 85 500 62 625 263 800 2 135 120 000 534 060 52 000 132 675 20 150 Help Analysis of Changes Debit Credit Save Exit Sub Check my wom 4 December 31 Current Year 67 90 67 90

Answer the questions for the function f x 3 A At the critical number x 3x 3x x 4 f x 0 at x OB At the critical number x OC At the critical number x OD At the critical number x E No conclusion can be made using the second derivative test at this critical number CE d Set the formula for the derivative f x 0 to find any possible inflection points 1 3 OA the function f is concave down and corresponds to a relative maximum of f x the function f is concave down and corresponds to a relative minimum of f x the function f is concave up and corresponds to a relative minimum of f x the function f is concave up and corresponds to a relative maximum of f x Use the table feature for the graph of f x to examine the concavity of the graph of f x What can you conclude Select the correct choice below and if necessary fill in the answer boxes within your choice OB There is a point of inflection at x where the graph off changes from concave down to concave up The slope of the graph off at this inflection point is There is a point of inflection at x where the graph of f changes from concave up to concave down The slope of the graph of f at this inflection point is Oc No conclusion can be made

2 of 2 Sales Cost of goods sold Gross profit FORTEN COMPANY Income Statement For Current Year Ended December 31 Operating expenses excluding depreciation 144 400 32 750 Depreciation expense Other gains losses Loss on sale of equipment Income before taxes Income taxes expense Net income Assets Cash Accounts receivable Inventory Prepaid expenses Total current assets Total assets Equipment Accumulated depreciation Equipment FORTEN COMPANY Comparative Balance Sheets December 31 Liabilities and Equity Accounts payable Long term notes payable Total liabilities Equity 642 500 297 000 345 500 177 150 17 125 151 225 41 050 110 175 Current Year 67 900 83 890 293 656 1 330 446 776 145 500 42 625 549 651 65 141 72 600 137 741 Prior Year 85 500 2 62 263 800 2 135 414 060 120 000 52 000 482 060 132 675 69 150 201 825

Answer the questions for the function f x 3x 3x x 4 L Enter f x f x and f x into your grapher to examine the table b Set the first derivative f x 0 to find any critical values Tip You may wish to graph f x by itself to explore if it has any zeros It can be helpful to know that the formula of f x factors Select the correct choice below and if necessary in the answer boxes within your choice OA There are no critical numbers B The function f has a critical number at x 1 3 at this critical number the second derivative f x 0 Type an exact answer c What conclusion can be made from your answer to part b Select the correct choice below and if necessary fill in the answer box within your choice A the function f is concave down and corresponds to a relative maximum of f x the function f is concave down and corresponds to a relative minimum of f x OA At the critical number x OB At the critical number x OC At the critical number x OD At the critical number x the function f is concave up and corresponds to a relative maximum of f x QE No conclusion can be made using the second derivative test at this critical number the function f is concave up and corresponds to a relative minimum of f x

According to a study a vehicle s fuel economy in miles per gallon mpg decreases rapidly for speeds over 65 mph a Estimate the speed at which the absolute maximum gasoline mileage is obtained b Estimate the speed at which the absolute minimum gasoline mileage is obtained c What is the mileage obtained at 10 mph a The speed at which the absolute maximum gasoline mileage is obtained is approximately Type a whole number Fuel economy mpg 36 30 24 18 12 6 O 5 15 25 35 45 55 65 75 85 95 Speed mph A

Answer the following questions for the function f x 4x 12x 180x 14 a Find formulas for f x and f x f x Enter f x f x and f x into your grapher to examine the table

Find the absolute maximum and minimum values of each function over the indicated interval and indicate the x values at which they occur f x 15x4 4x 2 2 The absolute maximum value is 272 at x 2 Use a comma to separate answers as needed The absolute minimum value is at x Use a comma to separate answers as needed

7 A warehouse is 42 yards long and 26 yards wide with a height of 13 yards What is the volume of the warehouse A 1092 yd2 C 14 196 ft3 D 14 196 yd3 B 1092 ft2 8 How many square inches are in 6 square yards A 216 in 2 B 72 in 2 C 7776 in 2 10 How many cubic inches are in 19 cubic feet A 2736 in 3 B 886 464 in 3 9 A swimming pool 3 meters deep 14 meters long and 6 meters wide is filled with water What volume of water does the pool contain A 18 m2 B 252 m3 C 273 m3 D 84 m2 D 864 in 2 C 32 832 in 3 D 24 624 in 3 11 An average 12 ounce can of beer contains about 15 grams of alcohol Consider a person with approximately 4 liters 4000 milliliters of blood who quickly drinks two cans of beer If all the alcohol were immediately absorbed into the bloodstream what blood alcohol content would we find A 0 75 g 100 ml B 0 0375 g 100 ml C 0 075 g 100 ml D 0 375 g 100 ml 7 8 9 10 11

easurements are made at two different times Find the absolute change and then find the percentage change Round swers to the nearest tenth if necessary 19 The value of Anna s house increased from 160 000 when she bought it 20 years ago to 1 38 million today A Absolute change 1 220 000 Percentage change 762 5 C Absolute change 1 220 000 Percentage change 762 5 B Absolute change 1 220 000 Percentage change 76 3 D Absolute change 1 220 000 Percentage change 88 4 19

Answer the following question involving a conversion within the USCS system 4 The container holds 4 gallons of water How many fluid ounces is that A 128 fl oz B 1024 fl oz C 512 fl oz 5 If a horse ran 4 furlongs how many yards did it run A 880 yd B 21 120 yd C 7040 yd 6 The baby weighs 8 2 pounds How many ounces is that A 82 ounces B 0 51 ounces C 131 2 ounces D 256 fl oz D 3520 yd D 98 4 ounces 4 5 6

a The graph of y h x is shown Draw the graph of y h x 4 8 2 6 2 8 6 8 X 3

Write an equation of the form ya sinbx or y a cosbx to describe the graph below MA 3x 0 119 5x JU 0 0 H sin cos

The cost function for a certain commodity is C q 86 0 15q 0 005q2 0 00079 a Find C 100 Interpret C 100 This is the rate at which the production level is decreasing with respect to the cost when x 100 This is the number of items that must be produced before the costs reach 100 This is the amount of time in minutes it takes to produce 100 items This is the cost of making 100 items This is the rate at which costs are increasing with respect to the production level when x 100 b Find the actual cost of manufacturing the 101st item Round your answer to the nearest cent

An employee s monthly productivity M in number of units produced is found to be a function of the number t of years o service For a certain product a productivity function is shown below Find the maximum productivity and the year in which it is achieved M t 4t 240t 120 0sts 40 The maximum productivity is achieved in year

g Sketch the graph of R x blem 6 The total yield Y N of a specific crop as a function of nitrogen level N in the soil measured in parts per million is modeled by Y N a State the domain of Y N b Find Y 2 and interpret its meaning c Find all zeros N 144 N d Find all intercepts e Find all poles and identify all vertical asymptotes f Generate a sign chart to determine where Y N is positive and where it is negative g Identify all horizontal asymptotes h In the long run describe what happens to the total yield Y N i Sketch the graph of Y N

List the set in roster form Enter only the first five values of this set 3 5 I

uragging statements from the left column to the right column below give a proof by induction of the following statement For all n 1 4 7 10 3n 1 n 3n 5 2 The correct proof will use 8 of the statements below Statements to choose from Thus P k 1 is true Let P n be the statement 4 7 10 3n 1 4 7 10 3 k 1 1 k 3k 5 3 k 1 1 3k 5k 2 3k 5k So 3k 4 6k 8 2 2 3k 11k 8 2 k 1 3 k 1 5 2 Observe that 4 Therefore by the Principle of Mathematical Induction P n is true for all nz 1 n 3n 5 2 By the inductive hypothesis 4 7 10 3k 1 Note that 4 7 10 3 k 1 1 4 7 10 3k 1 3 k 1 1 k 3k 5 2 Now assume that P k is true for an arbitrary integer k 1 1 3 1 5 is true So the base case P 1 Your Proof Put chosen statements in order in this column and press the Submit Answers button

1 point Below are the steps of a proof by induction that 2n 1 2 for all integers n 3 Arrange the given steps in the correct order 2k 1 2 2k 2 by inductive hypothesis By the principle of mathematical induction we conclude that the statement is true for all integers n 3 Assume that 2k 1 2k for some integer k 3 2 k 1 1 2k 1 2 by algebra The statement is true for n 3 because 2 3 1 7 8 2 2k 2 2k 2k because k 3 v 2k 2k 2 2k 2k 1 by algebra Therefore 2 k 1 1 2k 1 which shows the statement is true for k 1

oblem 4 The concentration C of a drug in the bloodstream is given by 5 C t 2 3t 1 where t is the time in hours after ingestion of the drug and C is measured in milligrams per liter a State the domain of C t b Evaluate the average rate of change of C t on the interval 4 5 include units and interpret the answer c Graph the function Page 1 of 2

1 point Let P n be the predicate 8n7 n where the domain of n is all integers Suppose you are using induction to prove P n is true for all integers n 9 Which of the following do you prove in the basis step A 8n n for some integer n B 8 9 O c 8n n for n 8 OD 8n n for n 9 E If 8n7 n for n 9 then 8n7 n for n 10 OF None of the above Which of the following is the inductive hypothesis OA If 8k7 k for some integer k9 then 8 k 1 7 k 1 8 B 8k7k for all integers k with 9 k n C 8k7k8 for all integers k 9 O D 8k7 k for some integer k 9 E None of the above Which of the following do you prove in the inductive step OA 8n n for all integers n k B 8 k 1 k C 8k7 k 1 8 D 8n n for all integers n 9 E 8 k 1 7 k 1 OF None of the above

At June 30 Assets Cash Accounts receivable net Inventory IKIBAN INCORPORATED Comparative Balance Sheets 2021 Prepaid expenses Total current assets Equipment Accumulated depreciation Equipment Total assets Liabilities and Equity Accounts payable Wages payable Income taxes payable Total current liabilities Notes payable long term Total liabilities Equity Common stock 5 par value Retained earnings Total liabilities and equity Sales Cost of goods sold Gross profit 105 700 69 500 66 800 4 700 Other gains losses Cain en 246 700 127 000 28 500 345 200 28 000 6 300 3 700 38 000 33 000 71 000 IKIBAN INCORPORATED Income Statement For Year Ended June 30 2021 226 000 48 200 345 200 Operating expenses excluding depreciation Depreciation expense 2020 47 000 54 000 91 000 6 000 198 000 118 000 10 500 305 500 34 500 15 600 4 400 54 500 63 000 117 500 163 000 25 000 305 500 693 000 414 000 279 000 70 000 61 600 147 400

1 point Let P n be the predicate 7 6 7 6 7 5 Suppose you are using induction to prove P n is true for all integers 0 Which of the following is the basis step OA 7 7 n B 7 6 1 0 71 C 7 6 7 61 7 I 0 n D 7 6 0 7 6 1 7 5 n E Hf7 6 B 7 6 0 5 7 6 1 7 10 OF None of the above D 7 6 C H7 6 7 6 10 1 0 A 8 7 6 7 6 1 7 5 7 6 1 7 5 Which of the following is the inductive hypothesis 7 6k 1 7 A 7 6 for all integers k 0 5 ANO 1 0 k 1 c 7 6 10 INO E None of the above 7 6 1 7 5 7 6 1 7 5 7 61 7 5 7 6 2 7 5 D 7 6 7 6 2 7 1 0 k 1 IO for n 1 5 E 7 6 7 6 7 1 0 OF None of the above for some integer n is true for 72 0 5 Which of the following do you prove in the inductive step A 7 6 7 6 7 for all integers n 0 for r 0 then 7 6 7 6 10 for some integer k 0 where the domain of it is all integers k 1 for some integer k 0 then 7 6 7 6 2 7 5 for all integers nk for all integers k with 0 k n 1 0 for n 1

balance my family responsibilities During this course I aim to dever and how culture and social norms influence our lives When it comes to addressing a local issue my primary concern would be poverty Poverty is a complex problem with underlying factors such as unemployment lack of educational opportunities and unaffordable housing Researching these specific causes in my community can provide valuable insights Moreover poverty isn t confined to one region it has global connections highlighting broader issues of income differences and financial gaps When we take action against poverty in our local area we become part of a global initiative to fight inequality and develop strategies that can benefit more than just our community

1 On a map the scale is 3 4 cm 8 miles The actual the distance between these cities on the map Scale 3 48 miles 0 75cmX 8 miles Zsumiles 2 Jacob made a drawing of his land using a scale 1 inch 14 yards The actual length of his land is 84 yards long What is the length of Jacob s land in the drawing 75 140 3 A scale drawing of a basketball court has a scale of 1 inch 9 feet The basketball court is 94 feet by 50 feet Find the dimensions of the court in the drawing VLength and width 5x10 6 5x Yo 142 X 24mles 4 Andrew draws a scale drawing of his office On the drawing his office is 6 cm by 7 cm If the scale of the drawing is 5 cm 10 ft what is the actual area of Andrew s office Stepiti Scale 5cm lopt 56 197 5 26 x width Step 5cm tcm 10PX 5 X 27 5cm 10 F 12 14 168 F 5 Finley has blueprints of her house that use a scale of 1 cm 2 5 m The actual distance between two rooms in Finley s house measures 28 m How far apart are these roons on the bluerint Scale 1cm 2 5m 2 5 28 1 2 5 28 2 5 2 5 6cm Toms 2 2 5 m2 28m X 11 2 6 The scale on a set of blueprints of a house is 1 in 3 ft On the blueprint one of the bedrooms measures 3 75 in wide and 4 5 in long What is the perimeter of the actual bedroom 7 Jill s room is 12 5 feet long and 11 5 feet wide She made a scale drawing of the room with a scale of 0 5 inch 2 feet What is the perimeter of Jill s room in the drawing 8 Taylor made a scale drawing of his room using a scale of 0 25 inch 1 foot On the drawing the length

By dragging statements from the left column to the right column below give a proof by induction of the following statement For all n 1 1 22 n n n 1 2n 1 6 The correct proof will use 8 of the statements below Note that 1 Statements to choose from 1 1 1 2 1 1 6 Now assume that P k is true for an arbitrary integer k 1 1 2 P 1 is true Let P n be the statement 1 2 k 1 k k 1 2k 1 6 So the base case n n 1 2n 1 6 Then we see that k 1 k k 1 2k 1 6 k 1 6 6 2k 3k k 6k 12k 6 6 6 2k 9k 13k 6 6 k 1 k 2 2k 3 Then 12 22 k 6 k 1 k 1 1 2 k 1 1 Note that 12 22 k 1 2 12 2 k k 1 k k 1 2k 1 6 Therefore by the Principle of Mathematical Induction P n is true for all n 1 Thus P k 1 is true Your Proof Put chosen statements in order in this column and press the Submit Answers button

Problem 3 According to data from the National Traffic Safety Institute the stopping distance y in feet of a car traveling a miles per hour can be described by the equation y 0 0560572 1 06657z Source National Traffic Safety Institute a Find the stopping distance for a car traveling 40 mph b How fast can you drive if you need to be certain of stopping within 150 ft

A payday loan provides short term loans ranging from 250 to 2 000 Assume the cost of the loan is 1 00 per day per 100 borrowed until the loan is repaid What is the cost of a 650 payday two week loan

Consider the following loan purchase a refrigerator for 1 900 at 15 add on interest for 3 years Give the formula used to approximate the annual percentage rate or APR for an add on loan where r is the annual interest rate as a decimal and N is the number of monthly payments APR Determine the following values for this loan r N Find the APR rounded to the nearest tenth of a percent for the loan 6