Basic Math Questions and Answers

2 In a small rural town city hall kept records on the number of cell phone users in the town Their results are shown below a b C I Q YEAR 2001 2002 2003 2004 2005 2006 2007 2008 NO OF USERS 499 875 1527 2672 4677 8186 14325 25069 1ST DIFF 2ND DIFF Fill in the appropriate columns in the table 3 marks What type of relationship does this situation represent HOW DO YOU KNOW 2 marks Is the rate of change increasing decreasing or remaining constant GIVE A REASON FOR YOUR ANSWER 2 marks 3 Lisa Carr purchases a truck 55200 and plans to pay for the vehicle through the dealership s financing plan She makes monthly payments on this balance for 5 years and the financing rate is 5 20 compounded monthly What will Lisa s monthly payments need to be to pay off her balance in 5 years 3 marks 14 Marks APPLICATION 4 Rick O Shay has weekly payments of 85 over the next 5 years on his student loan The interest rate on the loan is 9 36 compounded weekly How much is his loan worth NOW 4 marks

The following data were summarized from the accounting records for Ruiz Industries Inc for the year ended November 30 2018 Cost of goods sold Commercial Division Residential Division Administrative expenses Commercial Division Residential Division 3 400 000 1 800 000 Operating income 750 000 375 000 Feedback Support department allocations Commercial Division Residential Division Sales Prepare divisional income statements for Ruiz Industries Inc Commercial Division Residential Division Sales Cost of goods sold Gross profit Administrative expenses Operating income before support department allocations Support department allocations Ruiz Industries Inc Divisional Income Statements For the Year Ended November 30 20Y8 Commercial Division 6 120 000 3 400 000 2 720 000 1 970 000 800 000 1 170 000 800 000 200 000 6 120 000 2 850 000 S Residential Division 2 850 000 1 800 000 1 050 000 0000

6 An outdoor wedding takes place under a rented tent Material for the tent costs 4 90 per SQUARE METRE If the TENT HAS NO BASE determine the cost to make the tent Hint Think Surface Area 5 marks 4 m 10 m 3 m 15 m

1 Solve for x in each exponential equation HINT Make the bases the same on each side 5 marks a 45x 1 4x 11 b 2 64 1

17 Tanks A and B are rectangular tanks 25 cm Tank A 30 cm 15 cm 21000 7000m 40 cm Tank B 28 cm 25 cm V 25000 At first Tank A was empty and one quarter of Tank B was filled with water Then b taps were turned on at the same time Water from each tap flowed out at the rate 3 tres per minute How long did it take for the height of the water level to be the same in both tanks and oren

A company has budgeted shours to complete a project with of the time spent on research How much time does the company plan to spend on research Express your answer as a mixed number O 12 hours hours 5 hours hours

A 5 foot tall woman walks at 7 ft s toward a street light that is 25 ft above the ground What is the rate of change of the length of her shadow when she is 15 ft from the street light At what rate is the tip of her shadow moving Let L be the length of the woman s shadow and let x be the woman s distance from the street light Write an equation that relates L and x

A street light is fastened to the top of a 16 5 ft high pole If a 5 5 ft tall woman walks away from the pole in a straight line over level ground at a rate of 5 ft s how fast is the length of her shadow changing when she is 12 ft away from the pole Let L be the length of the woman s shadow and let x be the woman s distance from the pole Write an equation that relates L and x

7 Determine the point of intersection for the graphs of y 82x and y 2 8 5 Round your answer to three decimal places

Given The box crate is being lifted up the plane which is inclined at an angle using the motor winch M and the cord and pulley arrangement shown on the right The weight Fw of the crate is 500 Lb The surface on which the crate rest is very rough and the coefficient of static friction between the crate and the inclined plane supporting surface is 0 61 For this problem assume that the angle is 26 Kinematics a Label the pulley arrangement and derive the four kinematic equations which describe the crate s motion i e position displacement velocity and acceleration b Find the speed vp at which the cable must be taken up by the motor in order to move the crate up the plane with a speed of 1 ft sec c Find the relative velocity of the point P with respect to point A on the cord that is VPIA if the crate moves up the plane with a speed of 1 ft sec land oy 140 120 100 M

The management team of Floyd s Corner Markets has decided to expand by adding a retail shop on a vacant lot they own They will build a new building at an estimated cost of 1 5 million They will spend another 100 thousand on the parking and access roads The land was purchased ten years ago at a cost of 500 thousand Today the land could be sold for 1 6 million They will also need to add to the landscaping at a cost of 200 thousand Finally two new managers will be needed and the CFO has allocated 200 thousand in executive salaries to the project What is the cost of this expansion project 3 6 million 3 4 million 4 1 million 3 7 million

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A project has the following cash flows What is the PI when the required return is 10 Year 0 1 2 3 CF 50 000 37 000 12 000 10 000 0 48 1 43 0 0213 1 02

2 Solve each of the following a 2x 1 x 2x

8 Let f x x 3 and g x x 9 Develop and algebraic and graphical model for the following f x g x y

9 Evaluate the limit if it exists 9x lim x 0 2x 5x

2 This amortization table shows the first 3 payments of William s mortga Payment Monthly Interest Principal Outstanding number payment paid paid balance 0 1 2 3 789 25 789 25 789 25 534 12 533 32 532 51 a How much money did William borrow b How much is their monthly payment 255 13 255 93 256 74 170 000 00 169 744 87 169 488 93 169 232 20

Given A student of weight Fw who runs at a known speed of vo grabs a cord and swings out over a lake He releases the rope when his velocity is zero 0 R A p Find a Draw a COMPLETE free body diagram FBD of the student as he swings on the rope using the normal and tangential coordinate system b The equations of motion from the FBD in part a c The angle when he releases the rope as an expression of the given values Fw vo p etc d The tension Fe in the cord just before he releases it e Draw a COMPLETE free body diagram FBD of the student as he swings on the rope using the radial and transverse coordinate system Please assume that point C is the origin of the radial and transverse coordinate system Solution

When Albertina opened her law office she bought 19 000 worth of law books and 6800 worth of furniture She pai 1500 down and agreed to amortize the balance with semiannual payments for 5 years at 11 compounded semiannually Find the amount of each payment Then use the formula for the remaining balance to find the number of remaining payments when the loan has been reduced below 9000 What is the amount of each payment 0 Round to the nearest cent as needed How many payments remained when the loan had been reduced below 9000

Write any fractions like this 5 2pi Here is the graph of a sin wave function y 4sin x 1 4pi 2 1 Origin horizontal vertical e g pi 2 2 High value 3 Low value 4 Value of interval A 5 Value of interval B 6 Value of interval C 7 Value of interval D 8 Value of interval E High T A Low Given the

Application Simple Interest Rate Interest Principal x Time 4 INTEREST RATE An investment of 6000 paid 540 00 in SIMPLE INTEREST over a 2 year period Calculate the interest rate State your answer as a PERCENTAGE rounded to 1 decimal place 0 045 Knowledge Compound Interest 0 45 4 5 5 Penny Saver purchased a Canada Savings Bond in the amount of 1400 The interest on 84 7 12 For COMPOUND INTEREST A P 1 i 6 Penny Saver purchased a Canada Savings Bond in the amount of 1400 The interest on the bond was 5 7 compounded monthly She has the bond for 7 years What is i 0 457 0 0457 0 00457 7 Penny Saver purchased a Canada Savings Bond in the amount of 1400 The interest on the bond was 5 7 compounded monthly She has the bond for 7 years What is A or the total that the bond is worth after 7 years 3302 45 2053 36 59748 23 8 A car loan payment of 5000 is due in 4 years The bank will accept payment today at a discounted interest rate of 7 interest compounded quarterly If the payment was made today how much it be 3466 81 2981 12

1 340 is invested at the end of every 6 months for 7 years into an account that earns 4 9 interest per annum compounded semi annually What is i 0 0245 2 340 is invested at the end of every 6 months for 7 years into an account that earns 4 9 interest per annum compounded semi annually What is n 2 45 0 245 14 7 42 3 340 is invested at the end of every 6 months for 7 years into an account that earns 4 9 interest per annum compounded semi annually Calculate the Future Value 5367 23 5998 45 5597 58 4 Payments of 231 are made monthly for 3 years at 12 interest compounded monthly What is i 0 001 0 01 0 1 36 5 Payments of 231 are made monthly for 3 years at 12 interest compounded monthly What is n 24 12 6 Payments of 231 are made monthly for 3 years at 12 interest compounded monthly Calculate the Present Value 6954 83

You have charged 1 950 on a credit card that charges 14 interest If you want to make 25 monthly payments how many payments will you have to make to pay off this charge That is how many months will it take you to pay off the charge Round up to the month 7

6 24 30 36 4 6 Table 2 8 10 48 W M Part 0 2 192 Part 1 of 2 240 288 7500 5000 3750 3000 a Identify the table that displays direct variation and find the direct variation equation matching

Match the following Down Payment Fixed Rate Appreciation Amortization Mortgage Annuity Principal Future Value Application 1 5 6 7 8 2 An RRSP is an example of a 3 A mortgage with a constant interest rate one that doesn t change over time 4 A loan used for real estate property The amount still owed on a mortgage A series of equal payments or deposits made at regular intervals over a fixed period of time The rate at which the value of an item increases in value over time A lump sum of money paid towards the cost of a home to decrease the mortgage amount The time it takes to fully pay back a mortgage

1 Consider the 2 dimensional vector field F given by F x y e cos y e sin y Show that F is not globally invertible but that F is locally C invertible about every x y R

Determine whether the equation is homogeneous if it is solve it If there is an initial value find the particular solution satisifying the initial value 1 y y x x 2 y xy y 2 x 2 y 1 2

Solve the following differential equations 1 y y 6y 0 2 y 2y 0

Find the explicit general solution of the differential equation If an explicit solution cannot be found an implicit solution is acceptable If there is an initial value find the solution to the initial value problem 1 y xye x 2 yy 4x y 1 3

The accompanying data shows the fossil fuels production fossil fuels consumption and total energy consumption in quadrillions of BTUs of a certain region for the years 1986 to 2015 Complete parts a and b Click the icon to view the energy consumption a Develop line charts for each vanable and identify the characteristics of the time series that is random stationary trend seasonal or cyclical What is the line chart for the variable Fossil Fuels Production OA Fuss Fuels Prod 100 1945 Your 2015 Fess Fusts Prod B 100 1945 Year 2015 O C Fossil Fues Pr 100 1945 Your 2015 Fossil Fuel Pres D FOOD 1945 Year 2015 Year 1949 9 1950 1951 1952 1953 1954 1955 1956 10 1957 11 2958 12 1959 13 1980 14 1961 15 1967 15 1963 1964 1965 1966 1967 1968 22 1969 23 1920 24 1971 25 1972 16 1975 27 1974 28 1975 1975 1977 1978 1979 1980 1981 1982 29 30 31 32 7 a 4 15 6 J W 17 NE 39 20 12 33 34 35 Fossil Fueh Production Fossil Fuel Consumption Total Energy Consumption 28 748176 32562667 3579151 34 976732 35 349936 35 76433 37 36368 39 771452 40133484 37216337 39045218 39869117 40 307136 41781845 44 IRIZED 45 788951 47234902 50 035557 52597132 54306187 56 285569 59186071 504758 58937904 18241491 56 330758 54 733273 54 722896 55100782 55074118 58005609 59007873 58 529320 57457822 29 002099 31 631956 34008105 33 799903 34 826156 393275 37 410105 38 888151 38 925593 38716707 40 550068 42 136751 42 758245 44 08077 46500283 48 54305 50 576504 53 513987 15126873 55 50247 61 361751 63522289 54595645 67 69588 70 31386 0 62 905124 65356532 9 107176 70 991129 71893522 72 890521 69 827758 675 1093 65888374 11 981503 34615768 3697403 36 747825 37 564468 35 639382 40 307971 41 754252 41 787186 41 545028 43 465722 45 086455 45 737817 47 825437 49 644195 51 814788 54 015001 57014352 58904521 62 414507 651402 67618325 69 282843 72687967 7568569 75 962365 71 964553 75 974826 7796133 79 950406 80 858584 78 066668 76105776 25 099185 T F 1980 56 5753 060333 76647 1987 57 1667 6852067901545 1988 5 875 715571 2 7092 1989 57 4827 72 9112 84786 1990 585506 22 3322 84 485 1991 5 8717 71 8803 24 414 1903 57 6551 73 3052 1783 1993 55 0221 74 8357 87 4236 1994 58 0416 76 2564 85 0013 1995 575401 77 259591 0291 1996 58 3872 79 7847 140222 1997 58 8567 808755 56 6022 1998 593141 RE369950120 1999 576145 82 4272 652 2000 57366 4 790688145 2001 58 5413 82 9018 96 1882 2002 568557 8699 97 6451 2009 560320 04 0335 97342 2004 55 9423 85 8188 10010 2005 55 044 57943 100282 2006 55 9379 34 702 99 6295 2007 56 4556 86 2114 101 314 2008 57 587 H35521 292929 2009 56 5703 78 4966 04101 2010 54 2066 81 4121 400104 2011 60 5490 79 4469 968417 2013 07 3028 77 4868 54 416 2013 64 2015 754396 97157 2014 89 6526 8024 383174 2015 702208 79 3297 973436

The table shows the distribution of the number of motor vehicles per household Find the cumulative distribution for the table Use a value of 5 to stand for 5 or more vehicles No of Motor Vehicles 0 1 2 3 4 5 or more Proportion 0 17 0 26 0 31 0 16 0 09 0 01 Cumulative Percent Find the mean median and mode for the table If an answer does not exist enter DNE Round your mean to two decimal places mean motor vehicles median mode motor vehicles motor vehicles

Suppose that people s heights in centimeters are normally distributed with a mean of 170 and a standard deviation of 5 We find the heights of 90 people You may need to use the standard normal distribution table Round your answers to the nearest whole number a How many would you expect to be between 170 and 180 cm tall people b How many would you expect to be taller than 177 cm people

A normal distribution has a mean of 85 1 and a standard deviation of 4 84 Find the data value corresponding to the value of z given Enter your answer to four decimal places z 0 85

A nurse is preparing to administer amoxicillin 100 mg PO every 8 hr to a toddler who weighs 20 kg The recommended dosage range is 20 to 25 mg kg day Which of the following actions by the nurse is appropriate The nurse administers the prescribed dosage The nurse determines the prescription is above the recommended dosage range The nurse contacts the pharmacist to adjust the prescribed dosage The nurse determines the prescription is insufficient to achieve the desired effect O

a cos 3 b sin a c tan 3x and cos 2 3x 13 2 3 tan a 2 CCXX a cos a 8 Type an exact answer using radicals as needed Simplify your answer Rationalize all denominators Use integers or fractions for any numbers in the expre sin Type an exact answer using radicals as needed Simplify your answer Rationalize all denominators Use integers or fractions for any numbers in the expr tan a all denominatore Lise inteners or fractions for any numbers in the expr

What is the oxidation state of N in HNO3 If the number is positive just put in number If it is negative put in number So if the answer is 2 put in 2 If the answer is 2 put in 2

A project provides cash inflows of 50 000 each year for four years What is the payback period if the cost is 220 000 3 4 years 4 50 years 4 38 years 5 50 years None of the above

A project has cash flows of 5 200 5 000 and 4 800 in years 1 2 and 3 If the cost is 15 000 and the required return is 12 what is the NPV 45 37 465 82 2 954 63 851 49

The cash flows for a project are as follows 1 000 000 500 000 400 000 200 000 and 50 000 fa years 0 1 2 3 and 4 What is the payback period 2 75 years 2 50 years 3 75 years 2 67 years None of the above

Your firm is considering two projects that are independent Both have standard cash flows and required return is 13 You have computed the IRRs and find the following IRR Project A IRR Project B 12 5 10 8 What is your recommendation Accept B Accept A Reject both A and B I cannot make a recommendation using the IRR criteria and B ent

A three year project has an initial requirement of 900 000 for fixed assets and 300 000 for net working capital The fixed assets will be depreciated to a zero book value over the 3 year life of the project The estimated salvage value is 120 000 All of the net working capital will be recouped at the end of the 3 years The annual operating cash flow is 700 000 and the discount rate is 10 percent The tax rate is 28 percent What is the cash flow in year 0 700 000 820 000 1 200 000 900 000

A firm is considering a project that requires 150 000 of fixed assets that are classified as 7 year property for MACRS What is the book value at the end of year 3 Year 1 2 3 4 5 6 7 8 14 29 24 49 17 49 12 49 8 93 8 93 893 4 45 84 405 18 732 91 830 65 595

dering two projects that are mutually exclusive You have computed the NPVs at the firm required return and find the following NPV Project A NPV Project B 190 896 240 622 What is your recommendation Reject both projects Accept B Accept A

A four year project is expected to generate revenues of 800 000 annual variable costs of 300 000 and fixed costs each year of 100 000 The annual depreciation is 100 000 and the tax rate is 20 percent What is the annual operating cash flow 129 000 260 000 325 000 340 000 Sm

A project requires an initial investment of 100 000 and has cash inflows of 15 000 each year for 30 years What is the NPV if the required return is 10 12 041 65 69 437 40 305 56 41 403 72

Write an estimate of the number in scientific notation 406793 40670

A certain sector in a circle has an arc length of 10cm and an area of 20cm Determine the radius of the circle and the angle of the sector

Call centers typically have high turnover The director of human resources for a large bank has compiled data on about 70 former employees at one of the bank s call centers The accompanying table shows this data In writing an article about call center working conditions a reporter has claimed that the average tenure is no more than two years Formulate and test a hypothesis using these data to determine if this claim can be disputed Use a level of significance of 0 05 Click the icon to view the call center data Is there sufficient evidence at the 0 05 level of significance that the average tenure is no more than two years Determine the null hypothesis Ho and the alternative hypothesis H Ho H 2 H H 2 Type whole numbers Compute the test statistic Round to two decimal places as needed 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 A Gender 0 1 0 0 0 0 0 1 1 1 0 0 0 1 1 0 1 1 1 0 0 0 0 0 1 1 1 B Length of years 7 03 3 48 2 07 1 78 4 43 3 28 3 05 0 47 0 59 3 12 2 94 2 15 4 01 3 52 2 47 2 14 3 27 1 08 1 77 1 94 2 89 3 03 2 54 1 82 2 87 2 21 1 44 C D 1 1 1 0 1 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 0 0 1 0 1 1 1 E 2 53 1 41 1 08 0 98 0 64 1 31 2 13 2 28 2 06 2 14 2 11 2 16 2 04 1 71 2 11 1 73 2 13 2 13 0 36 1 95 1 02 1 27 1 04 1 64 1 76 1 71 1 27 F G 0 0 1 1 1 0 0 1 0 0 TOOOOO 1 0 0 0 0 0 H 1 47 1 29 1 46 1 88 1 15 1 16 1 04 0 95 1 25 0 79 0 87 0 99 0 74 0 31 0 34 0 56

On the evening of the famous final the stadium was packed Fortunately the Soci t de transport de Montr al has provided free shuttles to avoid traffic congestion at the end of the game The fact remains however that a good number of people have found a place to park their car in one of the neighboring parking lots and will leave the premises at roughly the same time The diagram below illustrates the expected traffic flow around the stadium after the game The numbers and the xi variables indicate the average number of vehicles traveling per hour and the arrows indicate the direction of traffic The city hires you as a traffic management specialist to analyze the situation Des Pins 300 P 100 200 University Stade Percival Molson C 150 Aytmer 400 600 550 D Du Pare 750 1200 P a Give the system of linear equations associated with this graph and express it in the form of a matrix equation AX B b Use the Gauss Jordan method to invert if possible the matrix A found previously c Establish the circulation flow by solving the system of linear equations by the inverse matrix method

The figure shows a small plane flying at a speed of 182 miles per hour on a bearing of N47 E The wind is blowing from west to east at 42 miles per hour The figure indicates that v represents the velocity of the plane in still air and w represents the velocity of the wind The ground speed of the plane is miles per hour Simplify your answer Round to the nearest tenth as needed Plane s speed 182 miles per hour ON35 3 W 47 N54 7 W Wind s speed 42 miles per hour V W Simplify your answer Type an integer or decimal rounded to the nearest hundredth as needed Type your answer in the form bj c The magnitude of v w called the ground speed of the plane gives its speed relative to the ground Find the ground speed in miles per hour V W d The direction angle of v w gives the plane s true course relative to the ground Approximate the true course to the nearest tenth of a degree What is the plane s bearing Choose the correct answer below N54 7 E ON35 3 E