Mathematical Induction Questions and Answers

40102b 55 40102c 53 40102d 48 83 ec 28 401031 48 89 e6 401034 e8 e3 03 00 00 read six numbers 401039 83 3c 24 01 push push sub mov callq cmpl rbp rbx 0x28 rsp rsp rsi 40141c 0x1 rsp Additionally here is partial register states of the CPU before the callq instruction rip 0x401034 rdi 0x100 Zrbx Ox101 rax 0x102 rcx 0x103 a Suppose we now execute the command stepi What are the values stored in the registers rip rdi rbx rax and rex Report N A if a state is unknown

Suppose that for a certain mathematics class the scores are normally distributed with a mean of 75 and a standard deviation of 8 The teacher wishes to give A s to the top 7 of the students and F s to the bottom 7 The next 17 in either direction will be given B s and D s with the other students receiving C s Find the bottom cutoff for receiving an A grade You may need to use the standard normal distribution table Round your answer to the nearest whole number

AA Airlines has 100 000 shares of common stock outstanding The stock is currently selling for 50 a share The firm also has 2 bond issues outstanding Each bond in all issues has a face value of 1 000 The first bond issue has a total face value of 500 000 and pays 8 percent interest annually This bond is selling at 82 0 percent of face value The second bond issue consists of 10 000 bonds which are selling for 1 100 each These bonds pay 12 percent interest annually and mature in 15 years The tax rate is 20 percent What is the capital structure weight of the firm s debt 69 53 30 47 79 11 33 33

Exercise 2 van der Pol with parameter Consider the van der Pol oscillator with parameter 0 x y x X 1 7 2 3 Y f Solve the system numerically Show phase plane plots for 0 5 0 5 1 3 and 5 In each case evolve to time 15 starting at xo yo 2 2 to obtain the solution curve In each case the limit cycle should be apparent as the solution curve appears to nearly connect to itself in reality it just gets really close On each plot overlay the graph of the cubic y x on the interval 2 x 2 in another color

rate of 30 per year a Write an equation to represent the value of the car after n years b What is the value of the car after 3 years alue of the car depreciates at a C 13 T 13 c What is the value of the car after 6 years 9 A loaf a bread costs 2 but the rate of inflation is 3 per year C 13 T 13 a Write an expression to represent the cost of a loaf of bread after n years b How much would the loaf of bread cost in 2 years c How much would the loaf of bread cost in 10 years

Match the sign chart for the derivative with the correct graph of the function O N O 4 er 5 2 4 f f f f A B A C

15 2 Determine the reactions at the supports El is constant 3 6 kN m 2m 2 1 m Prob 15 2 12 kN 2 1 m 3

4 Solve the given IVPS a yv 5y 4y 10 b x y xy y x e x y 0 1 y 0 0 y 0 0 y 0 C y 1 1 y 1 3 y 1 14

an A bank found that in recent years the average monthly charge on its credit card was 1 350 With an improving economy they suspect that this amount has increased A sample of 40 customers resulted in average monthly charge of 1 376 11 with a standard deviation of 182 57 Do these data provide statistical evidence that the average monthly charge has increased Formulate the appropriate hypothesis test and draw a conclusion Use a level of significance of 0 05 Is there sufficient evidence at the 0 05 level of significance that the average monthly charge has increased Determine the null hypothesis Ho and the alternative hypothesis H Ho H 1350 H H 1350 Type whole numbers Compute the test statistic 0 90 Round to two decimal places as needed Using a level of significance of 0 05 what is the critical value 1 68 Round to two decimal places as needed Find the p value for the test 0 184 Round to three decimal places as needed What is your conclusion The p value is the chosen value of a so greater than the null hypothesis There is evidence to conclude that mean is greater than 1 350

A truck with 36 in diameter wheels is traveling at 55 mi h Find the angular speed of the wheels in rad min How many revolutions per minute do the wheels make rad min rpm

Production Budget Healthy Measures Inc produces a Bath and Gym version of its popular electronic scale The anticipated unit sales for the scales by sales region are as follows Northern Region unit sales Southern Region unit sales Total 40 000 25 000 75 000 35 000 115 000 60 000 The finished goods inventory estimated for March 1 for the Bath and Gym scale models is 11 800 and 8 100 units respectively The desired finished goods inventory for March 31 for the Bath and Gym scale models is 15 000 and 7 500 units respectively Prepare a production budget for the Bath and Gym scales for the month ended March 31 For those boxes in which you must enter subtracted or negative numbers use a minus sign Bath Gym Scale Scale Healthy Measures Inc Production Budget For the Month Ending March 31 Expected units to be sold Desired inventory March 31 Feedback Healthy Measures Inc Production Budget For the Month Ending March 31 Total units available Estimated inventory March 1 Total units to be produced Check My Work V Units Bath Scale Units Gym Scale 15 000 118 200 7 500 59 400

A three year project is expected to generate revenues of 600 000 variable costs of 100 000 and fixed costs of 300 000 The annual depreciation is 120 000 and the tax rate is 25 percent What is the annual operating cash flow

ent for fixed assets and 50 000 for net working capital The fixed assets will be depreciated using MACRS and the fixed asset falls into the three year MACRS class Depreciation rates for years 1 and 2 are 0 3333 and 0 4445 The estimated salvage value is 150 000 All of the net working capital will be recouped at the end of the 2 years Management estimates that sales revenues less costs will be 700 000 per year for years 1 and 2 The discount rate is 12 percent and tax rate is 35 percent What are the project s cash flows for years 0 1 and 2 Problem 10 For the two year project in question 9 what is net present

The Depot Restaurant has experienced growing sales and management is looking to expand They currently own a lot on Main Street a good location for a restaurant as indicated by a marketing survey The survey cost was 20 000 The lot was purchased five years ago at a cost of 300 000 Today the property could be sold for 560 000 because of the increase in real estate prices The land will have to be cleared before a new restaurant can be built at a cost of 30 000 The company can then build a new restaurant at an estimated cost of 600 000 Finally the management has recently allocated 100 000 in new executive salaries to the new store What is the cost of this expansion project

7 For the following function fill in the table of information and then graph two cycles of the transformed function using transformations of the parent function Choose an appropriate scale APP a y cos x 1 1 Amplitude Phase shift Max X y Period Vertical shift Min

A project has the following cash flows What is the payback period 2 Year 3 Cash flow 10 000 0 1 40 000 35 000 40 000

of the bond b annual interest and c annual yield 1 Giuseppe Caviness purchases an Internet Inc 100 000 bond at 102 25 that pays 3 5 interest H 2 Sandy and Morry Doran purchase a NYC Municipal 50 000 hond at a quoted price of 84 775 The

Solve the differential equation y 4y 3y e 3x x 1

A T omino is a tile pictured at the right Prove that every 2 x 2 n 1 chessboard can be tiled with T ominoes Eu

Find the orthogonal trajectories of each given family Also sketch several members of each family 1 y e x c 2 y ce x A tank originally contains 200 liters of fresh water i e contains 0 grams of salt Then water containing 1 2 grams of salt per liter is pumped into the tank at a rate of 2 liters per minute and the well stirred mixture leaves the tank at the same rate Find the amount of salt in the tank at time t after the process started

Complete the first two months of an amortization schedule for the fixed rate mortgage Mortgage 111 850 Interest rate 3 75 Term of loan 12 years Complete the first two payments of the amortization schedule below Do not round until the final answer Then round to the nearest cent as needed Payment Total Interest Principal Number Payment Payment Payment Balance of Principal

I List the First Five terms of the sequent an n ti an 1 1 5 3 An n 1

A consumer products company found that 48 of successful products also received favorable results from test market research whereas 14 had unfavorable results but nevertheless were successful That is P successful product and favorable test market 0 48 and P successful product and unfavorable test market 0 14 They also found that 26 of unsuccessful products had unfavorable research results whereas 12 of them had favorable research results that is P unsuccessful product and unfavorable test market 0 26 and P unsuccessful product and favorable test market 0 12 Find the probabilities of successful and unsuccessful products given known test market results that is P successful product given favorable test market P successful product given unfavorable test market P unsuccessful product given favorable test market and P unsuccessful product given unfavorable test market P successful product given favorable test market 0 80 Round to two decimal places as needed P successful product given unfavorable test market 0 35 Round to two decimal places as needed P unsuccessful product given favorable test market Round to two decimal places as needed

8 How does the degree of a polynomial affect its behaviour and solutions and how can we explore the relationship between degree and properties of polynomials TI

The mean is the most sensitive average because it is alre by Determine the mean median mode and midrange for 2 3 4 6 6 7 12 Change the 7 to 10 in part a Determine the mean median mode and midrange Which averages were affected by changing the 7 to 10 Which averages will be affected by changing the 12 to 10 in part a a Select the correct choice below and fill in the answer boxes within your choice Round to the nearest tenth as needed Use a comma to separate answers as needed A The mean is the mode s is are and the midrange is OB The mean is there is no mode and the midrange is D the median is the median is

The value halfway between the lowest and highest values in a set of data is called

the correct choice that completes the senten alue in the middle of a set of ranked data is ca

8 A recovery oriented person centered approach emphasizes which of the following That recovery is the expected outcome OO OO That recovery is not the norm but it is possible That recovery from substance misuse should be the first priority That recovery is possible if individuals comply with treatment recommendations 9 Which strategy is the BEST way to include persons with severe difficulties in person centered planning Create a treatment plan focused on the provider s recommendations Allow a loved one to make planning decisions for the person Be sensitive to and aware of the numerous ways that individuals may communicate their preferences Use association guidelines to determine what is typical for persons with severe difficulties

This problem involves mixed constraints Solve it with the simplex method Assume that all variables are nonnegative Maximize f 5x 7y subject to the following 2x 5y 37 5x y 34 x 2y 4 The maximum value of the objective function is which occurs at x y

Nast Inc is considering Projects S and L whose cash flows are shown below These projects are mutually exclusive equally risky and not repeatable If the decision is made by choosing the project with the higher MIRR rather than the one with the higher NPV how much value will be forgone Note that under some conditions choosing projects on the basis of the MIRR will cause 0 00 value to be lost WACC CFS CFL O a 6 66 O b 7 66 c 0 00 d 9 40 e 6 49 10 75 0 1 100 2 200 1 375 725 2 375 725 3 375 725 4 375 725

O Assume that on January 1 COMCAST issues 100 000 of 5 year 8 coupon bonds payable yielding an effective annual interest rate of 10 Interest is payable annually on December 31 Prepare an amortization table for the bonds for the three years 0 1 2 3 Total Interest Expense Coupon Interest Premium Amortization Premium Balance Bond Payable Net

In an electric instrument called a Wheatstone bridge electric resistances are related by Find R if R 3 02 R 87 50 02 and R 21 00 2 R 0 Simplify your answer Type an integer or decimal R R R R4 L Ri E

Consider the Venn diagram shown below A 6 C 5 11 9 3 8 Determine the following cardinalities n A 20 X n AUB 34 OF n ANT OF B 2 o

A supermarket has been experiencing long lines during peak periods of the day The problem is noticeably worse on certain days of the week and the peak periods sometimes differ according to the day of the week There are usually enough workers on the job to open all cash registers The problem the supermarket manager faces is knowing when to call some of the workers who are stocking shelves up to the front to work the checkout counters Use this information to answer the given questions How might business analytics help the supermarket manager Select all that apply A Business analytics can help to predict customer demand at the checkout counters and determine the appropriate number to have open B A model might be developed to find the number of checkout counters to open to ensure a reasonable wait time or maximize customer throughput C The manager can use analytics by examining historical data on customer flow during each hour of each day of the week and month A D The manager can use analytics to schedule the minimum necessary or predicted number of workers for cash registers in order to ensure that none of the cash registers are idle E A model can be developed to forecast customer demand for a set amount of time in the future

There are 800 deer in a national park and the deer population has been growing at an annual rate of 4 1 Write an equation to represent y the number of deer in the park n years from now 2 Graph the equation Use values of n from 0 to 40 in steps of 5 years 3 Use the graph to estimate when the deer population is 1000 4 Use the graph to estimate how long it will take for the current

Make a plot showing the median departure delay by month along with a shaded region indicating the lower and upper quartiles like the one below Hint Use a and but first think about how to compute the summaries that you ll need for each of these layers Make a plot showing the median departure delay by hour along with a shaded region indicating the lower and upper quarties like the one below departure delay 20 10 0 3 15 month Use flights from library nycflights13 to solve

For example assume Sophia wants to earn a return of 7 00 and is offered the opportunity to purchase a 1 000 par value bond that pays a 7 00 coupon rate distributed semiannually with three years remaining to maturity The following formula can be used to compute the bond s intrinsic value Intrinsic Value 1 C 1 0 Unknown Variable Name A B Complete the following table by identifying the appropriate corresponding variables used in the equation IS 1 0 1 0 1 0 Based on this equation and the data it is value equal to 1 000 Semiannual required return Variable Value 1 000 to expect that Sophia s potential bond investment is currently exhibiting an intrinsic Now consider the situation in which Sophia wants to earn a return of 5 00 but the bond being considered for purchase offers a coupon rate of 7 00 Again assume that the bond pays semiannual interest payments and has three years to maturity If you round the bond s intrinsic value to the nearest whole dollar then its intrinsic value of rounded to the nearest whole dollar is its par value so that the bond

20 2 points Determine the present value of monthly car payments of 590 at 6 9 per year compounded monthly for two years Show your steps 851 43 a b 13191 06 13644 67 d 15137 03

The following information pertains to the inventory of Parvin Company during Year 2 Beginning Inventory Purchased Purchased 400 units 30 2 000 units 35 600 units 38 January 1 April 1 October 1 During Year 2 Parvin sold 2 700 units of inventory at 90 per unit and incurred 41 500 of operating expenses Parvin currently uses the FIFO method but is considering a change to LIFO All transactions are cash transactions Assume a 30 percent income tax rate Parvin started the period with cash of 75 000 inventory of 12 000 common stock of 50 000 and retained earnings of 37 000 Determine the cash flow from operating activities under FIFO and LIFO Amounts to be deducted should be indicated with minus sign

2 12 Classify each of the frames as statically determinate or indeterminate If indeterminate specify the degree of indeterminacy All internal joints are fixed connected a b c

Sec 2 2 2 5 2 11 Classify each of the structures as statically determinate or indeterminate If indeterminate specify the degree of indeterminacy a b d

4t 6et and B t 4 5et Let A t a Find SA tydt 1 9 cost 8 sin t 3 sint 6 cost b Find B t dt d c Find A t B t dt

annually Unless otherwise indicated assume monthly payments are made Unless otherwise indicated assume the interest rate remains constant during the amortization period ur answers can be entered directly on this assignment but please hand in all rough work as ell Most lending institutions allow mortgage payments to be made monthly bi monthly twice a month or weekly Most even allow accelerated weekly mortgage payments With this option the weekly payment is calculated as a monthly payment divided by 4 1 a Complete this table for the mortgage defined above The equivalent interest rate interest for each compounding period has been calculated for you as discussed in section 6 4 in your text The Interest saved is the difference between the Total intere paid for monthly compounding and the Total interest paid for the compounding perio being calculated Payment Equivalent Number Total Frequency Interest rate Monthly 3 957 Bi monthly 3 954 Weekly 3 952 Accelerated 3 952 weekly payments number per year payments 1137 Payment Total amount paid Total interest paid Interest saved 0

Definition A complex fraction is a fraction where the numerator denominator or both contain a fraction Simplifying complex rational expressions Method 1 Division Method Step 1 Rewrite the complex fraction as a division use parentheses top expression bottom expression Step 2 Perform addition subtraction to combine the expressions in each group into a single rational expression using the LCD if necessary Step 3 Perform division Step 4 Simplify Method 2 Multiplying the LCD Step 1 Find the least common denominator of both the top and the bottom together Step 2 Multiply each term by the LCD and simplify Step 3 Simplify the resultant rational expression 5 Simplify Method 1 Method 2 Example 2 x 1 X 1 X 2 1 1 3 2 1 1 2 x 1 1 x 1 2x 2 x 1 x 1 2x 2 1 x 1 2x 3 x 1 2 x 1 X 2x 3 LCD x 1 x 1 x 1 2 x 1 x 1 x 1 X 1 Cross cancel x 1 2x 2 1 x 2x 3 x

a How would you show that for any whole number a a 0 a if you were starting from our definition of addition and the audience is your university class b How would you show that for any whole number a a 0 a if you were talking to your class of fourth graders a Choose the correct answer below OA O is the cardinal number of the empty set that is n 0 If the set A has a elements in it n A a then n A n n A U because A and are disjoint But A U A since there are no elements in to add to the set A Thus n A U n A a OB Start with two disjoint sets of the same cardinality A and B with n A n B a Then write the equation Since n A n B a n AUB a Since they are disjoint AnB Then a 0 n AU ANB which is equal to n AUB a OC Use manipulatives to show that the union of a collection with a collection with no elements has the same number of elements as the first collection OD O is the cardinal number of the empty set that is n 0 If the set A has a elements in it n A a then n A n n An because A and are disjoint But An A since there are no elements in to add to the set A Thus n AU n A a

4 The discussion of electricity costs in section 8 6 stated that coal costs of 1 00 1 50 per million BTU are equivalent to about 24 36 per ton and that natural gas costs of 2 00 5 00 per million BTU correspond on an equivalent energy basis to 12 30 per barrel of oil Use the data on fuel properties in table 8 1 to confirm these equivalencies

For the function f Z Z f n 31 complete the questions below 1 Graph the function use the graphing paper provided 2 Determine if the function f is a one to one function injective Justify your answer 3 Determine if the function f is an onto function surjective Justify your answer 4 Is f a bijection Explain why or why not Show

If one must always move upward or to the right on the grid shown below how many paths are there from A to B B How many paths are there from A to B

8 4x f 4 8 t Which of the following is the complex Fourier series representation of the signal

Object a Dimension 2 Height cm cm 1 Your measurement 2 3 4