Mathematical Induction Questions and Answers

Let p q and r be the propositions p You get an A on the final exam q You do every exercise in this book r You get an A in this class Write the following propositions using p q and r and logical connectives including negations a To get an A in this class it is necessary for you to get an A on the final exam b You will get an A in this class if an only if you either do every exercise in this book or get an A on the final exam Write your answer in the space provided For the toolbar press ALT F10 Por ALT 2510 ME

Find the x and y intercepts of the rational function If an answer does not exist enter DNE s x 3x x 7 x y x intercept y intercept x y x x

Which of the following sentences are propositions Select all that apply If x 4 then x 5 0 Happy 4th of July x is positive For any two real numbers a and b a b b a Sydney is the capital of Australia 3 is a prime number DEREN

3 Find a logical expression involving only the symbols A and as well as parentheses that is logically equivalent to p q q p

3 of 4 Book Print Assessment 4 Which of the following shows Which of the following shows the journal entry that is required to recogni Multiple Choice Account Titles Uncollectible Accounts Expense Allowance for Uncollectible Accounts De

15 art 1 of 2 45 ints eBook Company A starts the second accounting perind and 20 000 in retained earnings 1 Company A loans Company B 12 000 on Oc The note carried a 4 interest rate and a 1 ye Beg Bal 1 Adjusting End Bal Cash Balance Sheet Assets Notes Rec Interest Rec

17 Part 1 of 3 Lever inc provided 10 000 of Services to a CD The customer used a credit card to purchase the st The credit card company charged a 5 fee Denver received payment from the credit card com Assets Cash Accts LEER TORE Equity R Com

A perfect gas enclosed by an insulated upright cylinder with a weightless piston on top is at equilibrium conditions p1 V1 and T1 A weight is placed on the piston After a number of oscillations the motion subsides and the gas reaches a new equilibrium at conditions p2 V2 and 72 Find the temperature ratio T2 71 in terms of the pressure ratio p2 p1 a Show that the change in entropy is given by S S Rln 2 S S1 R b Show that if the initial disturbance is small such that 1 where 1 then f 1 y 1 a Y 27 x 1 c Using isentropic relations show that the frequency of small oscillations about the equilibrium position is 178 PA 27 L W d Justify the isentropic assumption in part c using your result from part b How does the result in part c compare with the frequency of a pendulum where is the height of the cylinder and Wis the weight of the mass on the piston

Assume you are the manager of a shop that assembles power tools You have just received an order for 50 chain saws which are to be shipped at the start of week 8 Pertinent information on the saws follows Item Lead Time weeks On Hand Components Saw 2 A B C D LL E 1 1 2 A 2 B 1 C 2 Saw 2 LL Develop the material requirements plan for component E using lot for lot ordering for all items Leave no cells blank be certain to enter 0 wherever required 1 Assume you are the manager of a shop that assembles power tools You have just received an order for 50 chain saws which are to be shipped at the start of week 8 Pertinent information on the saws follows 2 Item Lead Time weeks On Hand Components 15 A 2 B 1 C 4 E 3 D 1 D 2 F 3 E 2 D 2 2 15 1 E 1 10 5 2 65 20 10 30 10 5 65 A 2 B 1 C 4 E 3 D 1 D 2 F 3 E 2 D 2 20 10 30

4 The flow chart for Group B Liability Exclusion walks you through the process of determining whether or not there is liability coverage for an exposure What is the second question in the process 9 ProA Is the vehicle excluded B Is the person an insured C Is the person excluded D None of the above ney

The Resource Conservation and Recovery Act RCRA was passed in 1976 to address issues associated with hazardous waste The act established a system that regulates the handling of hazardous waste from its origin to its disposal Which action is regulated by this act Subsidizing installation of solar panels on commercial buildings Identifying placement of wind turbines on private property Utilizing crop rotation practices on private farmland Recycling used motor oil at designated facilities

A company is considering two insurance plans with coverage and premiums shown in the table For example this means that 50 buys Fire Theft Liability one unit of plan A consisting of 10 000 fire and theft insurance and 180 000 of liability insurance Answer parts a and b Premium Policy A 10 000 180 000 50 units of Policy A and a The company needs at least 300 000 fire and theft insurance and at least 3 600 000 liability from these plans How many units should be purchased from each plan to minimize the cost of the premiums What is the minimum premium The company should purchase Policy B 15 000 120 000 40 units of Policy B for a premium of

10 10 Question 5 15 Match each polynomial function to its graph Show relevant work for partial credit a f x x 2 x 1 b f x x x 2x c f x x x 1 x 2 d f x x 2 x 1 5 5 5 10 10 10 5 10 5 10 10 Mich Duroa 10 10 5 0 5 10 10 5 10 10 10

Given that U 2y 2 3x2 4xyz 3 Ax Ay and Az denote the errors in x y and z respectively such that x y z 1 5 and Ax Ay Az 0 001 Find the maximum error in U

105 50 35 105 85 20 STATION CUT DISTANCE FT CUT AREA SF A 50 SF A 35 SF STA 15 75 30 AVG CUT AREA SF Total Cut Volume CF Total Net Earthwork A 120 CUT VOLUME CF A 105 SF FILL AREA SF CY AVG FILL AREA SF Total Fill Volume CF FILL VOLUME CF

8 Find the measurement of all the angles Find the value of x and y 3x 15 120 AV

124 484 236 236 484 56 304 276 524 positive angle and a negative angle that is coterminal to the given angle QUESTION 20 Use an addition or subtraction formula to find the exact value sin 31x 18 O 1 1 COS 2n 31 9 cos 18 sin 2 9

What is the probability rock paper scissors in a row A B 3 of winning 2 rounds of 1 3 2 C 6 D 1

Read the following quote Use your knowledge and information from the lesson to answer the question below Leadership in telecommunications is also essential since we are now in the age of e commerce Michael Oxley What do you think Michael Oxley means by the term e commerce O Mail order telephones O Order by phone catalogs O Internet buying selling and trading O Computer sales Complete Later Complete

Landmarks are placed along the road from London to Edinburgh and the distance between each landmark is 16 1 km The first milestone placed on the road is 124 7 km from London and the last milestone is near Edinburgh The length of the road from Edinburgh is 667 km a After analyzing the problem can this problem be solved with sequences If your answer is yes explain what kind of sequence and why b Find the distance between the fifth milestone and London c Determine how many milestones there are along the road

A chest shaped as a rectangular prism can hold 432 wooden cube blocks with edge lengths of ft What is the volume of the chest Enter your answer in the box

Choose the best unit of measure by writing inch foot yard ounce pound ton cup quart or gallon 12 serving of trail mix 14 weight of a newborn kitten 13 height of a person 15 gasoline Measurement Conversions 16 Michael is 4 feet tall Explain how Michael could find his height in inches Then explain how he could find his height in yards

A cabinetmaker gets paid monthly at a rate of 350 for each cabinet she completes Last month she made 6 cabinets and got halfway through a 7t cabinet How much money was she paid last month OA 1225 B 2100 C 2450 D 2275

Question 9 The Federal Reserve was created in O 1911 O 1913 O 1931 Points 2 O 1941

YOUNGRADES 183415 Actes Samantha gathered the following information on a given day at the dog park There are 32 dogs playing at the dog park 15 of the dogs are puppies 11 of the dogs are not puppies and have long hair There are 6 more dogs that have long hair than dogs that do not have long hair Fill in the table completely to represent Samantha s data Dogs with Long Hair Dogs That Do Not Have Long Hair Total Dogs That are Puppies Dogs That are Not Puppies 111025 Total

In addition to providing immediate relief to developing nations foreign aid is used for capital flight comparative advantage O investment subsistence farming Complete Later Complete 9

Match the appropriate word from the Word Bank to the correct scenario Foreign Aid Work Bank I Economic Assistance II Technical Assistance III Military Assistance IV Emergency Aid O I II III IV O III I II IV Answer Scenario The president of the United states deploys troops to a foreign nation to assist after an earthquake American teachers are sent to a foreign country to help teach students The United States loans farm equipment to help farmers of a foreign nation become more productive The president of the United States deloys troops to a foreign nation with the mission of developing important infrastructure

Choose the correct answer The economic model that displays income as moving continuously between businesses and consumers is called equilibrium balance the circular flow of income O Keynesian economics Ofree market economics

Which of the following is an example of government regulation of externalities O Legislation that fines companies for dumping by product waste in rivers O Legislation that prohibits the sale of certain drugs O Legislation that promotes competition within industries Legislation that sets a minimum wage

Use the simplex method to maximize the following Maximize f 3x1 9x2 subject to 4x1 2x2 6 2x1 x2 8 x1 3x2 24 1 0 x 0 If no solutions exist enter DNE in all answerboxes 21 x2 X2

An initial population of 820 quail in function to model the quail populati 820 1 23 1526 a x M

Find the 5 number summary for the data shown X 1 8 2 5 3 5 8 10 2 11 8 12 9 22 3 22 9 5 number summary 2 5 X 3 5 10 2 11 8 X 22 9 Use the Locator Percentile method described in your book not your calculator

What is the maximum number of presidents the Chairman of the Federal Reserve can serve under O 1 O2 O 3 O Indefinite

Let W Wn be a random sample from N 7 4 with 7 Find a minimal suf ficient statistic for y Justify your answer

Karnaugh Maps are useful for finding minimal implementations of Boolean expressions with only a few variables However they can be a little tricky when don t cares X are involved Using the following K Maps 8 cd ab 00 01 11 10 00 X 0 01 0 0 100 X 0 11 10 1 0 0 0 1 X 1 1 cd ab 00 01 11 10 00 1 1 0 X 11 01 X 1 0 0 0 1 X 1 10 i Find the minimal sum of products expression Show your groupings ii Find the minimal product of sums expression Show your groupings iii Are your solutions unique If not list and show the other minimal expressions MRS MSD2 1 0 0 1

SHOW SOLUTION Consider these Make or Buy alternatives Make Annual fixed cost rent capital is 2000 Unit variable cost labor material transportation is 10 raft Sales price is 20 raft Buy Annual fixed costs is 9000 Unit variable cost is 5 raft Sales price is 20 raft st what demand quantity they will be indifferent between MAKE and BUY alternatives how your solution below with all labels and units

Find the quotient x48x 41x 8 x 3 The quotient is and remainder using long division The remainder is

5 Tom and Jenny are newlyweds in their late 20s Together they earn 90 000 a year They have a significant start on their retirement savings and several thousand dollars in a regular savings account They also have 5 000 invested in various stocks and government bonds Level of risk Your reasoning

3 Jeremiah is 23 years old and single He started his own auto repair business and is able to only just started saving for retirement He also has 38 000 invested in a classic car that he pay himself a small salary He does not have any money in a personal savings account and restored himself Level of risk Your reasoning

Use a linear approximation to approximate 3 7 as follows Let f x 2 The linear approximation of f x at x 4 can be written as L x Using this we find our approximation for 3 7 is 3 7

9 A sample of tritium 3 decayed to 94 5 of its original amount after a year a What is the half life of tritium 3 b How long would it take the sample to decay to 20 of its original amount

7 The half life of cesium 137 is 30 years Suppose we have a 100 mg sample I a Find the mass that remains after t years b How much of the sample remains after 100 years c What is the rate of decay after 100 years d After how long will only 1 mg remain

51 ALLOCATION OF LABOR Using x hours of skilled labor and y hours of unskilled labor a manufacturer can produce Q x y 10xy 2 units Currently 30 hours of skilled labor and 36 hours of unskilled labor are being used Suppose the manufacturer reduces the skilled labor level by 3 hours and increases the unskilled labor level by 5 hours Use calculus to determine the approximate effect of these changes on production

10 Problems and Applications Q10 Consider public policy aimed at smoking Studies indicate t

A company manufactures two types of electric hedge trimmers one of which is cordless The cord type trimmer requires 2 hours to make and the cordless model requires 4 hours The company has only 800 work hours to use in manufacturing each day an packaging department can package only 300 trimmers per day If the company profits are 36 50 for the cord type model and 73 00 for the cordless model how many of each type should the company produce per day to maximize profits Scenario 1 with the smaller number of cord type trimmers corded models cordless models Scenario 2 with the larger number of cord type trimmers

7 Suppose you want to complement the right 4 bits of a byte and leave the other 4 bits unchanged What mask must you use together with what operation 4 points

Graph the function z x 4 X for 4 x 2 for 2 x 1 x 1 for x 1

Which of the following were goals of the civil rights movement 2 ending criminal justice practices that discriminatorily targeted Black people for policing and prosecution wefare rights 3 ending the Vietnam War

The FBI sent a letter to Martin Luther King Jr urging him to commit suicide T True F False

Use the six step procedure to grap f x 2x x 2