Mathematical Induction Questions and Answers

0 1 point A bacteria population quadruples every hour What type of relation best describes how the population is related to time

49 How does subjective value make gains from trade possil

Use the following to answer question 20 Figure The Demand and Supply of Wheat Price per bushel 10 9 8 7 C D 654 3 2 1 0 x 2 S 4 6 8 10 12 Quantity of wheat thousands of bushels per period D 20 Figure The Demand and Supply of Wheat Look at the figure The Demand and Su of Wheat If a price of 10 temporarily exists in this market A a shortage of 10 000 bushels will result B a shortage of 8 000 bushels will result a surplus of 8 000 bushels will result a surplus of 4 000 bushels will result

Bianca and Meredith are sisters Meredith s height is of Bianca s height plus 32 inches Meredith is 60 inches tall Write an equation to find Bianca s height in inches

Q1 10 Compare the annual CO2 emission in kg year for a 120 000 BTU hr residential furnace assuming the following fuels a natural gas b fuel oil The furnace in average funs hrs day for 160 days year AFUE of natural gas furnace is 85 and that of oil burning furnace is 75

20 pts An investor can design a risky portfolio based on two stocks A and B Stock A has an expected return of 18 and a standard deviation of return of 20 Stock B has an expected return of 14 and a standard deviation of return of 5 The correlation coefficient between the returns of A and B is 50 The risk free rate of return is 10 The expected return on the optimal risky portfolio is

Big time Floats makes and sells floats shaped like mythical beasts and their weekly cost function is given by C 3100 16 0 4z where is the cost in USD when a floats are made each week How many floats must be made each week in order to minimize the average cost per float floats per week NOTE Round to 3 decimal places if needed

The greatest problem facing the United States during the period of Manifest Destiny was whether Native Americans would be moved to North Carolina whether states would let women vote whether labor unions would be allowed to form whether slavery would expand across the United States into newly acquired territory

The Valuation of Financial Assets LO7 7 16 Bondholders expected rate of return Sakara Co bonds are selling in the 1 000 par value If they are purchased at the market price what is the expected market for 1 045 These 15 year bonds pay 7 percent interest annually holders expected rate of return The market price is 900 for a 10 year bond 6 percent interest 3 percent semiannually What is the rate of return MyLan on a

Question 3 Learning A plant draws 400kW with a lagging power factor of 0 75 Determine the rating in KVAr of a compensating capacitor to bring the power factor to 0 85 Draw the power riangle for the compensated load 16

Question 9 For the graph below determine if it represents a function that is increasing or decreasing Select an answer v Select an answer Increasing Decreasing

Let r be a compound proposition involving p and q and suppose the truth table for r is given below PqT 001 010 101 111 Which of the following propositions implies r In other words for each proposition s below is it true that s r Select al that apply DA P OB P OC pVq

Let p q r be the following propositions p Grizzly bears have been seen in the area q Hiking is safe on the trail r Berries are ripe along the trail Match each proposition with its symbolic representation 1 For hiking on the trail to be safe it is necessary but not sufficient that berries not be ripe along the trail and for grizzly bears not to have been seen in the area 2 Berries are ripe along the trail but grizzly bears have not been seen in the area 3 Hiking is not safe on the trail whenever grizzly bears have been seen in the area and berries are ripe along the trail 4 If berries are ripe along the trail hiking is safe if and only if grizzly bears have not been seen in the area 5 Grizzly bears have not been seen in the area and hiking on the trail is safe but berries are ripe along the trail 6 It is not safe to hike on the trail but grizzly bears have not been seen in the area and the berries along the trail are ripe A pq B p q C q p r D r q p E p r q F p q G p q r H q r p r p q I TAP

For each of the statements below state True T or False F or pick the correct option Explain your answer in 1 2 sentences For every part below 1 point for correct assertion and 1 point for correct explanation a T F Ridge regression does not have a closed form solution b T F If we have m values for a hyperparameter of a classifier and we use k fold cross validation for hyperparameter tuning then we train the classifier mk times from scratch c T F Consider a linear function basis o x 1 log x x2r3 where x R There exists a closed form solution for minimizing the mean squared error for the hypothesis he x eTo x If True state the solution Otherwise give a justification d Which of the following is a major drawback of linear regression A It assumes a linear relationship between the independent and dependent variables B It can handle only numerical data C It is not suitable for high dimensional data D It is prone to overfitting E None of the above e Which of the following is a common method for preventing overfitting in machine learning A Increasing the complexity of the model B Decreasing the size of the training data set C Regularization D Using a simpler evaluation metric

Part III Order of Operations 1 24 9 2 6 3 2 35 17 2 5 3 4 9 3 8 2 Algebra 1 Review Sheet for Test 1 4 26 25 11 2 Part IV Evaluating Expressions 1 n 13 n 5 for n 8 2 8y 3x 2n when x 5 y 2 and n 3 3 2x y z when x 10 y 4 and z 8 2 17 9 0 4 8 6 8 4 8 41 4 5k mn when k 4 m 3 and n 5 100 substitate jos Pempas 9121

List category and average price of all tasks in each category for those categories ending with a letter M or N

1 List name balance and city of all clients in city Sunland

The following table lists some of the empirical results that were obtained in experiments in cross breeding plants Assume that genetically pure tall plants were cross bred with genetically pure shor plants Use this information to assign the probability that a second generation plant will be short How consistent is this with the theoretical results expected from cross breeding Characteristics That Were Crossbred Tall vs short Smooth seeds vs wrinkled seeds First Generation Plants All Tall All smooth seeds Second Generation Plants 753 tall 221 short 5 407 smooth 1 556 wrinkled The probability that a second generation plant will be short is Round to the nearest hundredth as needed

E7 Let B 0 1 consist of the bits 0 and 1 Show that B is a Boolean algebra i e that the bits 0 and 1 form a two element Boolean algebra As said before a logic circuit can be designed using elementary gates where the output from an AND gate or an OR gate or a NOT gate is used as an input to other such gates in tlie circuitry The different levels of voltage in these circuits starting from the input lines move only in the direction of the arrows as shown in all the figures given below For instance one combination of tlie three elementary gates is shown in Fig 9 Fig 9 A logic circuit of elementary gates Now let us try to see the connection between logic circuits and Boolean expressions We first consider the elementary gates For a given pair of inputs x and x2 the output in the case of each of these gates is an expression of the form x A x2 or x V x or x Next let us look at larger circuits Is it possible to find an expression associated with a logic circuit using the symbols A V and Yes it is We will illustrate the technique of finding a Boolean expression for a given logic circuit with tlie help of some examples But first note that the output of a gate in a circuit may serve as an input to some other gate in the circuit as in Fig 9 So to get an expression for a logic circuit the process always moves in the direction of the arrows in the circuitry With this in mind let us consider some circuits Example 7 Find the Boolean expression for the logic circuit given in Fig 9 above 1 Solution In Fig 9 there are four input terminals Let us call themi X1 X2 X3 and x4 So x and x2 are inputs to an OR gate wliicli gives X V x2 as an output expression see Pig 9 a Similarly the other two inputs x3 arid x4 are inputs to an AND gate They will give x3 A x4 as an output expression This is in turn an input for a NOT gate in the circuit So this yields x3 Ax4 as the output expression Now both the expressions x V x2 and x3 Ax4 are inputs to the extreme right AND gate in the circuit So they give x V x2 x3 x as the final output expression which represents the logic circuit X1 X X3 X1 V X X3 X4 X3 X4 Fig 9 a x V X X X Boolean A

operations with rational numbers Also 7 NS 2a 7 NS 2c 7 EE 3 nur and mathematical problems involving the four 1 Solve One month Kaeden made 3 withdrawals for 20 and 1 withdrawal for 80 from his account How did the withdrawals change the amount in his account 2 Solve Hannah made four withdrawals of 20 from her checking account She also wrote a check for 215 By how much did the amount in her checking account change 3 Solve Ned took a test with 25 questions He lost 4 points for each of the 6 questions he got wrong and earned an additional 10 points for answering a bonus question correctly How many points did Ned receive or lose overall gift card to rent a tiller for 4 days It costs 35 per day to rent b has a gift card for a local lawn and garden s She also buys a rake for 9 Find the change to the value on her gift card 5 Solve Evaluate the expression 6 5 12 6 Evaluate the expression 6 7 15 13

The price of a certain ice cream cone is increasing at the rate of 15e0 06t cents per year where t is measured in years and t corresponds to 2014 Find the total change in price between the years 2014 and 2027 Round your answer to the nearest cen

point y dragging statements from the left column to the right column below give a proof by induction of the following statement For all n 1 we have 1 1 2 3 5 8 Fn Fn 2 1 where Fr is the nth Fibonacci number F 1 F 1 and Fn Fn 1 Fn 2 he correct proof will use 8 of the statements below Statements to choose from Your Proof Put chosen statements in order in this column and press the Submit Answers button Let P n be the statement 1 1 2 3 Fn Fn 2 1 That is assume 1 1 2 3 Fk Fk 2 1 For the base case note that P 1 is true becuase F 1 2 1 F3 1 Now assume that P k is true for an integer k 1 Then adding Fl 1 to both sides of this equation we get 1 1 2 3 Fe F 1 Fk 1 Fk 2 1 Using the recursive formaul for Fibonacci numbers this simplifies to 1 1 2 3 Fe 1 Fk 3 1 Therefore P k 1 is true Therefore by the Principle of Mathematical Induction P is true for all m

art 1 of 2 ints Skipped eBook Print eferences Required information The following information applies to the questions displayed below Golden Corporation s current year income statement comparative balance sheets and additional information follow For the year 1 all sales are credit sales 2 all credits to Accounts Receivable reflect cash receipts from customers 3 all purchases of inventory are on credit 4 all debits to Accounts Payable reflect cash payments for inventory and 5 any change in Income Taxes Payable reflects the accrual and cash payment of taxes Assets GOLDEN CORPORATION Comparative Balance Sheets December 31 Accounts receivable Inventory Total current assets Equipment Accumulated depreciation Equipment Total assets Liabilities and Equity Accounts payable Income taxes payable Total current liabilities zquity Common stock 2 par value Paid in capital in excess of par value common stock B Current Year 172 000 95 000 613 000 880 000 356 500 162 000 1 074 500 103 000 36 000 139 000 601 600 210 400 133 600 Prior Year 115 800 79 000 534 000 728 800 307 000 108 000 927 800 79 000 29 100 108 100 576 000 172 000 71 700

1 point By dragging statements from the left column to the right column below give a proof by induction of the following statement For all n 0 8 divides 32 1 The correct proof will use 8 of the statements below Statements to choose from We have 32 k 1 13 32k 1 9 3 k 1 9 3 k 9 9 1 9 32k 1 9 1 9 3 k 1 8 Now assume that P k is true for an arbitrary integer k 0 Then 32k 1 8j for some integer j Let P n be the statement 8 divides 32 1 Therefore by the Principle of Mathematical Induction P n is true for all n 0 Thus P k 1 is true So 32 k 1 1 9 8j 8 8 9j 1 which is divisible by 8 Note that the base case P 0 is true since 32010 which is divisible by 8 Your Proof Put chosen statements in order in this column and press the Submit Answers button

1 point Suppose you wanted to prove the following statement by mathematical induction 2 4 6 2n n n 1 for all n 1 What would the first line of a proof by induction be OA Let P n be the statement 2 4 6 2n n n 1 B Let P n 2 4 6 2n C Suppose P n n n 1 for all n 1 D Assume P n is true for all n 1 E Let P n be the statement 2 4 6 2n n n 1 for all n 1 What would you need to show to establish the base case OA Show that P 1 is true that is that 2 1 1 1 B Show that P 2 is true since the sum starts with 2 OC Show that 2 4 6 2n P 1 D Show that P 0 P 1 and P 2 are true E There is no need to establish a base case since the sum has at least four terms What is the first line of the inductive case for this proof OA Assume P k is true for some arbitrary k 1 that is that 2 4 6 2k k k 1 B Assume P k is true for some large k 1 say that 2 4 6 432 216 217 C Assume P k implies P k 1 for all k z 1 OD Assume P k is true for all kz 1 that is that 2 4 6 2k k k 1 OE Assume P k and P k 1 are both true for an arbitrary k 1 that is that 2 4 6 2k k k 1 and 2 4 6 2k 2k 2 k 1 k 2 www

In a proof by mathematical induction that a statement P n is true for all n 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 0 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 F That assuming P k is true for an arbitrary k 0 we can prove that P k 1 is true

If 12 000 is invested at 4 5 for 30 years find the future value if the interest is compounded the following ways Round your answers to the nearest cent a annually b semiannually c quarterly d monthly e daily N 360 f every minute N 525 600 9 continuously h simple not compounded

1 point A and B are n x n matrices Check the true statements below A Adding a multiple of one row to another does not affect the determinant of a matrix OB The determinant of A is the product of the pivots in any echelon form U of A multiplied by 1 where r is the number of row interchanges made during row reduction from A to U c If the columns of A are linearly dependent then det A 0 OD det A B det A det B

S The equity sections for Atticus Group at the beginning of the year January 1 and end of the year December 31 follow Stockholders Equity January 1 Common stock 4 par value 100 000 shares authorized 30 000 shares issued and outstanding Paid in capital in excess of par value common stock Retained earnings Total stockholders equity Stockholders Equity December 31 Common stock 4 par value 100 000 shares authorized 35 200 shares issued 4 000 shares in treasury Paid in capital in excess of par value common stock Retained earnings 40 000 restricted by treasury stock Less cost of treasury stock Total stockholders equity The following transactions and events affected its equity during the year January 5 March 20 April 5 July 5 July 31 August 14 October 5 Declared a 0 40 per share cash dividend date of record January 10 Purchased treasury stock for cash Declared a 0 40 per share cash dividend date of record April 10 Declared a 0 40 per share cash dividend date of record July 10 120 000 80 000 320 000 520 000 Declared a 208 stock dividend when the stock s market value was 12 per share Issued the stock dividend that was declared on July 31 Declared a 0 40 per share cash dividend date of record October 10 140 800 121 600 420 000 682 400 40 000 642 400

pped Book Print rences Kohler Corporation reports the following components of stockholders equity at December 31 of the prior year Common stock 10 par value 100 000 shares authorized 45 000 shares issued and outstanding Paid in capital in excess of par value common stock Retained earnings Total stockholders equity During the current year the following transactions affected its stockholders equity accounts January 2 Purchased 4 000 shares of its own stock at 15 cash per share January 5 February 28 July 6 August 22 September 5 Directors declared a 4 per share cash dividend payable on February 28 to the February 5 stockholders of record 450 000 70 000 370 000 890 000 Paid the dividend declared on January 5 Sold 2 000 of its treasury shares at 19 cash per share Sold 2 000 of its treasury shares at 11 cash per share Directors declared a 4 per share cash dividend payable on October 28 to the September 25 stockholders of record October 28 Paid the dividend declared on September 5 December 31 Closed the 368 000 credit balance from net income in the Income Summary account to Retained Earnings Required 1 Prepare journal entries to record each of these transactions 2 Prepare a statement of retained earnings for the current year ended December 31 3 Prepare the stockholders equity section of the balance sheet as of December 31 of the current year Complete this quest Check my work

5 rt 2 of 2 42 pints York s outstanding stock consists of 60 000 shares of cumulative 8 0 preferred stock with a 5 par value and also 280 000 shares of common stock with a 1 par value During its first four years of operation the corporation declared and paid the following total cash dividends Note Round your Dividend per Preferred Share answer to 3 decimal places Annual Preferred Dividend Year 1 Year 2 Year 3 Year 4 Totals Par Value per Preferred Share 5 00 Total Cash Dividend Paid Answer is complete but not entirely correct Dividend per Preferred Share 13 200 22 000 240 000 390 000 665 200 Dividend Rate Paid to Preferred 0 1 0 400 Paid to Common 13 200 22 000 240 000 X 390 000 x 665 200 Number of Preferred Shares Dividends in Arrears at year end 13 200 22 000 X 24 000 X 24 000 X 83 200 60 000 24 000 Preferred Dividend 0x 0x 216 000 X 366 000 X Return to question

pok int ences Common stock 10 par value 89 000 shares authorized issued and outstanding Paid in capital in excess of par value common stock Retained earnings Total stockholders equity 1 Prepare journal entries to record the following transactions for Sherman Systems a Purchased 6 700 shares of its own common stock at 42 per share on October 11 b Sold 1 425 treasury shares on November 1 for 48 cash per share c Sold all remaining treasury shares on November 25 for 41 cash per share 2 Prepare the stockholders equity section after the October 11 treasury stock purchase Complete this question by entering your answers in the tabs below Required 1 Required 2 Prepare the stockholders equity section after the October 11 treasury stock purchase Revised Stockholders Equity Section of Balance Sheet After October 11 Total contributed capital 890 000 301 000 1 000 000 2 191 000 Check my work

A pharmaceutical 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 th salesperson to meet with each doctor List those schedules Click to view the doctors availability A Dr Brown Wed at 9 00 Dr Garcia Mon at 10 00 Dr Lopez Wed at 9 00 B Dr Brown Thu at 9 00 Dr Garcia Mon at 9 00 Dr Lopez Thu at 9 00 c Dr Brown Thu at 9 00 Dr Garcia Mon at 9 00 Dr Lopez Mon at 10 00 D Dr Brown Wed at 9 00 Dr Garcia Mon at 9 00 Dr Lopez Wed at 9 00 E Dr Brown Thu at 9 00 Dr Garcia Mon at 10 00 Dr Lopez Wed at 9 00 F Dr Brown Wed at 9 00 Dr Garcia Mon at 9 00 Dr Lopez Mon at 10 00 G Dr Brown Thu at 9 00 Dr Garcia Mon at 10 00 Dr Lopez Mon at 10 00 H Dr Brown Wed at 9 00 Dr Garcia Mon at 10 00 Dr Lopez Mon at 10 00 Dr Brown Wed at 9 00 Dr Garcia Mon at 10 00 Dr Lopez Thu at 9 00 J Dr Brown Mon at 10 00 Dr Garcia Mon at 9 00 Dr Lopez Mon at 10 00 K Dr Brown Mon at 10 00 Dr Garcia Mon at 10 00 Dr Lopez Wed at 9 00 L Dr Brown Thu at 9 00 Dr Garcia Mon at 9 00 Dr Lopez Wed at 9 00 M Dr Brown Mon at 10 00 Dr Garcia Mon at 9 00 Dr Lopez Wed at 9 00 N Dr Brown Mon at 10 00 Dr Garcia Mon at 10 00 Dr Lopez Mon at 10 00 O Dr Brown Mon at 10 00 Dr Garcia Mon at 9 00 Dr Lopez Thu at 9 00 L GPS

3 olve each quadratic equation using the quadratic formula Round to two decimal b 4x 3x 8 0 ay 2x 2x 17x 27 0

An equestrian club has eight members If the club wants to select a president vice president and treasurer all of whom must be different in how many ways can this be done How many ways can the three positions be filled U

15 1 point Which of the following is equivalent to the expression a 9x 88 b 144x y c 9x y 71 d x 88 18

An article in Nature Genetics Vol 34 1 2003 pp 85 90 Treatment Specific Changes in Gene Expression Discriminate in Vivo Drug Response in Human Leukemia Cells reported the study of gene expression as a function of treatments for leukemia One group received a high dose of the drug while the control group received no treatment Expression data measures of gene activity from one gene are shown in the accompanying table for all of the treated subjects and some of the control subjects Compute the sample mean and standard deviation for each group separately Construct a dot diagram for each group separately Comment on any differences betweer the groups High Dose 16 1 134 9 52 7 14 4 124 3 99 0 24 3 16 3 15 2 47 7 12 9 Control 297 1 491 8 1332 9 1172 0 1482 7 335 4 528 9 24 1 545 2 92 9 337 1

Given the annual interest rate and a line of an amortization schedule for that loan complete the next line of the schedule Assume that payments are made monthly Annual Interest Rate Payment 13 245 79 Interest Paid 41 13 Identify the problem solving method that should be used Choose the correct answer below OA The Always Principle B Relate a New Problem to an Older One C The Three Way Principle OD Guessing is OK Fill out the amortization schedule below Annual Interest Rate 13 Paid on Principal 204 66 Interest Paid 41 13 Payment 245 79 Round to the nearest cent as needed Balance 3 592 87 Paid on Principal 204 66 Balance 3 592 87

WILEY 4 1 The Minitab output for a random sample of data is shown below Some of the quantities are missing Compute the values of the missing quantities Variable N Mean SE Mean X 9 19 96 StDev Variance 3 12 Min Max 15 94 27 16

1 1 The Department of Industrial Engineering at a major university wants to develop an empirical model to predict the success of its undergraduate students in completing their degrees a What would you use as the response or outcome variable in this study b What predictor variables would you recommend using c Discuss how you would collect data to build this model Is this a retrospective study or an observational study

Let U 9 10 11 12 13 14 15 A 9 10 11 12 B 9 10 13 14 and C 11 13 15 Consider the following set Enter your answers as comma separated lists AU BNC First list all the members of B n C Then list all the members of AU B nC

The dependent variable is the percentages of the usage of computers X 1992 2 2016 y 20 7 42 63 1 67 1 75 2 76 7 78 9 83 8 85 1 86 8 89 3 Defining the linear regression function and creating x incremented by 1 for more data poin x1 1992 1 2016 p1 polyfit x y 1 y1 polyval p1 x1 Defining the polynomial p2 polyfit x y 2 Evaluating p2 to create y values for plotting yPoly polyval p2 x1 Ploting the original data plot x y o Titles and adds legends to the plot graph title Share Of US Housholds Using Specific Technologies Computers xlabel Years Between 1996 and 2016 ylabel Percent of Americans Who Are Using Computers hold on Ploting the linear regression data plot x1 y1 Ploting the polyfit data plot x1 yPoly

If Nasir drives 56 miles at a constant speed of 56 mph How long will it take Be sure to include the units Answer number then units

While on a tour in Greece Ashley saw that the temperature was 26 Celsius Solve for F in the formula 5 F 32 then use it to find the Fahrenheit temperature C F Enter your answer as an expression Be sure to preview your answer before submitting Round your answer to one decimal place if necessary F

In 21 and 22 complete each table 21 km 0 1 22 E 5 000

Solve each Bernoulli equation or IVP by making an appropriate substitution dy dx 3A SUBSTITUTION METH 1 y e y x 1 x y xy dy 3 3 1 1 2ty y 1 dt 2 dy dx dy 4 2 2 1 y 0 4 dx

Macmillan A person takes out a student loan of 26 000 at an APR of 3 and pays it back over 10 years as an installment loan What is her monthly payment Use decimal notation Give your answer to two decimal places monthly payment How much total does she pay in interest Use decimal notation Give your answer to two decimal places total interest dollars dollars I FO

K5 Leaning What is creative drama Kid s Theatre and Plays Worksheet Drama is a play acted out for an audience A play tells a story with characters The characters act out the story They also talk with their actions A play has a setting and events The characters wear costumes There are props used to help tell the story These props are on the stage Props can be lots of things like a cardboard building furniture or any small things needed in the play A Matching Draw a line from the drama word to the definition 1 where the play takes place 2 actors in a play 3 another word for drama 4 people who watch the play 5 what characters wear in a play 6 what happens in a play 7 different items used in a play 8 what a play tells 9 where the characters act audience props characters play events costumes setting stage story KS Learning B Choose which words describe these exa Word bank audience characters sett ARTH 1 a mother father grandfather and 2 a forest city and magical land 3 a crown pair of shoes fancy 4 the families friends and 5 a sign bench and ba 6 a raised area or f 7 there was a s

3 Using the equation you wrote and P volume V at a given depth d d 1 write an equation that defines 33

The length of one side s of a shipping box is s x 2x where x is the volume of the box in cubic inches A manufacturer needs the volume of the box to be between 108 in 3 and 256 in What are the minimum and maximum possible lengths of s