Mathematical Induction Questions and Answers

Graph y Nim 2 I 5 4 3 2 1 5 5 4 3 2 1 4 3 2 1 1 2 3 4 5 y 5 4 3 2 1 1 2 3 4 5 L 1 1 1 L 2 3 4 I 2 4 3 4 5 5 X L J 5 4 3 2 1 5 4 3 2 5 4 3 2 1 1 2 3 H 4 5 5 4 3 2 1 1 2 3 T 1 2 1 2 3 3 4 4 5 5 X X

Determine the ordered pair for the point labeled 8 in the figure below Here the x and y axes are labeled from 0 to 5 in 0 5 unit increments x y 5 4 3 2 0 5 1 1 5 2 2 5 3 3 5 4 4 5 5

9 Find the arc length function for the following curve with the given starting point y 7 4x5 2 P 1 3 A B C D E 1 413 2 dt 10t 2 dt S S S S V1 10t3 2 dt A e 20 B 1 e C e 5 D 1 e5 E e 1 100t dt 1 100t5 dt 10 A tank contains 100 liters of salt water Pure water is added to the tank at the rate o 20 liters per hour and the well stirred mixture is drained at the same rate After 5 hour the tank contains 1 kg of salt Determine how many kilograms of salt were in the tan originally

The following data represent weights in kilograms of maize harvest from a random sample of 72 experimental plots on St Vin an island in the Caribbean 7 9 9 0 9 6 9 9 10 3 10 4 11 0 11 6 11 9 12 1 12 3 12 4 13 0 14 3 14 4 14 5 15 3 20 4 20 6 20 8 21 0 21 3 17 1 17 7 18 3 18 9 19 2 19 4 22 4 22 6 22 7 22 9 23 0 25 1 25 2 25 6 26 0 15 6 LUSE SALT Q median Q3 maximum a Compute the five number summary minimum b Compute the interquartile range 13 6 13 6 13 6 13 9 16 1 16 1 16 2 16 6 23 8 23 9 23 9 23 9 24 0 24 0 24 6 24 6 21 9 19 7 20 1 20 1 21 9 22 1 11 8 23 2 23 3 23 7 26 5 26 6 26 8 27 0 22 3 23 7 24 8 29 6

outliers Outliers may represent data collection errors data entry errors or simply valid but unusual data values It is important to identify outliers in the data set and examine the outliers carefully to determine if they are in error One way to detect outliers is to use a box and whisker plot Data values that fall beyond the limits Lower limit Q 1 5x IQR Upper limit Q3 1 5 x IQR where IQR is the interquartile range are suspected outliers In the computer software package Minitab values beyond these limits are plotted with asterisks Students from a statistics class were asked to record their heights in inches The heights as recorded were as follows 66 73 69 63 61 56 74 70 51 64 60 73 68 68 73 51 5 74 68 63 a Make a box and whisker plot of the data 0 10 20 30 40 50 60 70 80 90 HI 0 10 20 30 40 50 60 70 80 90 b Find the value of the interquartile range IQR IQR o c Multiply the IQR by 1 5 and find the lower and upper limits lower limit upper limit d Are there any data values below the lower limit Yes No Are there any data values above the upper limit Yes No 67 81 65 64 IH 0 10 20 30 40 50 60 70 80 90 Q 0 10 20 30 40 50 60 70 80 90 List any suspected outliers Enter your answers as a comma separated list If an answer does not exist enter DNE What might be some explanations for the outlier s O There is a single outlier but it is possible this student is just far below average height There are multiple outliers but they are all likely to be errors O There are multiple outliers but it is possible these students are just far above average height There is a single outlier but it is most likely an error That acted outliers in this data

At one hospital there is some concern about the high turnover of nurses A survey was done to determine how long in months nurses had been in their current positions The responses in months of 20 nurses were as follows 50 40 30 Make a box and whisker plot of the data 20 25 4 7 16 27 38 29 10 9 25 31 28 30 13 22 33 10 38 LAUSE SALT Find the interquartile range 50 40 30 20 44 14 10 10 50 40 30 20 10 of 40 30 20 10

Consider the sample data 24 6 32 1 54 8 66 3 72 4 90 9 a Calculate Ex Ex Calculate Ex Ex b Use the results of part a and the appropriate computation formulas to compute the sample variance s and sample star deviation s s

In this problem we explore the effect on the standard deviation of adding the same constant to each data value in a data set Consider the following data set 13 9 19 5 15 USE SALT a Use the defining formula the computation formula or a calculator to compute s Round your answer to four decimal places S b Add 2 to each data value to get the new data set 15 11 21 7 17 Compute s Round your answer to four decimal places

You will use bullet points to respond to the following prompts 1 How do you perceive the systems approach to healthcare How different is it from a localized approach to healthcare 2 Can you give some examples relevant to the ten basic characteristics of the US healthcare system Please write about at least two basic characteristics and how your experiences connected to them

In this problem we explore the effect on the mean median and mode of multiplying each data value by the same number Consider the following data set 5 5 6 9 13 USE SALT a Compute the mode median and mean What is the mode What is the median What is the mean b Multiply each data value by 3 Compute the mode median and mean What is the mode What is the median What is the mean c Compare the results of parts a and b In general how do you think the mode median and mean are affected when each data value in a set is multiplied by the same constant O Multiplying each data value by the same constant c results in the mode median and mean increasing by a factor of c Multiplying each data value by the same constant c results in the mode median and mean remaining the same Multiplying each data value by the same constant c results in the mode median and mean decreasing by a factor of c There is no distinct pattern when each data value is multiplied by the same constant d Suppose you have information about average heights of a random sample of airline passengers The mode is 66 inches the median is 71 inches and the mean is 75 inches To convert the data into centimeters multiply each data value by 2 54 What are the values of the mode median and mean in centimeters What is the mode cm What is the median JAIL cm

Consider the accompanying cash flow diagram which represents three different interest rates applicable ove the five year time span shown 0 P 4 2 100 2 100 1 Compounded quarterly 2 7 Years 3 150 3 Compounded quarterly a Calculate the equivalent amount P at the present time The equivalent amount P at the present time is 2 100 2 100 4 5 8 Compounded quarterly Round to the nearest dollar Q Q

ompute the value of P in the accompanying cash flow diagram assuming that i 9 250 250 100 100 P 1 150 150 2 3 200 200 4 Years 5 6 7

10 Betermining consumers and producers surplus Identify whether each statement in the following table best illustrates the concept of consumers surplus producers surplus or neither Consumers Producers Surplus Surplus Statement Even though I was willing to pay up to 291 for a cell phone I bought a one for only 283 Even though I was willing to pay up to 376 for a used football jersey and even though the seller was willing to go as low as 369 in order to sell it we couldn t reach a deal because the government imposed a price ceiling of 361 on the sale of jerseys I sold a used smart watch for 370 even though I was willing to go as low as 362 in order to sell it O O Neither O

The following graph shows the market for peanut butter in Detroit where there are over a thousand stores that sell peanut butter at any given moment Suppose the price of hazelnut spread decreases Assume that people regard peanut butter and hazelnut spread as substitutes Show the effect of this change on the market for peanut butter by shifting one or both of the curves on the following graph holding all else constara PRICE Dollars per jar Supply Demand Demand Supply

State why the system of equations must have at least one solution Select all that apply 3x 3y z 0 6x 3y 3z 0 3x 9y 11z 0 During the elimination process we obtain the equation 0 0 The point x y z 1 1 1 solves the system O The system contains three equations and three variables The point x y z 0 0 0 solves the system O During the elimination process we obtain a false statement Solve the system and determine whether it has exactly one solution or infinitely many solutions If the system has a infinite number of solutions express x y and z in terms of the parameter t X Y Z 0 0 0

Given the following information set up the problem in a transportation table and solve for the minimum cost plan Solve by modifying textbook Table 11 6 Demand Capacity Regular Overtime Subcontract Beginning inventory Costs Regular time Overtime Subcontract Inventory carrying cost Back order cost 550 500 50 120 100 PERIOD 2 700 60 per unit 80 per unit 90 per unit 500 50 120 1 per unit per month 3 per unit per month 3 750 500 50 100 Suppose that regular time capacity will be reduced to 440 units in period 3 to accommodate a companywide safety inspection of equipment What will the additional cost of the optimal plan be

Compute seasonal relatives for this data using the simple averaging SA method Year 3 Year 4 1 0 7 5 6 Quarter Year 1 11234 2 6 1 4 Quarter 1 Quarter 2 Quarter 3 Quarter 4 Year 2 1 6 4 4 Round all your answers to three decimal points 8898 6

Certain kinds of tumors tend to recur Suppose the following data represent the lengths of time in months for a tumor to recur after chemotherapy 20 19 18 1 22 21 55 47 44 38 6 10 39 17 15 46 18 37 37 39 42 42 11 51 42 26 18 40 28 19 USE SALT For this problem use five classes a Find the class width 1 1 26 50 49 1 59 38 53 59 47 51 30 11 b Make a frequency table showing class limits class boundaries midpoints frequencies relative frequencies and cumulative frequencies Round your relative frequencies to four decimal places Class Limits Class Boundaries Midpoint Frequency Relative Frequency Cumulative Frequency 0 0 000 000 000 000

92 Convert the fraction to a whole number percentage 248

For questions 7 10 solve the problem by following the procedure for solving an optimization problem Show all your steps Include a concluding statement that summarizes your answer and includes the correct units 7 An apple orchard now has 80 trees per hectare and the average yield is 400 apples per tree For each additional tree planted per hectare the average yield per tree is reduced by approximately four apples How many trees per hectare will give the largest crop of apples 8 Time to Travel advertises a package plan for an Arizona vacation The fare for the flight is 400 person plus 8 person for each unsold seat on the plane The plane holds 120 passengers and the flight will be cancelled if there are fewer than 25 passengers What number of passengers will maximize revenue

On October 3 2023 issues 20 000 shares of common stock for cash 2 On October 5 2023 purchases equipment on account for 3 500 payment due within the month On October 9 2023 receives 4 000 cash in advance from a customer for services not yet rendered On October 10 2023 provides 5 500 in services to a customer who asks to be billed for the services On October 12 2023 pays a 300 utility bill with cash On October 14 2023 distributed 100 cash in dividends to stockholders On October 17 2023 receives 2 800 cash from a customer for services rendered On October 18 2023 paid in full with cash for the equipment purchase on October 5 On October 20 2023 paid 3 600 cash in salaries expense to employees S 5 5 7 8 10 On October 23 2023 received cash payment in full from the customer on the October 10 transaction 1 On October 27 2023 provides 1 200 in services to a customer who asks to be billed for the services 2 On October 30 2023 purchases supplies on account for 500 payment due within three months

The postmaster of a small western town receives a certain number of complaints each day about mail delivery Number of complaints UCL LCL b Is the process in control 1 4 Yes 2 11 3 15 48 59 69 75 DAY 8 14 9 13 10 17 11 56 Click here for the Excel Data File a Determine three sigma control limits using the above data Round your intermediate calculations to 4 decimal places and final answers to 3 decimal places Leave no cells blank be certain to enter 0 wherever required Round up any negative control limit value to zero 12 13 14 2 10 4

Find the inverse of A 11 3 24

A factory manufactures three products A B and C Each product requires the use of two machines Machine I and Machine IL The total hours available respectively on Machine I and Machine per month are 6 240 and 8 080 The time requirements and profit per unit for each product are listed below ABC Machine 4 10 9 Machine 1714 Profi B 11 17 How many units of each product should be manufactured to maximize profe and what is the maximum profic Start by setting up the near programming problem with A B and C representing the number of units of each product that are produced Maximize P subject to Enter the solution below If needed round numbers of items to 1 decimal place and profit to 2 decimal places The maximum profit is 6 240 8 080 units aff product A units of product units of product C when the company produces

etz the number of cordless drills produced per day and y the number of corded drills roduced per day Write the system of inequalities 3 23 X 3 raph the system of inequalities 240 230 220 210 200 190 2828829222222222222 370 50 140 130 20 110 100 20 00 70 40 30 40 20 360 2

To save for retirement Karla Harby put 375 each month into an ordinary annuity for 10 years Interest was compounded monthly At the end of the 10 years the annuity was worth 55 382 What annual interest rate did she receive The interest rate she received was approximately Round to two decimal places as needed

d Let A and B be subsets of a universal set U Show that AC B if and on if BCA

On a baseball diamond with 90 foot sides the pitcher s mound is 60 5 feet from home plate How far is the pitcher s mound from first base Round your answer to one decimal place R

Problem 1 In an exam we have to speak about 1 topic out of 12 possible topics There are 3 retake opportunity We plan to apply one of the following two strategies 1 strategy For the first exam we learn perfectly 4 topics If we fail then for the second exam we learn another 4 topics so at this moment we know 8 topics Finally if we fail we learn all the 12 topics perfectly 2 strategy For the first exam we learn perfectly 6 topics If we fail then for the second exam we learn another 3 topics Finally if we fail we learn all the 12 topics perfectly In a given exam if we have to speak about a topic which we learned we pass the exam otherwise we fail Which strategy should we choose if we would like to minimize the expected number of the exams

instruct the Lagrange s interpolation formula b Use the table below to evaluate the formula in a above and hence compute 1 x 1 f x 2 3 6 10 7 12

O 6 A bolt is tightened by applying a force a 0 15 m wrench The angle between the wrench and the force vector is 40 and the magnitude of the torque about the centre of the bolt is 0 58 N m Determine the magnitude of the force applied to the wrench to the nearest unit 0 15 m 40

In a test a student gets an aggregate of 52 5 marks in for subjects Maths English Hindi and Science in the ratio of 4 3 2 5 If the passing marks are 50 and the maximum marks for each subject is same in which subject s did he fail in the examination

Hot 2 Sketch the graph of the continuous function f that satisfies all of the stated conditions 9 pts trpioiture ion zi nolemixoqqs fariseb s joviam TAH al to bollen instw f 0 2 f 1 0 2 2 Toile worla taumuoy GANI Y 42 20s moldong cut 3 f 0 0 f 2 0 sonen Shuleni vorla 21swage TUOY sidizzon f x 0 on 0 and 2 0 f x 0 on 0 2 berolamos f 1 0 6 isqe doteros 100 f x 0 on 1 00 f x 0 on 0 1 awab siin iso oluoso may oti bogguig too 2 1 AP 23 2 3 197 LET 4 LOV 150 D 6 the moy JORABO TV N 15y of Insom JOVJER 61

9 A ladder 13 feet long is leaning against the side of a building If the foot of the ladder is pulled away from the building at a constant rate of 8 inches per second how fast is the area of the triangle formed by the ladder the building and the ground changing in feet squared per second at the instant when the top of the ladder is 12 feet above the ground

17 57 The 10 kg wheel has a radius of gyration k 200 mm If the wheel is subjected to a moment M 51 N m where t is in seconds determine its angular velocity when t 3 s starting from rest Also compute the reactions which the fixed pin A exerts on the wheel during the motion M

What is the annual worth in the following situation North Carolina is building a monument with a perpetual life they assume 6 cost of money The cost to build the monument 2 000 000 Annual cost to maintain the monument 60 000 Every 20 years there will be a major cleaning required that will cost 175 000 O 60 000 O 109 165 O 138 875 184 757

Insert Draw Design Tell me A Q Styles Dictate Editor Year A Font 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 Paragraph V Unemployment rate 4 5 3 8 3 8 3 6 3 5 4 9 4 Use the table below to answer these questions In which years was the misery index a the highest b the lowest 5 9 5 6 4 9 5 6 8 5 Inflation rate 1 6 Comments 2 9 3 1 4 2 5 5 5 7 4 4 3 2 6 2 11 0 9 1 Editing LE

Cash flows from used for operating activities indirect method The income statement disclosed the following items for the year Depreciation expense Gain on disposal of equipment Net income The changes in the current asset and liability accounts for the year are as follows Increase Decrease 8 960 5 120 1 920 6 080 1 410 2 200 Accounts receivable Inventory Prepaid insurance Accounts payable Income taxes payable Dividends payable 57 600 33 600 508 000 a Prepare the Cash flows from used for operating activities section of the statement of cash flows using the indirect method Use the minus sign to indicate cash out flows cash payments decreases in cash or any negative adjustm Statement of Cash Flows partial Line Item Description Cash flows from used for operating activities Net income Adjustments to reconcile net income to net cash flows from used for operating activities Depreciation Gain on disposal of equipment Changes in current operating assets and liabilities Increase in accounts receivable Decrease in inventory Decrease in prepaid insurance Amount 000 0000 Amount

The accompanying table gives the gross domestic receipts for the top 10 movies Find the mean median and mode for each data set Explain which measure best describes a typical value in this distribution EB Click the icon to view the data table Find the mean Select the correct choice below and if necessary fill in the answer box to complete your choice OA The mean is Round to two decimal places as needed OB There is no mean for these data Find the median Select the correct choice below and if necessary fill in the answer box to complete your choice A The median is Round to two decimal places as needed OB There is no median for these data Find the mode s Select the correct choice below and if necessary fill in the answer box to complete your choice OA The mode s is are Round to two decimal places as needed Use a comma to separate answers as needed OB There is no mode for these data Which measure best describes a typical value in this distribution Domestic Receipts of Top 10 Movies Movie Title Movie A Movie B Movie C Movie D Movie E Movie F Movie G Movie H Movie I Movie J Print OA The median best describes a typical value in this distribution since the distribution appears to be slightly asymmetrical and contains some extreme values OB The mean best describes a typical value in this distribution since the distribution is roughly symmetrical and does not contain any extreme values OC For this distribution the mean median and mode are equal so any value can be used to describe this distribution OD The mode best describes a typical value in this distribution since each value occurs roughly the same number of times Total Gross millions 453 0 201 4 354 0 356 2 652 2 331 0 200 0 936 8 281 2 228 8 Done D

K The accompanying table gives the gross domestic receipts for the top 10 movies Find the mean median and mode for each data set Explain which measure best describes a typical value in the distribution Find the mean Select the correct choice below and if necessary fill in the answer box to complete your choice OA The mean is Round to two decimal places as needed OB There is no mean for these data Find the median Select the correct choice below and if necessary fill in the answer box to complete your choice OA The median is Round to two decimal places as needed OB There is no median for these data Find the mode s Select the correct choice below and if necessary fill in the answer box to complete your choice A The mode s is are Round to two decimal places as needed Use a comma to separate answers as needed B There is no mode for these data Domestic Receipts of Top 10 Movies Movie Title Movie A Movie B Movie C Movie D Movie E Movie F Movie G Movie H Movie I Movie J Print Which measure best describes a typical value in this distribution OA The median best describes a typical value in this distribution since the distribution appears to be slightly asymmetrical and contains some extreme values OB The mean best describes a typical value in this distribution since the distribution is roughly symmetrical and does not contain any extreme values OC For this distribution the mean median and mode are equal so any value can be used to describe this distribution OD The mode best describes a typical value in this distribution since each value occurs roughly the same number of times Total Gross millions 453 0 201 4 354 0 356 2 652 2 331 0 200 0 936 8 281 2 228 8 Done

The officers of a high school senior class are planning to rent buses and vans for a class trip Each bus can transport 40 students requires 2 chaperones and costs 1200 to rent Each van can transport 8 students requires 1 chaperone and costs 100 to rent Since there are 440 students in the senior class that may be eligible to go on the trip the officers must plan to accommodate at least 440 students Since only 28 parents have volunteered to serve as chaperones the officers must plan to use at most 28 chaperones How many vehicles of each type should the officers rent in order to minimize the transportation costs What are the minimal transportation costs

List all the ways to select two different members from S without repetition The order in which members are selected is important For example AB is not the same selection as BA S C D E F G Identify the list of all the ways to select two members from S Choose the correct answer below OA CE CF CG DE DF DG EF EG O B CD CE CF CG DC DE DF DG EC ED EF EG FC FD FE FG GC GD GE GF OC CC CD CE CF CG DD DE DF DG EE EF EG FF FG GG D CD CE CF CG DE DF DG EF EG FG B

0 10 pts 399 Given the equation y 5 tan 3x 6 The period is Details The horizontal shift is units to the Select an answer

2 Identify comprehend and analyze the quantitative nature of the business problems in topics such as depreciation inventory valuation estimation breakeven analysis financial statements ratio analysis simple compound interest discount annuities and amortization A Given the following X Corp s financial information regarding their fixed physical assets perform the following analysis by applying appropriate techniques methods where necessary in C Keep in mind that it is absolutely essential for you to figure out even the highlighted areas other than questions though not directly asked to correctly perform the task The answer choices are found at the end of the problem group Cost 31 000 00 Year Jan Mar April Nov GAS 3 3 444 44 a 23 600 00 b 17 962 22 Purchase S Principal 1 2 S a 6 633 50 320 000 00 320 000 00 Salvage Value 1 000 00 Principal Bal 24 000 00 BV YR Beg 31 000 00 10 333 33 a 23 409 32 Principal Q ty 1 500 00 Life in yrs Depreciation Deprec Rate APR simple 7 25 7 25 c 1 90 B Given the following X Corp s financial information regarding their inventory perform the following tasks by applying appropriate techniques methods where necessary in D Keep in mind that it is absolutely essential for you to figure out even the highlighted areas other than questions though not directly asked to correctly perform the task The answer choices are found at the end of the problem group U Cost APR comp 7 25 35 80 14 00 13 00 15 00 900 00 Amount 490 00 1 040 00 60 50 17 00 850 00 3 Deprec Expense 66 67 20 666 67 66 67 6 888 89 tl Skdl 66 67 2 444 45 d 30 000 00 1 May 1 May d 1 997 16 Weight APR simple time in days 4 75 35 4 75 55 4 75 30 a 1 179 00 b 1 860 00 c 1 420 00 C Given the following X Corp s options to use debt financing perform the following tasks by applying appropriate techniques methods where necessary in F Keep in mind that it is absolutely essential for you to figure out even the highlighted areas other than questions though not directly asked to correctly perform the task The answer choices are found at the end of the problem group 12 15 Aug 15 Aug b 6831 11 c 32 6831 11 d 4 429 e 326 737 53 Method WAVG FIFO LIFO m frequency e 1 282 84 360 time in yrs time in exact vrs 2 88 tm Dep Expense 1 Life 1 25 2 BV where Accel factor 1 25 1 5 1 75 or 2 S Accumulated Deprec End INV Q3 Q5 Q7 20 666 67 27 555 56 D Given the following X Corp s plan to retire their debt at uneven interval perform the following tasks by applying appropriate techniques methods where necessary in H Keep in mind that it is absolutely essential for you to figure out even the highlighted areas other than questions though not directly asked to correctly perform the task The answer choices are found at the end of the problem group e 1 000 00 Interest e 167 55 Interest Q1 6 737 53 09 CGS Q4 Q6 PMT b 21 576 87 c 109 32 d 21 661 11 E Given the following X Corp s customized CD holdings perform the following tasks by applying appropriate techniques methods where necessary in K Keep in mind that it is absolutely essential for you to figure out even the highlighted areas other than questions though not directly asked to correctly perform the task The answer choices are found at the end of the problem group FV Maturity in vrs BV YR End 10 333 33 3 444 44 FV Q8 Q10 Interest 112 78 Q2 S 700 00 S 2 000 00 S Exact yr Ordinary yr Princi Paid FV Maturity Val 590 68 1 832 45 Q11 APY Maturity Value effective r 012

Tutorial Exercise The probability that an 80 year old male in the U S will die within one year is approximately 0 069941 If an insurance company sells a one year 13 000 life insurance policy to such a person for 432 what is the company s expectation Part 1 of 3 Let S be the event that the person dies within one year Then P S 0 069941 Submit Skip you cannot come back In this case the company has to pay out 13 000 Since the company charged 432 for this policy the company s actual loss is 506 264

Tutorial Exercise The probability that an 80 year old male in the U S will die within one year is approximately 0 069941 If an insurance company sells a one year 13 000 life insurance policy to such a person for 432 what is the company s expectation Part 1 of 3 Let S be the event that the person dies within one year Then P S 0 069941 Submit Skip you cannot come back In this case the Fompany has to pay out 13 000 Since the company charged 432 for this policy the company s actual loss is X

Exercise a Part 1 of 2 The total number of candies is the odds of getting a green M M Let E be the event of getting a green M M Because there are 6 green M M s there are 6 Exercise b 15 11 6 14 5 11 63 Part 2 of 2 Write the odds in favor of E in fractional form 2 19 2 19 Part 1 of 2 the probability of getting green M M Because there are 63 M M s in the bag there are 63 elements in the sample space green M M There are 6 green M M s so there are 6 favorable outcomes leaving 57 57 unfavorable outcomes X elements in E

skipped part A snack size bag of M Ms candies contains 15 red candies 11 blue 6 green 14 brown 6 orange and 11 yellow If a candy is randomly picked from the bag compute the following Exercise a the odds of getting a green M M Part 1 of 2 The total number of candies is 15 11 6 14 6 11 63 Part 2 of 2 part of the question you will not receive any points for the skipped part and you will not be able to come back to the 63 Let E be the event of getting a green M M Because there are 6 green M M s there are 6 Write the odds in favor of E in fractional form 6 favorable outcomes leaving 57 unfavorable outcomes

Table Nike and Reebok Advertising Game Use Table Nike and Reebok Advertising Game The sneaker industry is dominated by Nike and Reebok and each firm spends a lot of money on advertising Suppose each firm is considering a costly television commercial during the World Series The table shows the payoff matrix of profits that each firm would receive from its advertising decision given the advertising decision of its rival Profits in each cell of the payoff matrix are given as Nike Reebok If each firm independently decides whether to advertise the Nash equilibrium is for Nike and Reebok during the World Series Nike and Reebok Advertising Game Reebok advertises Reebok does not advertise Nike advertises 800 700 1 500 600 not to advertise to advertise not to advertise not to advertise Nike does not advertise 650 900 1 000 800

Use the following to answer question 16 Figure An Increase in Aggregate Demand Price level P3 P P LRAS SRAS Y Yp Y SRAS AD Real GDP AD 16 Figure An Increase in Aggregate Demand Assume that the economy is initially long run equilibrium at Yp and P Now suppose that there is an increase in the leve government purchases at each price level This will A shift aggregate demand from AD to AD B shift aggregate demand from AD to AD2 C lead to increased output and a decrease in the price level D lead to decreased output and price level