Math - Others Questions

The following graph shows an economy s short run aggregate supply curve SRAS current equilibrium aggregate price level P and real GDP Q The economy currently has Natural Real GDP QN of 6 trillion Use this information to place the orange long run aggregate supply curve LRAS square symbols in the correct position on the graph PRICE LEVEL 0 REAL GOP Trilions of dolara REAL GDP Trillions of usag SRAS 1 above or below It LRAS The equilibrium A shown on the graph reveals that real GDP Q1 is shifting SRAS Natural Real GDP As a result wages will over time Save Continue Continue without saving

A B Ready 53 Modified see template for modifications to the problem You would like to have 500 000 in 20 years To accumulate this amount you plan to deposit an equal sum in the bank each year that will earn 7 interest compounded annually Your first payment will be made at the end of the year a How much must you deposit annually to accumulate this amount b If you decide to make a large lump sum deposit today instead of the annual deposits how large should this lump sum be Assume you can earn 7 on the deposit c At the end of 10 years you will receive 120 000 and deposit this in the bank toward your goal of 500 000 at the end of 20 years In addition to this deposit how much must you deposit in equal annual deposits to reach your goal at 7 PV I nper pmt FV PV nper pmt FV C Step 1 PV 1 nper pmt FV 7 20 12 196 46 500 000 00 129 209 50 7 20 0 00 500 000 00 Hint first in Step 1 determine how much 100K will be worth at the end of 20 years 100 000 00 7 10 H 196 715 14 500 000 K Step 2 Hint in Step 2 for the FV figure use 500 000 minus the amount from Step 1 Instructions Questions P6 53M P6 54M P6 24M Accessibility Investigate L M H M

In the accompanying data table the entries are for five different years and consist of the weights metric tons of lemons imported from another country and car crash fatality rates per 100 000 population The data are based on dat from a scientific publication Lemon Imports Crash Fatality Rate 226 16 3 Choose the correct answer below 263 362 16 2 16 1 473 16 2 538 14 8 Given that the data are matched and considering the units of the data does it make sense to use the difference between each pair of values Why or why not OA Yes it does make sense to use the difference between each amount of lemon imports and car crash fatality rate in the same column because they are measurements obtained from the same year B No it does not make sense to use the difference between each amount of lemon imports and car crash fatality rate in the same column because lemon imports and car crash fatality rates use different units of measurement OC No it does not make sense to use the difference between each amount of lemon imports and car crash fatality rate in the same column because the terms should be added O D Yes it does make sense to use the difference between each amount of lemon imports and car crash fatality rate in the same column because car crashes are caused by lemon imports

Use the following information for the Exercises below Algo The following information applies to the questions displayed below On December 1 Jasmin Ernst organized Ernst Consulting On December 3 the owner contributed 85 460 in assets in exchange for its common stock to launch the business On December 31 the company s records show the following ite and amounts Cash Accounts receivable Office supplies Office equipment Land Accounts payable Common stock Exercise 1 20 Algo Preparing a balance sheet LO P2 Assets 6 650 Cash dividends 18 650 Consulting revenue Rent expense 4 640 19 560 Salaries expense 46 000 Telephone expense 9 890 Miscellaneous expenses 85 460 Use the above information to prepare a December 31 balance sheet for Ernst Consulting Cash Accounts receivable Office supplies Office equipment Land ERNST CONSULTING Balance Sheet 6 650 Common stock 18 650 4 640 19 560 46 000 Accounts payable Equity Liabilities X S X XX 85 460 85 460 X X 3 490 18 650 4 920 8 500 X 9 890 X 890 700

21 2 We call a circle Ca Yeppeun circle for P and P if C contains P and P C is tangent to the z axis at a point P 0 and the z coordinate of the point of tangency lies between the z coordinates of P and P that is 12 For example the circle C in the following diagram is a Yeppeun circle for the given P and P Given any two such points P and P above the z axis does a Yeppeun circle always exist Explain

here are 12 eggs in a dozen If a farmer s chickens produce an average of 666 dozen eggs in a m gs are reported per month 36 dozen x 12 eggs dozen his answer has Submit Answer significant figures Retry Entire Group eggs 9 more group attempts remaining

The following crosstabulation summarizes the data for two categorical variables x and y The variable x can take on values low medium or high and the variable y can take on values yes or no x Low Low High X 100 Medium 90 80 70 60 50 40 30 20 10 High Total Yes No Total 25 Medium 20 30 y 20 5 a Compute the row percentages Round your answers to three decimal places Yes 5 30 50 65 40 105 25 Lour Medium High b Construct a stacked percent frequency bar chart with x on the horizontal axis 100 90 80 70 60 50 No Total No Yes 40 30 20 10 LOW Medium High No Yes 100 90 80 70 60 50 40 30 20 10 Low Medium High No Yes 100 90 80 70 60 50 40 30 20 10 Low Medium High No Yes

In Italy the price of gasoline averages around 1 64 per liter Using unit analysis calculate the cost of gasoline in Italy in dollars per gallon 1 64 1 L X 128 fl oz 1 Drag and drop your selection from the following list to complete the answer 1 gal 3 79 L gal 29 6 mL 1000 mL

4 Consider the following vectors in R V 141214 U 0 V3 Let V Span 7 U2 U3 a Determine if each of the following aree vectors is in V If so write it as a linear combination of 1 2 and 73 If not show work explaining why 15 0 8 and let W Span w Determine all vectors in R which are in both V and b Now let W hint without doing any work you can determine that there is at least one

Consider the following linear system 2x1 x1kx22x3 k 1 x3 1 k 3kx2 k 4 3 3 k

a When 48 68 and 39 24 are divided the answer should have significant figure s Enter the answer using the correct number of significant figures 48 68 39 24 b When 39 24 is subtracted from 48 68 the answer should have Enter the answer using the correct number of decimal places 48 68 39 24 P A digit s after the decimal point

she used the ideas just developed in class about density First she measured the mass of the metal to be 360 2 grams Then she dropped the metal into a meas found that it displaced 18 4 mL of water Calculate the density of the metal Density g mL Use the table below to decide the identity of the metal This metal is most likely Densities of Some Common Substances Substance Density g mL 1 00 Aluminum 2 72 Chromium 7 25 8 91 8 94 10 50 11 34 Water Nickel Copper Silver Lead

Consider the following 13 18 25 18 17 19 23 22 22 21 17 21 25 26 18 15 19 20 22 12 18 19 23 26 22 20 21 25 21 19 12 14 2 Class 25 14 21 23 a Develop a frequency distribution using classes of 12 14 15 17 18 20 21 23 and 24 26 Class Frequency 15 17 2 18 20 2 21 23 2 24 26 2 Total 10 Total 25 15 15 b Develop a relative frequency distribution and a percent frequency distribution using the classes in pa 12 14 2 15 17 2 Relative Percent Frequency Frequency 18 20 2 16 21 18 21 23 2 24 26 2 10

Data File Available Download Snow xlsx The file Snow contains temperature and snowfall data for 51 major U S cities over 30 years For example the average low temperature for Columbus Ohio is 44 degrees and the average annual snowfall is 27 5 inches a Construct a scatter diagram with the average annual low temperature on the horizontal axis and the average annual snowfall on the vertical axis 120 120 120 100 100 100 80 80 80 60 60 40 20 Avg Snowfall inches 120 100 80 60 40 20 0 30 60 50 Avg Low Temperature degrees Fahrenheit 70 40 80 Avg Snowfall inches 4 40 20 0 8 40 30 50 60 Avg Low Temperature degrees Fahrenheit b Does there appear to be any relationship between these two variables Colder average low temperature seems to lead to higher 70 80 amounts of snowfall c Based on the scatter diagram comment on any data points that seem to be unusual Two of the cities have an unusually low average snowfall Avg Snowfall inches 60 40 20 0 50 60 30 Avg Low Temperature degrees Fahrenheit 40 70 80 Avg Snowfall inches 0 30 50 60 70 Avg Low Temperature degrees Fa 40

Consider the following frequency distribution Class Frequency 10 19 20 29 30 39 40 49 50 59 Class less than or equal to 19 less than or equal to 29 Construct a cumulative frequency distribution and a cumulative relative frequency distribu Cumulative Relative Frequency less than or equal to 39 less than or equal to 49 10 less than or equal to 59 14 16 9 Cumulative Frequency

c Prepare a histogram Frequency 10 8 11 12 13 14 15 16 Hours per week in Meetings 4 Comment on the shape of the distribution The distribution is Select Frequency 10 006 8 Hours per week in Meetings 7 62 Frequency 10 8 2 Hours per week in Meetings 23 24 6 Frequency 10 8 PNA 11 12 3 19 A 15 16 17 18 Hours per week in Meetings 12 12

The Northwest regional manager of an outdoor equipment retailer conducted a study to determine how managers at three store locations are using their time A summary of the results are shown in the following table Store Location 100 r 90 80 70 60 50 40 30 20 10 0 Bend 100 90 80 Portland 70 60 Seattle Percentage of Manager s Work Week Spent on Bend Meetings 18 52 32 Reports Portland 11 Seattle 11 17 Customers Idle a Create a stacked bar chart with store location on the horizontal axis and percentage of time spent on each task on the vertical axis 100 p 90 80 70 60 50 Idle Customers Reports Meetings 52 Idle Curtomers 24 37 4 19 100 90 80 70 60 50 40 30 20 10 0 13 14 Bend Portland Seattle Idle Customers Reports Meetings 40 30 20 10 0 Bend Portland Seattle Idle Cus Rep Mee

27 1 B 6 0 1 2 3 4 5 6 7 8 9 0 1 2 3 A 6 648 00 9 6 8 9 52 11 289NAS NA M M 6 6 6 7 5 7 3 3 2 9 X B fx 0 00 644 8 2 8 8 5 8 9 7 669 667 MIN 8 7 9 7 2 D Data 10 2377S76 666889 5 3 9 9 1886755778 D 10 10 8 13 8 9 66997 11 7 E

0 1 2 13 15 16 17 P6 21 Modified use the modified numbers in bold below You ve just bought a new 85 inch flat screen TV for 2 499 and the store you bought it from offers to let you finance the entire package at an annual rate of 12 compounded monthly If you take the financing and make monthly payments of 83 how long in years will it take to pay off the loan How much will you pay in interest over the life of the loan 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Hint Use the NPER function in Excel to solve the problem The PV figure is the amount you are financing PV 1 m nper pmt FV Total payments PV Interest Paid 2 499 12 00 12 36 00 months 83 00 800 8 33 2 499 2 490 67 number of payme 489 3 00 years 1836 50 4150 36

2 Suppose that a linear system has fewer equations than variables What can you determine about the solution set of the system

5 53 Modified see template for modifications to the problem You would like to have 500 000 in 20 years To accumulate this amount you plan to deposit an equal sum in the bank each year that will earn 7 interest compounded annually Your first payment will be made at the end of the year a How much must you deposit annually to accumulate this amount b If you decide to make a large lump sum deposit today instead of the annual deposits how large should this lump sum be Assume you can eam 7 on the deposit A B 4 c At the end of 10 years you will receive 100 000 and deposit this in the bank toward your goal of 500 000 at the end of 20 years In addition to this deposit how much must you deposit in equal annual deposits to reach your goal at 7 PV 1 nper pmt FV PV T nper pmt FV C Step 1 PV i nper pmt FV Step 2 PV i nper pmt FV 7 20 12 196 46 500 000 00 129 209 50 7 20 0 00 500 000 00 Hint first in Step 1 determine how much 100K will be worth at the end of 20 years 100 000 00 7 10 196 715 14 500 000 Hint in Step 2 for the FV figure use 500 000 minus the amount from Step 1 Instructions Questions P6 53M P6 54M P6 24M

10 CHALLENGE PROBLEM Yen Luong owns a used pickup truck that she wants to sell A used vehicle guide shows that its average retail value is 17 600 She adds 1 700 for 4 wheel drive 475 for an entertainment system 800 for a special trim package and 225 for power locks She also adds 125 for a sliding rear window 325 for a towing package 250 for power windows and 3 125 for a diesel engine She deducts 675 for having a manual transmission She adds 450 for having less than the expected mileage What is the average retail price of Yen s vehicle

Q6 A graduating senior has been accepted by three universities for an M S in engineering Two criteria have been identified the first is the program and university s academic rating and the second is the cost A third criterion of location was considered but the student recognized that it is only for about a year and applications were only made to acceptable schools The student is currently enrolled in the first university which is rated as a 5 for academic rank and a 7 for cost The second is a larger out of state public university which is rated as a 7 for academic rank and a 6 for cost The third is s prestigious private school which is rated as a 10 academically and a 3 for its higher cost a What is the total score for each school if the academic rank has a weight of 40

2 For an arbitrary set of numbers S define S S to be the set of all sums x y where and y are in S Let A B C D be sets of integers such that AUB AUB CUD CUD For example if AB C D 1 2 then AUB AUB CUD CUD 1 1 1 2 2 1 2 2 2 3 4 1

4 State the equation of the line y 8x after it undergoes reflection in the x axis followed by a translation up 6 units 2C

Let A x y z w u and R is a relation on A that is represented by the following matrix 1 0 1 0 0 0 1 001 1 0100 0 0 0 1 0 0 1 001 1 Show that R is an equivalence relation 2 Find all equivalence classes of A over R

Dropbox Assignments Calculate the break even point for a new toy that costs 12 to make and market and that will be sold for 15 The total quantity that will be sold at that price is 200 000 Submit your answer to the dropbox titled Factors Involved in Price Planning

E B C AF BE ABCD BA gl go S b AF BE

he following signal has To x t A To 2 To 1 Non symmetric real coefficients with non zero DC component 2 imaginary coefficients with non zero DC component 3 Complex coefficients with non zero DC component 4 Complex coefficients with zero DC component None of the answers

The system dy t dt 2ty t x t is O 1 Distortion less but can distort some of the input signals O 2 None of the answers O3 With distortion and introduces frequency amplitude and phase distortion O4 With distortion and introduces only phase and amplitude spectra O 5 Distortion less

The average power contained in the frequency band 0 100 for the signal with fo 26 Hz for n 0 for n 0 the Fourier Series coefficients Xn O1 49 6 Watts 2 9 3 3 47 6 Watts 04 None of the answers n is

The Fourier series determines O 1 The expression of a signal as sum of its period O 2 None of the answers 3 The spectral representation of a periodic signal 4 The frequency response of a periodic signal O 5 The phasor representation of the response to any signal

Find the sum difference or product Simplify your answer completely 2x 3x 1 3x 5x 5 Your answer cannot be understood or graded More Information

Factor the expression completely x 5 x 8 2 x 5 x 8

Factor the expression completely This type of expression arises in calculus when using the Product Rule x 1 1 7 2x x2 1 8 7

Factor the expression completely This type of expression arises in calculus when using the Product Rule 5 x 5 4 2x x 3 4 x 5 5 4 x 3

Factor the expression completely This type of expression arises in calculus when using the Product Rule x1 2 9x 4 1 2 2x1 2 9x 4 1 2

Write the expression in simplest form If it is in simplest form enter the original expression Assume that the denominator is not 0 See Example 3 01 4x 2

Use the following information for the Quick Studies below Algo The following information applies to the questions displayed below On December 31 Hawkin s records show the following accounts Cash Accounts Receivable Supplies Equipment Accounts Payable Common stock Retained earnings December 11 Dividends Services Revenue Wages Expense Rent Expense Utilities Expense QS 1 17 Algo Preparing a balance sheet LO P2 Use the above information to prepare a December balance sheet for Hawkin Hint Retained Earnings on December 31 equal Assets HAWKIN Balance Sheet December 31 Liabilities 8 100 1 000 2 400 14 900 7 500 11 000 5 500 1 900 17 500 8 000 3 000 2 200 Total Liabilities Equity

Use the following information for the Exercises below Algo The following information applies to the questions displayed below On December 1 Jasmin Ernst organized Ernst Consulting On December 3 the owner contributed 85 460 in assets i exchange for its common stock to launch the business On December 31 the company s records show the following it and amounts Cash Accounts receivable Office supplies Office equipment Land Accounts payable Common stock 6 650 Cash dividends Consulting revenue Rent expense 18 650 4 640 19 560 Salaries expense 46 000 Telephone expense 9 890 Miscellaneous expenses 85 460 Exercise 1 18 Algo Preparing an income statement LO P2 Using the above information prepare a December income statement for the business ERNST CONSULTING Income Statement 3 490 18 650 4 920 8 500 890 700

Change each of the following to decimal degrees 25 45 12 26 74 18

Business at your design engineering firm has been brisk To keep up with the increasing workload you are considering the purchase of a new state of the art CAD CAM system costing 360 000 which would provide 6 000 hours of productive time per year Your firm puts a lot of effort into drawing new product designs At present this is all done by design engineers on an old CAD CAM system installed five years ago If you purchase the system 30 of the productive time will be devoted to drawing CAD and the remainder to CAM While drawing the system is expected to out produce the old CAD CAM system by a factor of 3 1 You estimate that the additional annual out of pocket cost of maintaining the new CAD CAM system will be 200 000 including any tax effects The expected useful life of the system is eight years after which the equipment will have no residual value As an alternative you could hire more design engineers Each normally works 1 800 hours per year and 60 of this time is productive The total cost for a design engineer is 65 per hour There are five design engineers Identify the net cash flows benefits and costs associated with the drawing activities if the CAD CAM system is purchased instead of hiring more design engineers In year 0 the net cash flow associated with the drawing activities if the CAD CAM system is purchased instead of hiring more design engineers will be Round to the nearest dollar

Suppose 44 patients arrive at a hospital emergency department on any given day Recent data indicate that approximately 19 of these patients are admitted for inpatient care We will consider these 44 patients to be a representative sample of people who are served by this hospital and compute probabilities for the following situations 1 State the single outcome that is most likely to occur along with its probability 2 The probability that x is at most 4 3 The probability that x is at least 10 4 The probability that x is more than 3 and less than 14 5 The probability that x is more than 15 6 The probability of no successes in the trials 7 The probability that all n trials results in a success LUSE SALT After you have clicked the tab for your selected topic and read the problem answer the questions below a The Binomial Experiment consists of a sequence of trials with the following conditions Verify that each condition is satisfied for your chosen scenario 1 There are a fixed number of trials We do n 44 have a fixed number of trials in this scenario and the number of trials is defined to be 2 Each trial can result in one of only two possible outcomes labeled success and failure There are exactly two outcomes for each trial The outcome to be counted is defined as success and for this scenario x is defined to be the number of patients admitted for inpatient care 3 Outcomes of different trials are independent It is reasonable to assume that the sample for this scenario is a random representative sample from the population of interest This means the trials are 4 The probability that a trial results in a success is the same for each trial For this scenario the probability of success is defined to be p 0 19 a percent and will not change for each trial 1 x 8 2 3 4 5 independent entered as a decimal not b The Binomial Random Variable X is defined as X number of success observed when a binomial experiment is performed The probability of x is called the Binomial Probability Distribution Use SALT s Binomial Distribution Calculator to determine the probabilities for your selected scenario Round your answers to five decimal places with probability of X

Geo Star Manufacturing Company is considering a new investment in a punch press machine that will cost 98 000 a has an annual maintenance cost of 8 000 There is also an additional overhauling cost of 23 000 for the equipmen once every four years Assuming that this equipment will last infinitely under these conditions what is the capitalized equivalent cost of this investment at an interest rate of 10 Click the icon to view the interest factors for discrete compounding when i 10 per year The capitalized equivalent cost of this investment is thousand Round to the nearest whole number

Covington Corporation purchased a vibratory finishing machine for 15 000 in year 0 The useful life of the machine is 10 years at the end of which the machine is estimated to have a salvage value of zero The machine generates net annual revenues of 6 500 The annual operating and maintenance expenses are estimated to be 1 100 If Covingto MARR is 20 how many years will it take before this machine becomes profitable Assume that the cash flows occu continuously throughout the year It will take years before this machine becomes profitable Round to one decimal place

Convert each of the following to degrees and minutes 15 35 4 16 63 2 17 16 25 19 92 55 21 19 9 18 18 75 20 34 45 22 18 8

For our random sample of 24 people who dine out find the following probabilities rounded to five decimal places Recal that n 24 and p 0 33 were previously defined 1 The probability exactly 12 diners chose their restaurant based on a peer review site is P x 12

A national park is famous for its beautiful desert landscape and its many natural rock formations The following table is based on information gathered by a park ranger of all rock formations of at least 3 feet The height of the rock formation is rounded to the nearest foot Height of rock formation feet 3 9 10 29 Number of rock formations in park 114 86 X b 30 feet or taller 7 56 c 3 to 49 feet 87 28 For a rock formation chosen at random from this park use the preceding information to estimate the probability that the height of the rock formation is as follows Round your answers to two decimal places a 3 to 9 feet 39 17 X d 10 to 74 feet 12 72 X 30 49 50 74 75 and higher 39 e 75 feet or taller 22 10

A particular lake is known to be one of the best places to catch a certain type of fish In this table x number of fish caught in a 6 hour period The percentage data are the percentages of fishermen who caught x fish in a 6 hour period while fishing from shore P X P X 0 5 0 4 0 3 0 2 0 1 a Convert the percentages to probabilities and make a histogram of the probability distribution Because the data table has summarized the data into categories use SALT to create a bar chart 0 0 5 0 4 0 3 0 2 0 1 0 1 0 43 37 USE SALT 0 1 0 2 3 1 12 7 2 X 2 at least 4 X 1 3 at least 4 3 at least 4 P X 0 5 0 4 0 3 0 2 0 1 0 5 0 4 0 3 0 2 0 1 0 0 1 0 1 2 X 3 at least 4 2 3 at least 4 b Find the probability that a fisherman selected at random fishing from shore catches one or more fish in a 6 hour period c Find the probability that a fisherman selected at random fishing from shore catches two or more fish in a 6 hour period 0 20 d Compute the expected value of the number of fish caught per fisherman in a 6 hour period round at least 4 to 4 X fish e Compute the standard deviation of the number of fish caught per fisherman in a 6 hour period round at least 4 to 4 Round your answer to three decimal places Faoin

The Denver Post reported that a recent Audit of Los Angeles 911 calls showed that 85 were not emergencies Suppose the 911 operators in Los Angeles have just received three calls USE SALT a What is the probability that all three calls are in fact emergencies Round your answer to three decimal places 0 00338 b What is the probability that two or more calls are not emergencies Round your answer to three decimal places 0 7984 x c What is the smallest number of calls n that the 911 operators need to answer to be at least 96 or more sure that at least one call is in fact an emergency Enter your answer as a whole number 15 calls