# Mathematical Reasoning Questions and Answers

Math - Others

Mathematical ReasoningEvaluate lim f x where f x If an answer does not exist enter DNE lim f x 36 12

Math - Others

Mathematical ReasoningAn ice cream company sells ice cream in two containers a cylindrical tub and a rectangular box as shown in the figure Which container holds more ice cream and what is the positive difference in their volumes Which container holds more ice cream 3 in 6 25 in rectangular box The positive difference in the volume of both containers is Type an integer or decimal rounded to two decimal places as needed in 3 8 in rata 3 5 in

Math - Others

Mathematical ReasoningDetermine whether each statement is true or false You have one submission for each statement a The function x8 1 6 x 1 is a polynomial of degree 51 True False b The function x 5x x 1 is a polynomial of degree 4 True False c The function x5 1 6 x True False is a rational function nctions d The function 8x 6 2x 2 3 is a rational function True False

Math - Others

Mathematical ReasoningThe Nicols are buying a house selling for 235 000 They pay a down payment of 35 000 from the sale of the current house To obtain a 15 year mortgage at a 6 interest rate the Nicols must pay 2 5 points at the time of closing a What is the amount of the mortgage b What is the cost of the 2 5 points a The amount of the mortgage is

Math - Others

Mathematical ReasoningA particular candy comes in various colors According to the company the distribution of colors for the candy is as follows Purple Yellow Red Orange Green Blue Brown 17 23 19 6 10 10 15 Color Percentage Suppose you have a large bag of candies and you choose one candy at random a Find P green candy or blue candy Probabilities should be between 0 and 1 Are these outcomes mutually exclusive Why Yes Choosing a green and blue candy is not possible Yes Choosing a green and blue candy is possible No Choosing a green and blue candy is possible No Choosing a green and blue candy is not possible b Find P yellow candy or red candy Probabilities should be between 0 and 1 Are these outcomes mutually exclusive Why No Choosing a yellow and red candy is not possible Yes Choosing a yellow and red candy is not possible Yes Choosing a yellow and red candy is possible No Choosing a yellow and red candy is possible c Find P not purple candy Probabilities should be between 0 and 1 x

Math - Others

Mathematical Reasoning2 5 Pablo drives to work The probability that he leaves home before 07 00 is 4 If he leaves home before 07 00 the probability he will be late for work is If he leaves home at 07 00 or later the probability he will be late for work is Copy and complete the following tree diagram b before 07 00 07 00 or later 8 S late not late late not late Find the probability that Pablo leaves home before 07 00 and is late for work thot be leu home before

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Mathematical ReasoningPersonality types are broadly defined according to four main preferences Do married couples choose similar or different personality types in their mates Suppose the following data were collected to attempt to answer this question Similarities and Differences in a Random Sample of 375 Married Couples Number of Similar Preferences Number of Married Couples All four Three Two One None 1 2 25 3 132 115 Suppose that a married couple is selected at random a Use the data to estimate the probability that they will have 0 1 2 3 or 4 personality preferences in common Round your answers to 2 decimal places 64 39 4

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Mathematical ReasoningJohn runs a computer software store Yesterday he counted 131 people who walked by the store 66 of whom came into the store Of the 66 only 27 bought something in the store Round your answers to two decimal places a Estimate the probability that a person who walks by the store will enter the store b Estimate the probability that a person who walks into the store will buy something c Estimate the probability that a person who walks by the store will come in and buy something d Estimate the probability that a person who comes into the store will buy nothing

Math - Others

Mathematical ReasoningConsider a family with 4 children Assume the probability that one child is a boy is 0 5 and the probability that one child is a girl is also 0 5 and that the events boy and girl are independent a List the equally likely events for the gender of the 4 children from oldest to youngest Let M represent a boy male and F represent a girl female Select all that apply FMFF MMMF FFFM MMFM MMFF MFMM FFFF MFFF MMMM MFMF FFMM FMMF FMFM FFMF MFFM FMMM b What is the probability that all 4 children are male Enter your answer as a fraction X Notice that the complement of the event all four children are male is at least one of the children is female Use this information to compute the probability that at least one child is female Enter your answer as a fraction

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Mathematical Reasoningse Exhibit to answer question Bacon 50 40 30 20 10 A 10 B E C D 20 30 40 50 60 70 Eggs he economy is operating at point C the opportunity cost of producing an additional 15 units of bacon is a 20 units of eggs Ob 40 units of eggs c 50 units of eggs d 30 units of eggs e 10 units of eggs

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Mathematical ReasoningExhibit to answer question Bacon 50 40 30 20 A 10 B E F C D 10 20 30 40 50 60 70 Eggs he economy were operating at point E a the opportunity cost of 20 additional units of eggs is 10 units of bacon b the opportunity cost of 20 additional units of eggs is 20 units of bacon c the opportunity cost of 20 additional units of eggs is 30 units of bacon O d 20 additional units of eggs can be produced with no impact on bacon production

Math - Others

Mathematical Reasoning5 12 points Solve the homogeneous linear system corresponding to the coefficient matrix A 27 1 0 2 2 1 2 4 02 4 1 2

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Mathematical ReasoningSuppose a company makes surgical screws To pass inspection the screws must be 63 millimeters long and can vary by no mo than 0 03 millimeter a Write the possible screw lengths in mm using plus minus notation mm mm b Write the possible screw lengths in mm using interval notation Simplify your answer completely mm c All screw lengths must be between which two values in mm All screw lengths must be between a lower value of mm mm and an upper value of

Math - Others

Mathematical ReasoningA single bit comparator c A B s two numbers A and B and produces three outputs Y if A B Y if A B and Y3 if A B as given below A Y A B Y AB Y3 A B B Y A B Y AB Y3 A B C Y A B Y A B Y3 A B D Y B AB Y AB Y3 B Choose the correct answer from the options given below Da A and B only O b A B and C only O c A C and D only Od A and D only

Math - Others

Mathematical ReasoningQuestion 6 Not yet answered Marked out of 1 50 The converse of the statement If a b and a c then a b c is O a 0 b OC O d ab and a c or a does not divide b c If a b c then ab and a c If a b c then ac or ab ab and ac or a b c Previous page indows LudGE

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Mathematical ReasoningIn November 2012 Benjamin Pershouse bought a pair of women s indoor slippers through L L Bean s website Pershouse said that after a few years of indoor use the rubber soles of the slippers began to flake off in large chunks He did not say that the slippers were defective or that he was dissatisfied with their quality In February 2018 L L Bean s executive chairman posted a letter on the company s Facebook page announcing a change in founder Leon Leonwood Bean s longstanding policy of if something s not working or fitting or standing up to its task or lasting as long as you think it should we ll take it back The letter indicated that A small but growing number of customers has been interpreting our guarantee well beyond its original intent Some view it as a lifetime product replacement program expecting refunds for heavily worn products used over many years Others seek refunds for products that have been purchased through third parties such as at yard sales The letter then announced Based on these experiences we have updated our policy Customers will have one year after purchasing an item to return it accompanied by proof of purchase After one year we will work with our customers to reach a fair solution if a product is defective in any way In March 2018 Pershouse attempted to return the slippers to an LL Bean store in Burlington Massachusetts He had proof of purchase but the clerk refused to take the slippers back Pershouse then filed a class action lawsuit against L L Bean on several grounds including breach of contract breach of warranty and unjust enrichment Do you think Benjamin was in the right for filing suit Do you think LL Bean had an obligation here What could maybe have been a resolution without having to go to court This is a real court case but I m looking for your opinion on this issue No research needed just share your thoughts Be sure to meet minimum requirements for writing assignments

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Mathematical ReasoningA population of cattle is increasing at a rate of 600 80t per year where t is measured in years By how much does the population increase between the 6 th and the 9 th years Total Increase 840

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Mathematical ReasoningIf A and B are 3 3 matrices such that A 2 B 4 then B 2A O a 1 O b 1 4 O C O d None O e 4 8

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Mathematical ReasoningStatements I am BERE I can I have I like I will Answers 1 I am muslim and a student at National Louis University 2 I am I remember 1 2 I believe 1 I can speak urdu and English 2 I can 1 2 1 2 1 2 1 2 Visible or Invisible Visible O Invisible Both Visible Invisible Both Visible Invisible Both Visible O Invisible Both Visible Invisible Both Visible O Invisible Both Visible Invisible Both Reflect on the following questions in complete sentences Your responses should be clear and thoughtful How many of the characteristics included on your list fit neatly into one of the following categories Gender Ethnicity Race Religion Socioeconomic Status Language Sexual Orientation Education Career and Relationship Status Were you surprised by any of your answers

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Mathematical ReasoningIdentify the explanatory variable and the response variable the number of miles a person runs per week for three months and that person s time in a 5 km race the response variable is The explanatory variables represents Select Select 1 a person s time in a 5 km race 2 the number of miles a person runs per week for three months or the first sentence 1 the person s time in a 5 km race 2 the number of miles the person runs per week for three months for the second contorco

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Mathematical ReasoningLet f x 3 x Simplify each of the following expressions f 2 3 2 f 2 h 3 2 h f 2 h f 2 3 2 h f 2 h f 2 h 3 2 h 2 Make sure to cancel out the factor of h in the denominator

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Mathematical ReasoningThe Venn diagram here shows the cardinality of each set Use this to find the cardinality of the given set A A C 10 11 B 8

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Mathematical Reasoning54 55 In Australia the traditional food of Indigenous people is known as bush tucker Most famous is the witchetty grub which is a rich source of protein for communities living off the land Witchetty grubs are large moth larvae up to 12cm long that are found in the roots of the witchetty bush They taste like almonds when eaten raw and when cooked by rolling them in hot ashes they taste like a fried egg In the islands of Fiji duruka a delicious vegetable which looks like asparagus is an important part of the traditional diet It s found inside the stem of a long grassy plant similar to sugarcane and is sold in bundles The young unopened flower heads are very sweet Some say it tastes like sweetcorn It s eaten raw roasted on an open 56 Read the following article In sentences 54 60 fill in one or two words which you will find in the article The statements are not in the same order as the article 57 58 Oceania in the southern half of the Pacific Ocean is made up of 14 countries and several overseas territories or dependencies such as American Samoa and French Polynesia It s divided into four regions Australasia and the island groups of Melanesia Micronesia and Polynesia which are made up of over 10 000 islands There is a large variety of traditional food across Oceania some of it very strange The many Because of the way they are These regions are Duruka fuits Here the The flower is eaten The fruit s taste depends on the way it is served when fire or cooked in coconut cream This is one food that tourists are sure to enjoy Tahitian noni fruit grows wild on trees throughout Tahiti It looks like a potato with a pebbly surface and is yellowish greenish white in colour It has an extremely unpleasant cheese like smell Unripe noni is tough and is best cooked in stir fries or curries When ripe noni can be eaten raw However it s usually consumed in juice form mixed with other juices to mask the taste Noni fruit juice is sold in health food shops around the world because of its many health benefits as confirmed by medical research scientists have confirmed are the reason this fruit is so popular two words A traditional food from Samoa known as S ee consists of raw sea cucumber guts that is intestines in salted water yes sea cucumbers are animals not plants S ee comes in bottles and is sold in local fish markets or along the roadside in recycled Coca Cola bottles Sea cucumbers called rori in Tahiti belong to the family of echinoderms like starfish and sea urchins and are shaped like cucumbers S ee is supposed to be very healthy too However because it s slimy and looks like a bottle of water full of tapeworms it s probably one that tourists will skip these animals are named after a vegetable one word of thousands of separate islands two words The region includes several countries as well as various it reminds one of a kind of nut one word people have a proper English name for their cuisine one word and is known for its sweetness one word

Math - Others

Mathematical ReasoningDrag the measurements to the containers to show equal length 75 ft 900 in 360 in 3960 ft 1320 yd 10 yd 12 inches in 1 foot ft 3 ft 1 yard yd 5280 ft 1 mile mi 0 75 mi

Math - Others

Mathematical ReasoningExplain the role of managers in the area you think is most important to health care ie talent management succession planning etc Provide one example to support your rationale Your initial post should be a minimum of 10 collegiate level sentences and it should include a reference from the textbook chapter page number or full research article citation

Math - Others

Mathematical ReasoningHow expensive is Maui A newspaper gave the following costs in dollars per day for a random sample of condominiums located throughout the island of Maui 86 50 66 60 355 55 500 71 44 350 60 50 260 45 45 125 235 65 60 130 LUSE SALT a Compute the mean median and mode for the data What is the mean What is the median What is the mode b Compute a 5 trimmed mean for the data and compare it with the mean computed in part a Round your answer to two decimal places Does the trimmed mean more accurately reflect the general level of the daily rental costs Yes the trimmed mean is closer to the median and mode Yes the trimmed mean is further from the median and mode No the trimmed mean is further from the median and mode No the trimmed mean is closer to the median and mode c If you were a travel agent and a client asked about the daily cost of renting a condominium on Maui what average would you use Explain The median the data skews to the right seems to represent the costs most accurately since so it should be the one reported Is there any other information about the costs that you think might be useful such as the spread of the costs No other information about condominium costs would be useful The lowest and highest prices of the condominiums would also be useful The average price of a condominium in 1980 would also be useful

Math - Others

Mathematical Reasoning1 Write 3 examples of a valid statement in symbolic or set logic 1 2 3 2 Consider the following logic statements p Manila is the capital of the Philippines q Today is Friday r The weather is bad today Write the following logic statements according to the operations P p q q V r M p q qr ra

Math - Others

Mathematical Reasoning4 Individual and market supply Suppose that Shen and Valerie are the only suppliers of pizza slices in a particular market The following table shows their annual supply schedules Price Dollars per slice 1 2 PRICE Dollars per slice 5 Shen s Quantity Supplied Valerie s Quantity Supplied Slices Slices 20 35 45 50 55 20 30 35 40 On the following graph plot Shen s supply of pizza slices using the green points triangle symbol Next plot Valerie s supply of pizza slices using the purple points diamond symbol Finally plot the market supply of pizza slices using the orange points square symbol Shen s Supply Valene s Supply Macket Supply

Math - Others

Mathematical ReasoningIPE IPB I 5 IPBv The shear force and bending moment diagrams are presented for the given beam Use the following profil secitons design the beam and then discuss the results 21 2m FOURNER 2 8 2 3 m 5 tkN 2 2 4 4 2 m T t M t m

Math - Others

Mathematical ReasoningComplete the following table with either a yes or no regarding the attributes of a proprietorship partnership corporation and limited liability company LLC Attribute Present 1 Unlimited Indefinite life 2 Legal entity 3 Limited liability Proprietorship Partnership Corporation LLC

Math - Others

Mathematical ReasoningFor each of the accompanying control charts analyze the data using both median and up down run tests with z 1 96 limits a Are nonrandom variations present Assume the center line is the long term median UCL LCL Test Median Up Down Conclusion No non random variations are apparent in the data It appears there may be non random variations in the data b Are nonrandom variations present Assume the center line is the long term median

Math - Others

Mathematical ReasoningAfter a number of complaints about its tech assistance a computer manufacturer examined samples of calls to determine the frequency of wrong advice given to callers Each sample consisted of 100 calls Number of errors 1 2 5 3 UCL LCL 35 4 7 54 66 SAMPLE 7 8 9 10 11 12 13 14 15 16 8 459 3 4 5 6 6 7 Click here for the Excel Data File a Determine 95 percent limits Do not round your intermediate calculations Round your final answers to 2 decimal places Round up any negative control limit value to zero b Is the tech assistance process stable i e in control O The process is in control

Math - Others

Mathematical ReasoningThe fuel tank of a certain airplane can hold up to 200 gallons of fuel Let W be the total weight of the airplane in pounds Let F be the total amount of fuel in its tank in gallons Suppose that W 7F 4000 gives Was a function of F Identify the correct description of the values in both the domain and range of the function Then for each choose the most appropriate set o values Domain Range Description of Values O amount of fuel in airplane s tank in gallons Oweight of airplane in pounds O amount of fuel in airplane s tank in gallons Oweight of airplane in pounds Set of Values Choose one Choose one

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Mathematical ReasoningHow long does it take to finish the 1 161 mile Iditarod Dog Sled Race from Anchorage to Nome Alaska Finish times to the near hour for 57 dogsled teams are shown below 260 272 237 243 278 334 262 265 288 295 314 310 308 289 289 289 290 299 305 316 309 319 317 319 332 322 USE SALT For this problem use five classes a Find the class width 295 285 300 287 289 248 257 339 359 342 0 1 0 0 308 298 304 276 284 303 304 298 298 333 329 310 329 308 329 322 323 328 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 000 000 Class Limits Class Boundaries Midpoint Frequency Relative Frequency Cumulative Frequency 286 292 294 000 000

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Mathematical ReasoningAre cigarettes bad for people Cigarette smoking involves tar carbon monoxide and nicotine measured in milligrams The first tv are definitely not good for a person s health and the last ingredient can cause addiction stem 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Brand 17 Brand A Brand B Brand C Brand D Brand E Brand F Brand G Brand H Brand I Brand J Brand K Brand L Brand M Tar Nicotine CO leaf 14 2 16 1 29 7 8 1 4 0 14 9 8 9 12 5 16 5 15 0 13 6 15 2 7 9 0 96 13 5 Brand N 1 26 16 7 0 20 5 5 2 23 23 4 Brand P 0 57 10 3 Brand Q 1 04 14 9 0 86 9 1 1 05 12 4 1 02 16 2 0 92 15 3 0 91 12 9 0 80 Brand 14 3 0 47 9 9 Brand O Brand R Brand S Brand T Brand U Brand V Brand W Brand X Brand Y Tar Nicotine co 11 3 9 2 1 2 17 2 12 9 15 9 4 6 14 6 7 2 8 7 15 3 Use the data in the table above to make a stem and leaf display for milligrams of tar per cigarette smoked Enter numbers from smallest to largest separated by spaces Enter NONE for stems with no values 11 9 0 88 10 1 0 84 0 13 1 36 0 76 9 4 1 6 1 18 12 5 18 4 17 6 0 22 4 8 1 22 0 91 16 0 0 71 8 4 0 79 10 7 13 8 0 92 15 0

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Mathematical ReasoningIn the Aloha state you are very unlikely to be murdered However it is considerably more likely that your house might be burgled your car might be stolen or you might be punched in the nose That said Hawaii is still a great place for a vacation or if you are very lucky to live Suppose the following numbers represent the crime rates per 100 000 population in Hawaii murder 2 4 rape 32 5 robbery 92 4 house burglary 901 1 motor vehicle theft 545 4 assault 120 6 a Display this information in a Pareto chart showing the crime rate for each category 1000 p Crime Rate Crime Rate Crime Rate Crime Rate 800 600 400 200 120 6 1000 901 1 800 600 400 200 0 800 1000p 600 400 200 1000 800 600 400 200 545 4 2 4 Assault Theft Burglary Robbery Rape Murder 545 4 901 1 32 5 32 5 2 4 Burglary Theft Assault Robbery Rape Murder 32 5 92 4 120 6 92 4 92 4 92 4 32 5 120 6 2 4 Murder Rape Robbery Assault Theft Burglary 901 1 545 4 901 1 545 4 120 6 2 4 Murder Rape Robbery Burglary Theft Assault G Q b Could the information as reported be displayed as a circle graph Explain Hint Other forms of crime such as arson are not included in the information In addition some crimes might occur together

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Mathematical ReasoningDesign a schedule of work sampling observations in which eight observations are made during one eight hour day Using the following table read the last digit going down column 1 for hours e g 21520 and read across row 4 from left to right in sets of two for minutes e g 16 32 15 46 Arrange the times chronologically Note It is only possible to sample observations between 00 00 and 07 59 Therefore discard any sampled hour or minute values that do not conform to this time range Leave no cells blank be certain to enter 0 wherever required 1 6912 2 3491 3 4715 2486 2776 4 1632 5 8510 7209 0938 2376 0120 6 3950 1328 7871 7343 6083 2108 7752 0521 8511 3956 8 2716 1396 7354 0249 7728 9 2935 8259 9912 3761 4028 10 8533 9957 9585 1039 2159 11 0508 1640 2768 4666 9530 12 2951 0131 4359 3095 4421 HH2 7 2 3 7264 2801 8901 4627 8387 1192 0575 7547 2093 4617 2664 3856 1546 1950 1844 1123 0064 1908 4237 Chronological order Time Observation 1 2 3 4 5 6 7 0 0 1 1 225 2044 3957 8818 9207 2438 3352 3018

Math - Others

Mathematical ReasoningNow determine the frequencies The class frequency is the total number of data values in that class Recall that each dat value should fall into exactly one class Now examine the data set and determine how many data values fall into each class Note that with such a large number of values you may find it helpful to order the data first 28 38 Complete the table 39 49 50 60 28 33 33 35 38 39 40 40 41 41 41 42 43 43 44 61 71 45 46 46 47 Class Limits Class Boundaries 72 82 51 51 51 52 52 27 5 38 5 38 5 49 5 49 5 60 5 47 47 60 5 71 5 71 5 82 5 3 47 47 47 48 48 48 49 50 51 51 51 54 55 55 55 56 57 Frequency x X X x x 60 44 45 65 69 81

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Mathematical ReasoningCertain kinds of tumors tend to recur Suppose the following data represent the lengths of time in months for a tumor to recur after chemotherapy 1 13 20 19 18 1 22 21 55 47 26 50 49 1 25 44 37 18 For this problem use five classes a Find the class width 12 38 6 10 37 37 39 USE SALT Class Limits 12 24 36 39 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 48 2 0 5 12 17 24 1 36 15 Class Boundaries Midpoint Frequency 42 11 51 42 26 18 40 28 19 12 1 46 24 1 53 59 47 51 36 1 48 6 5 59 38 18 30 11 30 1 42 1 X X X X Relative Frequency X Cumulative Frequency x

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Mathematical ReasoningDetermine the optimum preventive maintenance frequency for each of the pieces of equipment if breakdown time is normally distributed Round Probability Ratio to 4 decimal places and all other answers to 2 decimal places Negative values should be indicated by a minus sign Use Table Equipment A201 B400 C850 Equipment A201 B400 C850 Equipment Average Time days between Breakdowns A201 0400 19 31 36 Click here for the Excel Data File Preventive Maintenance Cost 240 140 490 Probability Ratio Standard Deviation 2 3 6 Breakdown Cost 2 140 3 440 4 600 Interval days

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Mathematical Reasoninghour for 52 dogsled teams are shown below O O O 240 240 Draw or use technology to make a dotplot for the data above regarding the finish time number of hours for the Iditarod Dog Sled Race 240 260 270 235 243 278 295 285 298 287 287 248 257 337 360 342 332 262 267 286 297 312 312 308 240 278 282 305 306 287 289 289 290 296 298 331 329 329 308 327 306 327 327 286 290 294 297 307 314 311 317 317 321 PROCEDURE How to Make a Dotplot Display the data along a horizontal axis Then plot each data value with a dot or point above the corresponding value on the horizontal axis For repeated data values stack the dots Frequency 30 25 USE SALT 20 15 10 5 260 260 260 260 280 280 Consider the following histogram of the data 300 Finish Times 280 00000 280 300 Finish Times 300 Finish Times 000000 GD 300 Finish Times 0 234 5 260 5 286 5 312 5 338 5 364 5 Finish Times 320 n 308 300 320 320 300 304 320 Compare the dotplot to a histogram of the data above Select all that apply The dotplot and histogram both show a greater density from 280 to 340 O Histograms show the frequency of individual data values 340 340 340 340 360 360 360 360 G

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Mathematical ReasoningWhat is the difference between a class boundary and a class limit Select all that apply Class limits are not possible data values Class boundaries are possible data values 0000 Class limits are values halfway between the upper class boundary of one class and the lower class boundary of the nex Class boundaries specify the span of data values that fall within a class Class limits specify the span of data values that fall within a class Class boundaries are values halfway between the upper class limit of one class and the lower class limit of the next Class limits are possible data values Class boundaries are not possible data values

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Mathematical ReasoningDetermine which shipping alternative would be most economical to ship 135 boxes of parts when each box has a price of 200 and holding costs are 30 percent of price given this shipping information overnight 320 two day 260 six day 180 Round your intermediate calculations to 2 decimal places O Overnight O Six day O Two day

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Mathematical ReasoningThe frequency of breakdown of a machine that issues lottery tickets is given in the following table Repairs cost an average of 233 A service firm is willing to provide preventive maintenance under either of two options 1 is 503 and covers all necessary repairs and 2 is 369 and covers any repairs after the first one Do not round intermediate calculations Round your final answer to the nearest whole number Number of breakdowns month Frequency of occurrence Click here for the Excel Data File Pay for all repairs Service option 1 Service option 2 0 1 2 3 4 10 30 25 15 20 Which option would have the lowest expected cost pay for all repairs service option 1 or service option 2 O Pay for all repairs O Service option 1

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Mathematical ReasoningThe probability that equipment used in a hospital lab will need recalibration is given in the following table A service firm is willing to perform maintenance and do any necessary calibrations for a fee of 500 per month Recalibration costs 425 per time Round the answer of Expected cost of recalibration to nearest whole number Number of Recalibrations Probability of Occurrence Click here for the Excel Data File Expected cost of recalibration Service contract cost 0 15 1 30 2 30 3 15 4 10 Which approach would be most cost effective recalibration as needed or the service contract O Service contract O Recalibration

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Mathematical ReasoningPrepare a master production schedule for industrial pumps in the manner of the following table Use the MPS rule to schedule production when the projected on hand inventory would be less than 10 without production Suppose that there are currently 64 pumps in inventory and a production lot size of 70 pumps is used Leave no cells blank be certain to enter 0 wherever required Forecast Customer orders committed Projected on hand inventory MPS ATP 30 33 2 June 30 20 3 30 10 4 30 4 5 40 2 6 July 40 7 40 8 40

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Mathematical ReasoningWormwood Ltd produces a variety of furniture products The planning committee wants to prepare an aggregate plan for the next six months using the following information Demand Capacity Regular Overtime Regular time Overtime Cost Per Unit Period Subcontract Inventory holding per month MONTH 4 1 3 2 160 150 160 180 Forecast Output 150 10 Regular Overtime Subcontract Output Forecast Inventory 150 150 10 0 50 75 80 4 Click here for the Excel Data File Subcontracting can handle a maximum of 10 units per month Beginning inventory is zero Develop a plan that minimizes total cost No back orders are allowed Regular capacity Regular production Negative amounts should be indicated by a minus sign Leave no cells blank be certain to enter 0 wherever required 150 10 160 2 5 6 170 140 150 160 160 10 10 3 160 4 180 5 170 6 140 Total 960

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Mathematical ReasoningA manager has compiled estimat nature The payoff table is as follows Alternative A B C Profit in thousands Click here for the Excel Data File profits for various capacity STATE OF NATURE 1 2 30 131 105 O Alternative A Alternative B O Alternative C O None 155 98 51 a Is there any alternative that would never be appropriate in terms of maximizing expected profit b For what range of P 2 would alternative A be the best choice if the goal is to maximize expected profit

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Mathematical ReasoningThe lease of Theme Park Inc is about to expire Management must decide whether to renew the lease for relocate near the site of a proposed motel The town planning board is currently debating the merits of granting approval to the mo A consultant has estimated the net present value of Theme Park s two alternatives under each state of nature as shown below What course of action would you recommend using Options Renew Relocate Click here for the Excel Data File a Maximin O Renew O Relocate b Maximax Relocate Renew Motel Approved 500 000 5 000 000 c Laplace Relocate Renew Motel Rejected 4 000 000 100 000