# Mathematical Reasoning Questions and Answers

Math - Others

Mathematical Reasoning4 A stereo is marked down 75 If this is a 15 decrease find the sale price

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Mathematical Reasoning6 The average production of the excavator is the controlling factor in a highway ditch cleanin contract Excavators with four different bucket sizes are available as rental units The hourly renta rate is directly proportional to the bucket capacity of the excavator Assume that productio loose yd hr is equal to excavator cycles per hour x average bucket payload in LCY per cycle The excavator characteristics are as follows 0 0 0 0 Excavator O A B C D 1 2 3 4 Minimum Cycle Average Bucket Payload Time min LCY 0 50 1 00 1 75 2 00 The optimally efficient excavator is Excavator 1 Excavator 2 Excavator 3 Excavator 4 0 25 0 33 0 50 0 98

Math - Others

Mathematical ReasoningWashington Air Company is considering the purchase of a helicopter for connecting services between the company s base airport and the new intercounty airport being built about 30 miles away It is believed that the chopper will be needed only for six years until the Rapid Transit Connection is phased in The estimates on two types of helicopters under consideration the Whirl 2B and the ROT 8 are given in the table below Assuming that the Whirl 2B will be available in the future with identical costs what is the annual cost advantage of selecting the ROT 8 Use an interest rate of 8 Click the icon to view the estimates on two types of helicopters under consideration Click the icon to view the interest factors for discrete compounding when i 8 per year

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Mathematical ReasoningFor Randa Company the following information is available Capitalized leases 560 000 Copyrights 240 000 Long term receivables 210 000 In Randa s balance sheet intangible assets should be reported at O a 210 000 O b 240 000 O c 770 000 d 800 000 Clear my choice

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Mathematical Reasoning1 2 2024 Gaza company sold merchandise inventory of 50 000 to Jenin company terms 2 10 n 30 and on 11 2 2024 Gaza company received the amount for merchandise inventory sold The journal entry on 15 2 2024 under gross method is O a Cash debit 50 000and Accounts receivable credit by same amount O b Accounts receivable debit 49 000and cash credit by same amount O c Cash debit 50 000and Accounts receivable credit 49 000 and sales discount forfeited credit 1 000 O d Accounts receivable debit 50 000and cash credit by same amount

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Mathematical ReasoningJaser Company will invest 300 000 today The investment will earn 6 for 5 years simple interest with no funds withdrawn In 5 years the amount in the investment fund is O a 401 468 O b 402 087 O c 390 000 O d 300 000

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Mathematical ReasoningHamilton Company has cash in bank of 10 000 restricted cash in a separate account of 3 000 and a bank overdraft in an account at another bank of 1 000 Hamilton should report cash of O a 9 000 O b 12 000 O c 10 000 O d 13 000

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Mathematical ReasoningFlag questio Ola Company has the following items common stock 950 000 treasury stock 105 000 deferred income taxes 125 000 and retained earning 454 000 What total amount should Ola Company report as stockholders equity Oa 1 549 000 O b 1 424 000 O c 1 299 000 O d 1 174 000

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Mathematical ReasoningOn the following graph AD represents the initial aggregate demand curve in a hypothetical economy and SRAS represents the initial aggregate supply curve The economy s natural real GDP is 12 billion PRICE LEVEL 304 900 NRGOP AD O AD ADA AD 12 REAL GOP ons of dan The initial short run equilibrium level of real GDP is 21 100 103 104 SRAS Suppose the government seeking full employment borrows money and increases its expenditures by the amount it believes necessary to close the output gap According to critics of Keynesian fiscal policy which curve in the previous graph will most likely be the new aggregate demand curve 1 10 billion 14 billion 12 billion 2 and the initial short run equilibrium price level is

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Mathematical Reasoning5 3 Suppose there is a simple index of three stocks Stock X opens the day with 2000 shares at 3 80 per share Stock Y the day with 1000 shares at 3 50 per share Stock Z opens the day with 3000 shares at 4 30 per share This simple index rises 5 4 over the course of th day What is the value of the index at the end of the day Round your answer to the nearest hundred OA 24 600 B 25 800 O OC 24 000 6er 200

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Mathematical ReasoningSolve by completing the square and applying the square root property Express the solution set in exact simplest form 4m 2 28m 3 0 The solution set is 0 16 3

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Mathematical ReasoningA z score is a measure of relative standing for an observation because it tells us the number of standard deviations and direction an observation is from the mean In other words when we use the standard deviation as our measurement unit the absolute value of the z score tells us how far an observation is from the mean in number of standard deviations It is positive when the observation is found above to the right or greater than the mean and negative when the observation is found below to the left or less than the mean The following is the formula to compute the z score for an observation x from a population with mean and standard deviation d Alternatively when working with a sample instead of a population this formula is used with sample mean x and sample standard deviation s Recall the following summary statistics for our sample of white wine pH measurements Z Variable Name pH Wines with low pH taste tart and crisp whereas wines with higher pH are more susceptible to bacterial growth A pH of about 3 0 to 3 4 is most desirable for white wines z X X S 3 0 1 25 x 0 Z X X S X X 5 z score for pH of 3 4 3 4 1 25 Determine the relative standing for a pH of 3 0 and a pH of 3 4 by computing a z score for each observation using the rounded values above and rounding each z score to two decimals z score for pH of 3 0 3 1883 0 1510 3 1883 0 1510 N Mean X Standard Deviation 4 898 3 1883 0 1510 Median 3 18 Minimum Value 2 72 Taking the absolute value of each z score gives the following interpretations for each pH Maximum Value 3 82

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Mathematical Reasoning1 Assume that we want to verify if the following formula is a tautology by drawing a truth table with 8 rows p g p Vr p V g r How many ones true sentences are there in the column representing p V q r p q p Vr the entire considered formula

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Mathematical ReasoningEntries for Sale of Fixed Asset Equipment acquired on January 8 at a cost of 152 470 has an estimated useful lif of 18 years has an estimated residual value of 8 650 and is depreciated by the straight line method a What was the book value of the equipment at December 31 the end of the fourth year 120 510 Feedback Check My Work b Assume that the equipment was sold on April 1 of the fifth year for 111 947 1 Journalize the entry to record depreciation for the three months until the sale date If an amount box does not require an entry leave it blank Round your answers to the nearest whole dollar if required 88 Feedback Check My Work The depreciation account of the fixed asset being sold or discarded needs to be updated to reflect the months of use in the year it is being discarded or sold The straight line method of depreciation calculates the amount of depreciation to be recognized each year 2 Journalize the entry to record the sale of the equipment If an amount box doe not require an entry leave it blank Do not round intermediate calculations

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Mathematical ReasoningA large tank of fish from a hatchery is being delivered to a lake The hatchery claims that the mean length of fish in the tank is 16 inches and the standard deviation is 4 inches A random sample of 36 fish is taken from the tank Let X be the mean sample lengt of these fish What is the probability that x is within 0 5 inch of the claimed population mean Round your answer to four decimal places USE SALT

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Mathematical ReasoningRequired information Let P x be the statement the word x contains the letter a What is the truth value of P orange The truth value of Plorange is Click to select Click to select false true

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Mathematical ReasoningAssume that IQ scores are normally distributed with a standard deviation of 15 points and a mean of 100 points If 120 people are chosen at random what is the probability that the sample mean of IQ scores will not differ from the population mean by more than 2 points Round your answer to four decimal places LAUSE SALT

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Mathematical ReasoningP T TFF Required information NOTE This is a multi part question Once an answer is submitted you will be Fill the provided truth tables and check whether the given conditional staten contingency q paq F T Click to select Click to select Click to select F Click to select T p q p Click to select Click to select Click to select Click to select The conditional statement p A q pis a Click to select Click to select contradiction contigency

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Mathematical ReasoningFill the following truth table P 9 T T T F T F Required information NOTE This is a multi part question Once an answer is submitted you will be unable to return to this pa Show that each of these conditional statements is a tautology by using truth tables F F P F F T T pv q Click to select T T F p pv q F Click to select T Click to select PA pv q T T Click to select q

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Mathematical ReasoningAbe b c d Barb Student Cal N answer 2 1 3400 S 2 Perform the indicated operations to the correct number of significant figures using the rules for significant figure a 37 60 x 1 23 46 2 37 60 0 0130 13000 Questions 3 6 Three students named Abe Barb and Cal make measurements in m of the length of a table Find the means 1 using the data given L3 L 1 4717 1 4753 1 4719 L 1 4711 1 4759 b 0 75 6 7 8 975 1 4723 1 4722 1 4756 1 4727 LA 1 4715 1 4749 1 4705 c 0 0000089 x 6500 00 in scientific notation XLO L On l a 110 4916103 00040 0 0000 11 47540 00043 0 0002 1 4719 0 0004 0005 Only one significant figure is kept in the standard error a and this determines the number of significant figures in the mean The actual length of the table is 1 4715 m 3 Find the percentage differences in length measured by three students error 4 State how one can measure the accuracy of a measurement Apply your idea to the measurements of three students above and state which of the students has the most accurate measurement Why is that your conclusion 5 State the characteristics of data that indicate a systematic error Do any of the three students have data that suggest the possibility of a systematic error If so state which students it is and state how the data indicate your conclusion 6 Which student has the best measurement considering both accuracy and precision State clearly What the characteristics are of the student s data on which your answer is based

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Mathematical ReasoningWhat is a population parameter A population parameter is a numerical Give three examples Select all that apply 00 S Q XIX b descriptive meas

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Mathematical Reasoningdistributed with a mean of 82 minutes and a standard deviation of a 19 minutes Use the figure below to answer the following questions Area Under a Normal Curve 0 15 2 35 13 5 H 30 H 20 H 0 34 f 68 95 99 7 34 H o 13 5 2 35 0 15 H 20 H 30 a Estimate the probability that a randomly selected student will complete their final exam in less than 63 minutes b The final exam is scheduled to allow 2 hours Estimate the probability that a randomly selected student will need more than 2 hours to complete their exam c In a section with 160 students how many students do you expect will need more than 2 hours to complete their exams

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Mathematical Reasoninga 6 8 10 12 14 16 18 5 6 7 b 2 3 4 Which has the larger standard deviation figure a figure b What is the mean of the curve in figure a What is the mean of the curve in figure b 8

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Mathematical ReasoningThe following times were recorded by the quarter mile and mile runners of a university track team times are in minutes Quarter milers Standard deviation to 4 decimals Coefficient of variation to 1 decimal Quarter Mile Times Milers Mile Times 0 92 0 99 4 35 4 59 4 70 4 51 After viewing this sample of running times one of the coaches commented that the quarter milers turned in the more consistent times Use the standard deviation and the coefficient of variation to summarize the variability in the data 4 52 1 06 0 96 1 00 Standard deviation to 4 decimals Coefficient of variation to 1 decimal Does the use of the coefficient of variation indicate that the coach s statement should be qualified i Yes the coefficient shows that as a percentage of the mean the quarter milers times show less variability ii No the coefficient shows that as a percentage of the mean the quarter milers times show more variability

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Mathematical Reasoningdecreases The value of a new car depreciates as soon as it is driven off the car lot by 13 each year If a car is now worth 16 650 after 4 years what was the original cost of the car

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Mathematical ReasoningDETERMINE WHICH STUDENT DREW EACH TRIANGLE TYPE THE STUDENT S NAME IN THE WHITE RECTANGLE ABOVE THEIR DRAWING 57 10x 4 7x CLUE 1 The smallest angle in Gilroy s triangle measures 52 4x 2 4x CLUE 2 The value of x in Carmella s triangle is half the value of x in Gilroy s triangle 67 3x 10 61 CLUE 3 The smallest angle in Michael s triangle measures 44

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Mathematical Reasoning5 The half life of a radioactive substance is 8 hours How much of the substance will there be after 4 days if the initial mass of the substance is 600g Round to two decimal places

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Mathematical ReasoningCompute your average velocity in the following two cases a You walk 73 0 m at a speed of 1 06 m s and then run 73 0 m at a speed of 4 49 m s along a straight track b You walk for 1 00 min at a speed of 1 06 m s and then run for 1 41 min at 4 49 m s along a straight track a Number i b Number i Units Units

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Mathematical Reasoning2 Given the following set of triangles determine the value of angle 8 in degrees A 0 degrees B 20 H G F E

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Mathematical Reasoning1 What are the main differences between analog and digital signals 2 What are the common points between analog and digital system 3 Convert following decimal numbers to binary octa decimal I and hexadecimal nmbers a 128 62 b 935 04 4 Convert following binary numbers to decimal octal and hexadecimal numbers a 1101 01 b 11000101 1001 5 Convert following hexadecimal numbers to decimal binary and octal numbers a 1101 01

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Mathematical Reasoningshe 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

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Mathematical ReasoningData 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

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Mathematical ReasoningQ6 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

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Mathematical ReasoningA 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

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Mathematical ReasoningA 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

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Mathematical ReasoningThe 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

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Mathematical ReasoningWhen do creative people get their best ideas A newspaper did a survey of 966 inventors who hold U S patents and obtained the following information Time of Day When Best Ideas Occur Time 6 A M 12 noon 12 noon 6 P M Number of Inventors 271 145 326 6 P M 12 midnight 12 midnight 6 A M a Assuming that the time interval includes the left limit and all the times up to but not including the right limit estimate the probability that an inventor has a best idea during each time interval from 6 A M to 12 noon from 12 noon to 6 P M from 6 P M to 12 midnight from 12 midnight to 6 A M Round your answers to three decimal places 224 6AM 12PM 12PM 6PM 6PM 12AM 12AM 6AM b Do the probabilities add up to 1 Yes No Does this make sense Examining the above table we find the table Select the probabilities for all outcomes in the sample space Therefore the probabilities in the table Select So the above result Select make sense What is the sample space in this problem 6AM 12AM 4

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Mathematical Reasoning5 The box plots show the comparison of points scored and points allowed by the UConn women s basketball team in the 2017 season Use the boxplots to compare these distributions Allowed Scored 30 Shape Center Variability 40 50 60 70 80 90 100 110 120

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Mathematical ReasoningThe concentration of a certain drug in the bloodstream in mg 0 21 can be modeled by the equation C t where fis 1 cm the time since the injection in hours Answer the below questions from when the injection was initial given to 4 hours later Question 1 1 Part A 20 points Use your graphing calculator to graph the function in a reasonable window Sketch your graph on your paper and provide the graphing calculator window you used using the following format xmin xmax ymin ymax Remember to label your axes and include units Upload a PDF of your work in the correct orientation Only PDFs will be given credit Upload a PDF of your work in the correct orientation Only PDFs will be given credit Show all work Question 1 2 Part B 10 points Use your graph to determine the time in hours where the drug concentration was at its maximum Include units and round your answer to 2 decimal places if needed Question 1 3 Part C 10 points On what open interval s is the drug concentration increasing Round your answer to 2 decimal places if needed Put a comma between intervals if needed Question 1 4 Part D 10 points

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Mathematical ReasoningInnocent until proven guilty In Japanese criminal trials about 95 of the defendants are found guilty In the United States about 60 of the defendants are found guilty in criminal trialst Suppose you are a news reporter following eight criminal trials USE SALT a If the trials were in Japan what is the probability that all the defendants would be found guilty Round your answer to three decimal places 0 663 What is this probability if the trials were in the United States Round your answer to three decimal places 0 016 b of the eight trials what is the expected number of guilty verdicts in Japan 7 6 verdicts What is the expected number in the United Sates 4 8 verdicts What is the standard deviation in Japan Round your answer to two decimal places verdicts What is the standard deviation in the United States Round your answer to two decimal places X verdicts c As a U S news reporter what is the smallest number of trials n you would need to cover to be at least 99 sure of two or more convictions X trials What is the smallest number of trials n you would need if you covered trials in Japan

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Mathematical ReasoningIsle Royale an island in Lake Superior has provided an important study site of wolves and their prey Of special interest is the study of the number of moose killed by wolves During a particular period there were 296 moose deaths identified as wolf kills The age distribution of the kills is as follows Age of Moose in Years Number Killed by Wolves Calf 0 5 yr 1 5 6 10 1 5 LAUSE SALT 11 15 6 10 16 20 11 15 16 20 a For each age group compute the probability that a moose in that age group is killed by a wolf Round your answers to four decimal places Age of Moose in Years Number Killed by Wolves Calf 0 5 yr 0 3649 0 1824 0 2534 0 1824 108 0 0169 54 75 54 5 b Consider all ages in a class equal to the class midpoint Use 0 5 for the midpoint of the calf class Find the expected age in years of a moose killed by a wolf and the standard deviation of the ages in years Round your answers to two decimal places

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Mathematical ReasoningDetermine whether each statement is true or false You have one submission for each statement a All rational functions are continuous on their domain True False b The function f x True False x 25 X 5 is continuous at x 5 c If f x is defined at x a then f x is also continuous at x a True False d If f x is continuous at x a then x a is in the domain of f x True False e If f x and g x are continuous at x a then f x g x is also continuous at x a True False f If f x and g x are continuous at x a then f x is also continuous at x a g x

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Mathematical ReasoningELAPSED TIME 10 00 SKIP 2m 5m METHODS RESET 15 14 13 12 41 10 Lab Data Q Corn Syrup Concentration 10 Corn Syrup 20 Corn Syrup 30 Corn Syrup X Liquid Volume mL 1 2 3 4 PHASE 1 10 Corn syrup Complete the follow steps Attach selectively permeable memb to bottom of thist tube Add 10 corn syr thistle tube Add distilled wate beaker Wait 10 minutes measure volume liquid inside tube Record in Lab Dat

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Mathematical ReasoningQ4 Using counters and other logic devices design a traffic light that operates as follows Red light for 9 seconds Orange light for 3 seconds and green light for 12 seconds Assume a clock frequency of 1 Hz Show your work

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Mathematical Reasoningwashed off within 5 minutes For the other 500 subjects the oil was washed off after 5 minutes The results are summarized in the following table Time Within Which Oil Was Washed Off Reaction Within 5 Minutes 1 P N Column Total 0 467 11 P M None 0 416 Mild iii P S Strong b Find the following probabilities 1 P N W 0 802 ii P SW 0 058 X c Find the following probabilities 1 P NA 0 132 ii P SIA 0 176 401 Let s use the following notation for the various events W washing oil off within 5 minutes A washing oil off after 5 minutes N no reaction M mild reaction S strong reaction Suppose a person is selected at random from this sample of 1 000 subjects a Find the following probabilities d Find the following probabilities 1 P N and W 0 401 70 29 500 After 5 Minutes Row Total 66 346 88 500 467 416 117 1 000

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Mathematical Reasoning8x 56x 2x 4x 70 Evaluate each of the following limits If an answer does not exist enter DNE Letif x a lim f x 2 3 x 1 b lim f x X 7 c lim f x X 5 d lim f x X 8 e lim f x X118

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Mathematical ReasoningQ3 An example for fixed input in economic decision making is that a the project manager has 1 million for the project b the project manager must increase productivity by at least 10 c the project manager must choose the most cost effective design for the new machine d None of the above

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Mathematical ReasoningThis question 1 point s possible OA 200 B 30 O C 1 070 O D 300 Submit test Use the four step method in problem solving to solve the problem A couch sells for 1 040 Instead of paying the total amount at the time of purchase the same couch can be bought by paying 500 down and 70 a month for 12 months How much is saved by paying the total amount at the time of purchase

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Mathematical ReasoningDetermine a route whose distance is less than 11 miles for running errands to all three destinations and returning home Post Office 2 5 2 Choose the route that is less than 11 miles OA Home Bank Post Office Dry Cleaners Home OB Home Post Office Dry Cleaners Bank Home C Home Dry Cleaners Post Office Bank Home D Home Post Office Bank Dry Cleaners Home O E Home Bank Dry Cleaners Post Office Home Home 2 Bank 3 3 Dry Cleaners

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Mathematical ReasoningIdentify a pattern in the sequence of figures Then use the pattern to find the next figure in the sequence W W O D Choose the correct figure below O A OB Z N W W N N W Z N X W X O E y y y y W W Z Z W W N W W N O C O F N N W W N N W W N W