Math - Others Questions

In his book Chances Risk and Odds in Everyday Life James Burke states that there is a 72 chance a polygraph test lie detector test will catch a person who is in fact lying Furthermore there is approximately a 7 chance that the polygraph will falsely accuse someone of lying a Suppose a person answers 85 of a long battery of questions truthfully What percentage of the answers will the polygraph wrongly indicate are lies b Suppose a person answers 15 of a long battery of questions with lies What percentage of the answers will the polygraph correctly indicate are lies c Suppose 40 of the questions are answered truthfully and 60 are answered with lies What percentage of the answers will the polygraph wrongly indicate are lies d Suppose 40 of the questions are answered truthfully and 60 are answered with lies What percentage of the answers will the polygraph correctly indicate are lies e Suppose 20 of the questions are answered truthfully and the rest are answered with lies What percentage of the answers will the polygraph wrongly indicate are lies f Suppose 20 of the questions are answered truthfully and the rest are answered with lies What percentage of the answers

When 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

There are ten balls in an urn They are identical except for color Four are red five are blue and one is yellow You are to draw a ball from the urn note its color and set it aside Then you are to draw another ball from the urn and note its color a Make a tree diagram to show all possible outcomes of the experiment O b Let P x y be the probability of choosing an x colored ball on the first draw and a y colored ball on the second draw Compute the probability for each outcome of the experiment Enter your answers as fractions P R R P R B P R Y P B R P B B P B Y P Y R DOY D

Compute P 10 10

Aldrich Ames is a convicted traitor who leaked American secrets to a foreign power Yet Ames took routine lie detector tests and each time passed them How can this be done Recognizing control questions employing unusual breathing patterns biting one s tongue at the right time pressing one s toes hard to the floor and counting backwards by 7 are countermeasures that are difficult t detect but can change the results of a polygraph examinationt In fact it is reported in Professor Ford s book that after only 20 minutes of instruction by Buzz Fay a prison inmate 85 of those trained were able to pass the polygraph examination even when guilty of a crime Suppose that a random sample of five students in a psychology laboratory are told a secret and then given instructions on how to pass the polygraph examination without revealing their knowledge of the secret What are the following probabilities Round your answers to three decimal places USE SALT a All the students are able to pass the polygraph examination b More than half the students are able to pass the polygraph examination c No more than half of the students are able to pass the polygraph examination d All the students fail the polygraph examination

Given P A 0 4 P B 0 7 P A B 0 3 do the following a Compute P A and B b Compute P A or B

See the previous question for the formula for computing the angular size of an object as observed from some particular distance The red orange star Betelgeuse located on the shoulder of Orion has a diameter 1000 times the diameter of the Sun where the Sun s diameter D 1 4 million kilometers Betelgeuse is located d 640 light years away where 1 light year distance traveled in one year at light speed and light speed c 300 000 kilometers per second What is the angular diameter of Betelgeuse expressed in percents of an arcsecond Calculate your answer in arcseconds multiply by 100 to get a percentage and enter in the blank The angular diameter of Betelgeuse is how many of an arcsecond

To calculate the angular size of an object with diameter D as observed from a distance d we compute D d and then convert from radians the natural angular rheasure to the more common degrees arcminutes arcseconds system a D d angle a in radians The planet Mars has a diameter of 6800 km What is the angular size of Mars in arcseconds when it is observed at a typical distance of 270 million kilometers from Earth Using a calculator express your answer in arcseconds 3600 arcseconds per degree 206 000 arcseconds per radian and write the answer in the blank The angular diameter of Mars in arcseconds under the above circumstance is

Total weekly salaries expense for all employees is 9 000 This amount is paid at the end of the day on Friday of each five day workweek April 30 falls on Tuesday which means that the employees had worked two days since the last payday The next payday is May 3 Prepare the required adjusting entry if any Note Enter debits before credits Date April 30 General Journal Salaries expense Salaries payable Debit 9 000 Credit 9 000

The Prepaid Rent account had a 5 600 debit balance at December 31 before adjusting for the costs of expired prepaid rent An analysis of the rental agreement showed that 4 910 of prepaid rent had expired Note Enter debits before credits Transaction e General Journal Debit Credit

Given the system 2 2cos 2t is 01 y t 20cos 2t O 2 dy t 3y t 10x t the steady state response of the system to dt O 5 TT y t 4cos 2t tan 4 TU y t 10cos 0 5t 4 tan 03 O 4 The system does not have a steady state response tan 1 TU y t 20cos 2t 4 tan

5 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

9 7 4 pts Write a formula for the rational function graph 8 6 5 3 2 1 17 10 8 9 3 2 0 2 3 4 5 6 7 8 3x 1x 6

Use the figure below which shows the graph of y f x to answer the following questions 4 Click on the graph to get a larger version A Estimate the integral f f x dx 11 You will certainly want to use an enlarged version of the graph to obtain your estimate

Given the Fourier transform A t sinc f the Fourier transform of the signal in the figure is 01 Xb f j2sinc f 1 j2sinc f 1 2 X f 0 5j sinc f 1 0 5j sinc f 1 03 X f j4nfsinc f sinc 2f O 4 None of the answers 05 Xb f j0 5fsinc f sin 2 f x 1 0 2

aste A B 3 0 1 2 3 4 5 LB B FV Stocks BIUV Cell Styles X fx You are trying to plan for retirement in 10 years and currently you have 150 000 in a savings account and 250 00 C DE F G H P6 24 Modified see template for modifications to the problem CRECHERCHEHEHEHE PV i nper pmt FV Note there are multiple methods that can be used to solve this problem The template below is laid out for one of those methods A FV Savings Savings PV 1 You are trying to plan for retirement in 10 years and currently you have 150 000 in a savings account and 250 000 in stocks In addition you plan to deposit 8 000 iper year into your savings account at the end of each of the next 5 years and then 10 000 per year at the end of each year for the final five years until you retire a Assuming your savings account returns 8 compounded annually and your investment in stocks will return 12 compounded annually how much will you have at the end of 10 years b If you expect to live for 20 years after you retire and at retirement you deposit all of your savings including stocks in a bank account paying 11 how much can you withdrawal each year after you retire making 20 equal withdrawls beginning one year after you retire so that you end up with a zero balance at death nper pmt FV Hv FV 8K Annuity years 1 5 Step 1 A PV 1 nper pmt 5 150 000 00 8 10 323 838 75 Alignment 250 000 00 Number 12 10 776 462 05 Cells Editing

The population of a small mining town was 13 700 in 2000 Each year the population decreases by an average of 5 a Explain why the situation described is an example of exponential decay b Write an exponential function that models this situation Explain each part of the equation c Use your equation to estimate when the population will drop below 5000

Task 3 3p A stuntman attempted to jump across the street on his motorcycle speeding with initial velocity of 20 m s The takeoff ramp was inclined of 60 above horizontal The top of the truck on which he wanted to land was 5 m below the edge of the ramp The truck is moving towards the stuntman with 1 m s At what minimum distance D the truck should be located for the stuntman to land safely

The 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

Question 2 Graphs of Functions 50 points total The below graph is a function Using this graph answer the below questions 4 3 2 1 0 1 2 3 5 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 Question 2 1 Part A 17 points Define the open intervals where the function was increasing Put a comma between each interval if needed Question 2 2 Part B 17 points Define the open intervals where the function was decreasing Put a comma between each interval if neede Question 2 3 Part C 16 points

Suppose you are a junk bond broker who buys only bonds that have a 50 chance of default You want a portfolio with at least five bonds that do not default You can dispose of the other bonds in the portfolio with no great loss What is the smallest number of bonds you should buy if you want to be at least 91 sure that five or more bonds will not default LUSE SALT bonds

submitted by those under 25 years of age Suppose 9 property damage claims involving automobiles are selected at random a Letr be the number of claims made by people under age 25 Make a histogram for the r distribution probabilities 0 30 O O 2 P r 2 0 25 0 20 0 15 0 10 0 05 0 00 0 30 0 25 0 20 0 15 0 10 0 05 0 00 0 4 0 3 0 2 0 1 0 0 0 35 0 30 0 25 0 20 0 15 0 10 0 05 USE SALT 0 00 0 1 2 3 0 1 2 3 0 1 3 4 5 0 1 2 3 2 3 4 r r 5 6 7 8 9 6 7 5 6 7 8 9 4 5 6 7 8 9 r 4 5 6 7 8 9 b What is the probability that two or more claims are made by people under age 25 Round your answer to three decimal places

For all sets A B and C if AC B then AnCc is O a Anc CBC O b ANCC BNC OC ANC BNC O d AnCBUC

Consumer Banker Association released a report showing the lengths of automobile leases for new automobiles The results are as follows Lease Length in Months Percent of Leases of Leases of Leases 35 30 25 20 15 10 5 0 35 30 25 20 15 10 13 24 12000550 25 36 5 0 37 48 a Use the midpoint of each class and call the midpoint of the last class 66 5 months for purposes of estimating the expected lease term in months Also estimate the standard deviation in months of the distribution Round your answers to two decimal places expected lease term standard deviation 49 60 More than 60 b Sketch a graph of the probability distribution for the duration of new auto leases 35 30 25 20 13 3 36 7 18 5 30 1 19 6 0 3 x months x months 30 5 42 5 54 5 66 5 Lease Length in Months 18 5 30 5 42 5 54 5 66 5 Lease Length in Months of Leases of Leases 10 5 0 35 30 linnakes 15 10 5 0 18 5 18 5 30 5 42 5 54 5 66 5 Lease Length in Months 30 5 42 5 54 5 66 5 Lease Length in Months

What are the requirements for a probability distribution Select all that apply associated probabilities for each value of x The summation of the probabilities is 1 Each probability takes on values between 0 and 1 inclusive Each probability takes on a value of 0 or 1 a description of all the values of the random variable x Each value of x has the same probability The summation of the probabilities is 1 The summation of the probabilities equal 1

According to a magazine 55 of all federal inmates are serving time for drug dealing A random sample of 15 federal inmates is selected USE SALT a What is the probability that 11 or more are serving time for drug dealing Round your answer to three decimal places b What is the probability that 6 or fewer are serving time for drug dealing Round your answer to three decimal places c What is the expected number of inmates serving time for drug dealing 8 25

A stationary store has decided to accept a large shipment of ball point pens if an inspection of 16 randomly selected pens yields no more than two defective pens USE SALT a Find the probability that this shipment is accepted if 10 of the total shipment is defective Round your answer to three decimal places b Find the probability that this shipment is not accepted if 15 of the total shipment is defective Round your answer to three decimal places

Innocent 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

List the criteria for a binomial experiment Select all that apply The probability of success on each trial is constant a fixed number of trials repeated under identical conditions The trials have exactly three outcomes The probability of success can change from trial to trial The trials are independent The trials are mutually exclusive The trials have exactly two outcomes The trials may have two or more outcomes What does the random variable of a binomial experiment measure The random variable measures the number of successes in n trials The random variable measures the number of trials until the nth success The random variable measures the number of failures in n trials The random variable measures the number of trials until the 1st success

Isle 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

The Orchard Cafe has found that about 6 of the diners who make reservations don t show up If 83 reservations have been made how many diners can be expected to show up Round your answer to two decimal places 78 02 Find the standard deviation of this distribution Round your answer to two decimal places

Each year a random sample of 21 bird nests from McLaughlin Park are inspected Over many years it has been found that 74 of nests contain at least one egg This means that the expected number of nests out of 21 with at least one egg is 15 54 The standa deviation in the number of nests out of 21 with eggs is 2 01 The probability that 19 or more nests have at least one egg is 6 15 The probability that at most 10 nests have at least one egg is 0 88 Match the numerical values from the problem to the corresponding symbols If a symbol does not have a corresponding value and cannot be easily computed from the given information then enter NA For the purposes of this problem consider a value hard to compute if a calculator is required to make the computation convenient such as taking a square root or exponentiating a value Symbol Numerical Value P CT S C P x 10 P x 11 P x 19 P x 19 21 0 74 0 26 15 54 2 01 X X X X

Determine whether each statement is true or false You have one submission for each statement a For every function f x if lim f x does not exist then lim f x does not exist x a x a True False b For every function f x if lim f x exists then lim f x exists x a x a True False x c For every function f x if lim f x exists then lim f x also exists x a x a True False d For every function f x if lim f x and lim f x both exist then lim f x also exists x a x a x a True False e For every function f x if lim f x does not exist then lim f x does not exist x a x a True False f For every function f x if lim f x does not exist then lim f x does not exist x at x a True False

x k kx 4 Determine the value of k that will make f x continuous everywhere Let f x if x 4 if x 4 k

Directions Create a poem with each letter to describe empathy E M

Consider the function f x M 4 7x 3x 6X Determine the number of discontinuities of f x Determine the values of x at which f x has a discontinuity Enter your answer as a comma separated list of values The order of the values does not matter Enter DNE if f x does discontinuities

Determine 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

Let f x x 16 X 4 kx if x 4 12 if x 4 Determine the value of k that will make f x continuous everywhere

Limits Continuity Course Packet on limits Determine whether each statement is true or false You have one submission for each statement a For every function f x if lim f x does not exist then lim f x does not exist x13 x a True False b For every function f x if lim f x exists then lim f x exists x a x a True False c For every function f x if lim f x exists then lim f x also exists x at x a True False d For every function f x if lim f x and lim f x both exist then lim f x also exists x a x a True False e For every function f x if lim f x does not exist then lim f x does not exist x a x a True False x a f For every function f x if lim f x does not exist then lim f x does not exist x a True False

The graph of y f x is shown below lim f x X 1 lim f x X 1 lim f x 3 X 1 3 2 Use the graph of y f x to compute each of the following values If an answer does not exist ent f 1 3 X 1 A 2 1 X

Does crime pay The FBI Standard Survey of Crimes showed that for about 80 of all property crimes burglary larceny car theft etc the criminals are never found and the case is never solvedt Suppose a neighborhood district in a large city suffers repeated property crimes not always perpetrated by the same criminals The police are investigating ten property crime cases in this district LUSE SALT a What is the probability that none of the crimes will ever be solved Round your answer to three decimal places 0 107 b What is the probability that at least one crime will be solved Round your answer to three decimal places 0 893 c What is the expected number of crimes that will be solved 2 crimes What is the standard deviation Round your answer to two decimal places x crimes d What is the smallest number of property crimes in that the police must investigate before they can be at least 90 sure of solving one or more cases crimor

The probability that a single radar station will detect an enemy plane is 0 65 LAUSE SALT a What is the smallest number of stations required to be at least 98 certain that an enemy plane flying over will be d by at least one station 4 stations b If five stations are in use what is the expected number of stations that will detect an enemy plane stations

Question 14 Question 15 Question 16 B C Question 17 D F Question 18 P Q S Bob is gathering eggs Bob has fed the chickens Bob has fed the ducks Either Bob has fed the chickens or he isn t chasing the fox away Bob is chasing the fox away The ducks are playing in the pond The ducks are quacking loudly The chickens are playing in the pond The ducks are either quacking loudly or playing in the pond or the chickens are playing in the 2 points pond Either Bob has fed the ducks and is chasing the fox away or he has fed the chickens If the chickens are playing in the pond only if Bob is chasing the fox away then the ducks are playing in the pond 2 points 2 points 2 points

Insert the missing parentheses into each of the following formulae NOTE Click here for info on typing symbols and formulae in activities Question 19

For each of the following strings of symbols indicate whether the string is or is not an expression of sentential logic Question 12 E g F A B Yes it is an expression No it is not an expression Question 13 J v K L A Yes it is an expression Select one answer 3 points Select one answer 2 points

For each of the following formulae choose the sentence that provides the best English translation of the formula according to the following symbolization key Question 10 B C Question 11 D F P Q S Bob is gathering eggs Bob has fed the chickens Bob has fed the ducks Bob is chasing the fox away The ducks are playing in the pond The ducks are quacking loudly The chickens are playing in the pond Q F A It s not the case that if the ducks are quacking loudly then Bob is chasing the fox away B The ducks aren t quacking loudly if Bob isn t chasing the fox away C If the ducks aren t quacking loudly Bob isn t chasing the fox away D Either the ducks are quacking loudly or Bob isn t chasing the fox away Select one answer 2 points Select one answer 2 points F Q S A If the ducks are quacking loudly and the chickens aren t playing in the pond then Bob is chasing the fox away B The ducks are quacking loudly and the chickens aren t playing in the pond unless Bob is chasing the fox away C The ducks are quacking loudly and the chickens aren t playing in the pond if Bob is chasing the fox away D The ducks are quacking loudly and the chickens aren t playing in the pond only if Bob is chasing the fox away

According to a 2019 eMarketer poll 90 4 of individuals born between 1981 and 1996 millennials are active users of social media Compute the following probabilities out of a group of 55 millennials Round your answers to three decimal places LUSE SALT a Find the probability that more than 49 are active on social media b Find the probability that at most 46 are active on social media c Find the probability that between 43 and 48 including 43 and 48 are active on social media d Find the probability that exactly 49 are active on social media

What is the age distribution of patients who make office visits to a doctor or nurse The following table is based on information taken from a medical journal Age group years Percent of office visitors Under 15 15 24 25 44 45 64 65 and older 15 10 25 15 35 Suppose you are a district manager of a health management organization HMO that is monitoring the office of a local doctor or nurse in general family practice This morning the office you are monitoring has eight office visits on the schedule What is the probability of the following USE SALT a At least half the patients are under 15 years old Round your answer to three decimal places Explain how this can be modeled as a binomial distribution with 8 trials where success is visitor age is under 15 years old and the probability of success is 15 Let n 8 p 0 25 and compute the probabilities using the binomial distribution Let n 8 p 0 85 and compute the probabilities using the binomial distribution Let n 8 p 0 15 and compute the probabilities using the binomial distribution Let n 15 p 0 15 and compute the probabilities using the binomial distribution b From 2 to 5 patients are 65 years old or older include 2 and 5 Round your answer to three decimal places c From 2 to 5 patients are 45 years old or older include 2 and 5 Hint Success if 45 or older Use the table to compute the probability of success on a single trial Round your answer to three decimal places d All the patients are under 25 years of age Round your answer to three decimal places 0 000 e All the patients are 15 years old or older Round your answer to three decimal places

Sociologists say that 85 of married women claim that their husband s mother is the biggest bone of contention in their marriages sex and money are lower rated areas of contention Suppose that eleven married women are having coffee together one morning Find the following probabilities Round your answers to three decimal places USE SALT a All of them dislike their mother in law x b None of them dislike their mother in law 0 000009 c At least nine of them dislike their mother in law X d No more than eight of them dislike their mother in law

Richard has just been given an 8 question multiple choice quiz in his history class Each question has five answers of which only one is correct Since Richard has not attended class recently he doesn t know any of the answers Assuming that Richard guesses on all eight questions find the indicated probabilities Round your answers to three decimal places USE SALT a What is the probability that he will answer all questions correctly 0 0000001 b What is the probability that he will answer all questions incorrectly 0 1677721 c What is the probability that he will answer at least one of the questions correctly Compute this probability two ways First use the rule for mutually exclusive events and the probabilities shown in the binomial probability distribution table 0 8322278 Then use the fact that P r 2 1 1 P r 0 0 8322278 Compare the two results Should they be equal Are they equal If not how do you account for the difference They should be equal but differ substantially They should be equal but may differ slightly due to rounding error They should not be equal but are equal They should be equal but may not be due to table error d What is the probability that Richard will answer at least half the questions correctly