Mathematical Reasoning Questions and Answers

4 What is the total variance of the following portfolio consisting of 2 assets invested in the ratio of 1 2 choose the closest one Asset A E r 0 2 o 0 5 Asset B E r 0 4 o 0 7 Correlation 0 8 rf 0 1 A 0 14 B 0 12 C 0 10 D

Let p q and r represent the following statements p It is Tuesday q I am working r I am driving Write the following statement in its symbolic form It is Tuesday and I am not working and I am driving The symbolic form is

2 Some mopeds are in the crosswalk Choose the correct answer below O A All mopeds are in the crosswalk O B Not all mopeds are in the crosswalk O C Some mopeds are not in the crosswalk O D No mopeds are in the crosswalk

p The conductor is present q The orchestra is playing The orchestra is not playing or the conductor is not present The statement in symbolic form is

Determine whether the premises No juniors left campus for the weekend and Some math majors are not juniors imply the conclusion Some math majors left campus for the weekend Explain your answer Please show your work on paper digitize it and then upload it here Hint Use the logical form of the premises and conclusion to go through the steps of an argument

Let P x x studies Calculus Q x x is a Computer Science major R x x knows JavaScript Match given quantified statements with their logical form Every Computer Science major studies Calculus Some Computer Science majors study Calculus Every Computer Science major knows JavaScript There is a Computer Science major who can program on JavaScript A Domain set of all students 3x Q x AP x B Domain set of all Computer Science majors VxP x C Domain set of all people Vi Q x R x D Domain set of all Computer Science majors 3xR x

What relevant conclusion or conclusions could be drawn from the premises given below Every mathematics major knows logarithms Rob is a mathematic major Danny knows logarithms In the space provided write your conclusion and list two rules of inference that you used to draw the conclusion Note Use only names of the rules logical form is not required For the toolbar press ALT F10 PC or ALT FN F10 Mac

Completion Status Click on the logical form of the proof of equivalence p q T when q p T Vx P x Q x F if 3x P x AQ x p q T when p q q p T P q T when p Click Save and Submit to save and T implies that q T pq T when p A q implies Ar

6 The combined annual income for you and your partner is 170 000 Your accountant tells you to pay up to 20 of your annual income for mortgage What would be your monthly payments How much can you borrow on a 30 year mortgage at 5 5 compounded monthly

points Base your answer on the information presented in the World War II Sway Lesson Each answer should be about 2 paragraphs long Do not use outside sources Be sure to use specific examples included in our lesson including the assigned readings and videos Answer the questions in your own words 1 What did Executive Order 9066 do What was life like in internment camps What did the Supreme Court in 1944 rule in Korematsu v United States What were the lessons of Japanese Interment according to the Council on Foreign Relations Jim Lindsay

Problem 9 1 point A person borrows 36000 and agrees to repay the loan in monthly installments over 5 years The agreement is to pay 1 of the unpaid balance each month for using the money and 600 each month to reduce the loan What is the total cost of this loan that is what is the sum of all the monthly interest payments Cost of loan

A person borrows 9000 and agrees to repay the loan in monthly installments over 5 years The agreement is to pay 1 of the unpaid balance each month for using the money and 150 each month to reduce the loan What is the total cost of this loan that is what is the sum of all the monthly interest payments Cost of loan

As temperature is increased to slightly above 912 C 1674 F pure iron transforms into which one of the following phases O austenite cementite O delta

7 Assuming that the probabilities above remain true for future shots what is the probability that two shots in a row both land in the wastebasket wasteb Probabilite Stetement Work Answer 8 Assuming that the probabilities above remain true for future shots what is the probability that out of tw shots taken in a row 1 lands in the basket and the other misses

Find a general solution to the given differential equation 24y 14y 3y 0 What is the auxiliary equation associated with the given differential equation Type an equation using r as the variable

Find the intervals on which f x is increasing the intervals on which f x is decreasing and the local extrema f x 4x 16x 4 Select the correct choice below and if necessary fill in the answer box to complete your choice O A The function is increasing on Type your answer in interval notation Type integers or simplified fractions Use a comma to separate answers as neede OB The function is never increasing

A triangle has perimeter remaining side 2x 1 2x 1 and two of its sides are X x 1 and 1 x 2 Find the

In order to solve the equation 4x 4 a student graphs the equations f x 4x and g x 4 What are the solutions to the equation 4x 4 x 1 and 4 x 0 5 and 1 x 0 5 and 2 x 2 and 4

Problem 4 25 pts Consider the brass alloy for which the stress strain behavior is shown in the figure below A cylindrical specimen of this material with 6 mm in diameter and 50 mm long is pulled in tension with a force of 5000 N If it is known that this alloy has a Poisson s ratio of 0 30 compute the following to to to to 1 The total specimen length under load 5 pts tol 2 The diameter of the specimen under load 5 pts Stress MPa 500 400 300 200 100 Tensile strength 450 MPa 65 000 psi H MPa 40 200 100 0 10 psi 0 10 30 20 10 0 3 The total specimen length after load is removed 5 pts A1 4 5000 50 60 2 0 L 0 20 Strain 88 42mm 4 The diameter of the specimen after load is removed 5 pts Ad do Vez Ad 6 0 3 0 8 1 44mm Yield strength 250 MPa 36 000 psi Fy Oy Ao Tr Fus 450 MPa 6x50 135000 N why 0 005 0 30 70 60 50 40 30 20 10 0 40 5 Approximately what is the maximum load in N that can be applied to the specimen before yielding plastic deformation occurs 5 pts Stress 10 psi

Is achieving a basic skill level related to the location of the school The results of a random sample of students by the location of school and the number of students achieving basic skill levels in three subjects is shown in the contingency table At a 0 10 test the hypothesis that the variables are independent Complete parts a through d a Identify the claim and state the null and alternative hypotheses Ho Skill level in a subject is Ha Skill level in a subject is The is the claim location location b Calculate the test statistic If convenient use technology x 0 Round to three decimal places as needed c Decide to reject or fail to reject the null hypothesis Then interpret the decision in the context of the original claim Choose the correct conclusion below OA Fail to reject the null hypothesis There is not enough evidence to reject the claim that skill level in a subject is independent of location OC Reject the null hypothesis There is not enough evidence to reject the claim that skill level in a subject is independent of location Subject Location Reading Math Science 50 44 45 Urban Suburban 61 70 54 OB Fail to reject the null hypothesis There is enough evidence to reject the claim that skill level in a subject is independent of location OD Reject the null hypothesis There is enough evidence to reject the claim that skill level in a subject is independent of location

1 point Let the following statement For any z if then 0 Complete the sentences below filling in A G from the following list A Real numbers are all zero B For any if 0 then x 0 C There is some 0 such that 0 if x 0 then 0 D For any E For any if x 0 then x x F For any I I G For any if 0 then x 0 Sis The converse of S is The contrapositive of S is The negation of S is enter a letter from A G and that statement is and that statement is and that statement is V

9 On the first day of a biology experiment there are 10 bacteria in a Petri dish Every day after that the number of bacteria in the dish doubles A Write a recursive definition for the sequence representing the number o bacteria in the dish each day B Write an explicit definition for the same sequence C How many bacteria are in the dish on day 7

1 If 1 1 then 2 2 X L 3 The Conditional and the Bic 2 If 1 1 then 2 3 3 If 1 0 then 1 1 4 If 1 0 then 2 2 5 If 1 1 and 1 2 then 1 2

For this question let f x ln x and let ro 1 1 1 x 1 3 and x3 1 4 a Construct the Lagrange interpolating polynomials L3 k x for k 0 3 b Use your answer to construct the interpolating polynomial P3 x for the data Ti f xi for i 0 3 c Using a theorem stated in class find an upper bound for the error r P3 x

The following data are taken from the financial statements of Sigmon Inc Terms of all sales are 2 10 n 45 1 Accounts receivable turnover 2 Number of days sales in receivables The collection of accounts receivable has urnover and the 20Y3 20Y2 Accounts receivable end of year 725 000 Sales on account 5 637 500 a For 20Y2 and 20Y3 determine 1 the accounts receivable turnover and 2 the number of days sales in receivables Round interim calculations to the nearest dollar and final answers to on decimal place Assume a 365 day year 650 000 4 687 500 in the collection period 20Y1 600 000 20Y3 20Y2 days This can be seen in both the days in accounts receivabl

In contract management it is imperative that a hospital contract negotiator m take an aggressive and no compromise attitude True False

Macmillan Learning Cookie Monster loves cookies The table shows how his utility varies with cookie consumption but the table is missing some numbers possibly because Cookie Monster also loves to eat many other things Cookie Monster s marginal utility from the fourth cookie is What is Cookie Monster s total utility when he eats 6 cookies units units Cookies consumed cookies 0 1 2 3 4 5 6 7 Total utility units 0 100 250 390 530 630 Marginal utility units 100 140 100 75 70

1 An object is traveling around a circle with a radius of 12 centimeters If in 10 seconds a central angle of 3 radian is swept out what are the linear and angular speeds of the object The linear speed is v Type an integer or a simpli radians sec cm sec radians sec CICERID

10 Suppose f and g are two functions continuous at x 3 If lim 1 3 lim g x 2 find f 3 and g 3 Justify your solution ef x 8 2 9 2 17 and

A square pyramid has a length of 18 feet If the surface area is 575 feet squared what is the approximate slant height O 7 feet O 6 4 feet 5 feet 8 3 feet

Find the volume and surface area of the rectangular base pyramid 24 Volume 33 The height is 15 Round your answers to the first decimal place if needed Surface Area 14

A local coffee shop is testing out new flavors of coffee Caramel Apple Latte and Salted Minty Mocha A poll conducted by the coffee shop determined that 46 customers preferred only the Caramel Apple Latte 61 customers chose only the Salted Minty Mocha 27 customers chose both flavors but 18 liked neither flavor What is the probability that a randomly selected customer would only like the Caramel Apple Latte

The width of a rectangular box is 4 times its height and its length is 7 ft more than its height The volume of the box is 126 ft Use the ALEKS graphing calculator to find the height of the box Round your answer to two decimal places ft 3

The number of points held by a sample of the NHL s National Hockey League highest scorers for both Eastern Conference and Western Conference is shown below Ho Hi Hz 0 O H H1 H 0 Hoi Hi Hz ng i 0 O H H1 H 0 At a 0 10 can it be concluded that the mean of the Eastern Conference is higher than the mean on the Western Conference based on these data a Which are the null and alternative hypotheses Hoi H1 Hz 0 O H H1 H 0 H 1 Ho H Hz 0 H H H 0 Eastern Conference X b What are the sample means and sample standard deviations Round each to 2 decimal places H 2 83 60 75 58 78 59 70 58 62 61 59 Western Conference 77 59 72 58 37 57 66 55 61 x c What is the test statistic Round to 2 decimal places

The local government is concerned with the population of a new predatory fish the tiger gar which was first observed in Lake Richmond about 5 years ago The following table shows the approximate number of tiger gars living in the lake since 2016 2016 322 y hundredth 2017 399 2018 507 2019 618 2020 785 Using the Tl nspire calculator write an exponential function that models the population of tiger gar in the lake Round all numbers to the nearest 2021 975

Since the discovery of the tiger gar population in Lake Richmond the population of bluegill fish has also shown significant change 2016 y 2 794 2017 1 688 2018 1 008 2019 606 2020 363 Using the TI Nspire calculator write an exponential function that models the population of bluegill over the last 5 years 2021 218

Suppose z has standard normal distribution and x is related to zas x 2 3z What can you say about mean and standard deviation of x Mean of x 2 and standard deviation of x 3 Mean of x 2 and standard deviation of x 3 Mean of x 2 and standard deviation of x 3 Not enough information is given to figure out mean and standard deviation of x Mean of x 2 and standard deviation of x 9

A O BC 210 OBC 50 BC 180 O BC 100 m 8C 70 B 85

Digital Solutions Inc uses flexible budgets that are based on the following data Sales commissions 14 of sales 20 of sales 6 000 per month plus 12 of sales 28 000 per month 13 000 per month plus 20 of sales 32 000 per month Advertising expense Miscellaneous administrative expense Office salaries expense Customer support expenses Research and development expense Prepare a flexible selling and administrative expenses budget for October for sales volun model Digital Solutions Inc Flexible Selling and Administrative Expenses Budget For the Month Ending October 31 Total sales Variable cost Total variable cost 400 000 500 000 600 000

The table shows employment statistics for a fictional country Use the information to answer the questions Round your percentages to two decimal places Category Employed Unemployed Not in the labor force What is the total labor force Number of people 5505 452 591 What is the labor force participation rate mont rote 4997 Incorrect Incorrect

Macmillan Learning Information concerning the fictitious small island nation of Llamalandia is given in the table Use the information in the table to answer the related questions For the percentages round your answers to two decimal places What is the size of the labor force How many people are out of the labor force What is the unemployment rate What is the total labor force participation rate labor force Number of employed people Number of unemployed people Total population over age 16 out of labor force unemployment participation 335 915 15 483 415 999

A painter has been assigned to paint 2 600 Lf of trim He is to paint the trim with one coat of primer and two coats of paint Approximately how many hours will it take the painter to complete the work 5 10 hours 15 26 hours 25 31 hours 30 40 hours

ppose that the aggregate demand curve crosses the aggregate supply curve in either of the hypothetical zones Move the labels the zone that best describes that particular situation Price level long run 1 Aggregate supply non inflationary region Potential GDP Real GDP Keynes law Answer Bank Great Depression low unemployment rates recession

According to the lectures which of the following ideas are representative of neo classical orthodox theory which are representative of post Keynesian heterodox theory and which are shared by both theories The loanable funds market Capitalist economies tend to full employment at least in the long run Saving is a leakage out of and investment is an injection into the spending flow Output income and employment fall when money saved exceeds intended investment until savings equals investment In the long run we re all dead The paradox of thrift

Move the labels to their corresponding zone Price level Potential GDP Aggregate supply a high level of cyclical unemployment government spending to stimulate output is effective Real GDP Answer Bank a low level of cyclical unemployment government spending to stimulate output is not effective Keynesian zor

Approximately 3 of the eggs in a grocery store are cracked If you buy two dozen eggs without checking them first what is the probability that 7 none of your eggs are cracked 88 at least one of our eggs is cracked 99 exactly two of your eggs are cracked An Olympic archer is able to hit a bulls eye 86 of the time Assume each shot is independent of the others If she shoots 12 arrows what is the probability that 1010 She never misses 11 She gets exactly 11 bulls eyes 12 She gets less than 8 bulls eyes 13 She gets at least 8 bulls eyes 14 She gets at most 9 bulls eyes

Marcus reads in a magazine article that 62 of teenagers prefer Batman over Iron Man He decides to test this so he takes a simple random sample of 50 people at Wal Mart on a Saturday afternoon 1 1 What is the probability that he finds exactly 40 Batman fans 2 2 What is the probability that he finds fewer than 30 Batman fans 3 3 What is the probability that Marcus will find more than 35 Batman fans Suppose that 20 of the otters in a large aquatic community are typically infected with a parasite A biologist samples 16 otters at random and records whether or not the animal is infected 4 Find the expected number of infected otters in the sample 5 5 What is the probability exactly 4 of the sampled otters are infected 6 6 What is the probability that 8 or more of the sampled otters are infected

If the profit function for a firm is given by P x 1700 180x x2 and limitations on space require that production be less than 100 units find the break even points Enter your answers comma separated list X M X units

Find the number of solutions in non negative integers of the equation x1 x2 x3 3x4 8 For the toolbar press ALT F10 PC or ALT FN F1000

7 The owner of a regional retailer has noticed an increase in absenteeism among his work force He believes this is due to a lack of general health in his employees In an attempt to improve the situation six months ago he began a fitness program in which employees exercise during their lunch hour To evaluate the program he selected a random sample of nine employees who participated in the program and found the number of days each missed work in the 6 months prior to the program and in the 6 months after implementation of the program The results are summarized in the table below Construct a 90 confidence interval for the difference in employee absences before and after implementation of the program was implemented Interpret your interval i e what exactly does it mean in this case Round to 4 four quality decimal places Employee 1 23456789 n 9 df 8 Before 6 4356 ANNO 9 6 7 7 4 7 BIUA A L AA I After 5 21336353 x X EE 12pt 13 Paragraph fr