Mathematical Reasoning Questions and Answers

onsider the mathematical system indicated by the table Assume that the associative property holds for the Deration What are the elements of the set in this mathematical system What is the binary operation Is the system closed Is there an identity element for the system under the given operation Does every element in the system have an inverse Give an example to illustrate the associative property Is the system commutative Is the mathematical system a commutative group Yes No t S u r OA rs u u r s OB rs u r st OC ts u t0 su D t u 77 r t n S S t S u u FSF t u T I e Does every element in the system have an inverse O O f Which of the following illustrates the associative property S u 1 t

Two sets are specified by graphs Graph their intersection 4 10 10 OB 9 O C 9 10 Choose the correct graph below OA 10 4 8 8 9 7 9 7 8 8 6 6 F 7 7 5 5 6 Co 6 4 5 4 5 5 4 4 t 3 4 3 3 3 2 3 2 2 2 2 1 1 1 1 0 1 0 to 0 0 1 1 1 1 1 2 LUN 2 72 C 2 2 3 3 3 3 3 4 4 4 4 5 5 5 5 5 6 6 6 6 6 7 7 00 8 8 8 8 8 9 9 9 9 9

Evaluate the expression or state that the expression is not a real number 169 144 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The expression is a real number 169 144 OB The expression is not a real number Type an integer or a decimal

Each individual letter of the word Hawaii is placed on a piece of paper and all 6 pieces of one letter is selected at random from the hat find the probability that the letter i is selected What is the probability that the letter i is selected P i Type an integer or a simplified fraction www

Cheyenne Corp s net income for the current year was 422000 Depreciation was 55000 Accounts receivable and inventories decreased by 18000 and 28000 respectively Prepaid expenses and salaries payable increased respectively by 2000 and 14000 Equipment was sold at a gain of 7700 How much cash was provided by operating activities O 527300 O 507000 O 419000 O 471000

Use the standard normal table to find the specified area Between z 0 98 and z 1 84 Click here to view page 1 of the standard normal table Click here to view page 2 of the standard normal table The area that lies between z 0 98 and z 1 84 is Round to four decimal places as needed W Area under a normal curve to the Table of Areas to the Left of z When z Is Negative z 00 01 02 03 04 05 3 4 0003 0003 0003 0003 0003 0003 3 3 0005 0005 0005 0004 0004 0004 3 2 0007 0007 0006 0006 0006 0006 3 1 0010 0009 0009 0009 0008 0008 3 0 0013 0013 0013 0012 0012 0011 2 9 0019 0018 0018 0017 0016 0016 2 8 0026 0025 0024 0023 0023 0022 2 7 0035 0034 0033 0032 0031 0030 0043 0041 0044 0040 2 6 0047 0045 0057 0055 0054 0059 2 5 0062 0060 2 4 0082 0073 0071 0075 0080 0078 0102 0099 0096 0094 2 3 0107 0104 2 2 0139 0136 0132 0129 0125 0122 2 1 0179 0174 0170 0166 0162 0158 0207 0202 2 0 0228 0222 0217 0212 0262 0256 1 9 0287 0281 0274 0268 1 8 0359 0351 0344 0336 0329 0322 0409 0401 1 7 0446 0436 0427 0418 0505 0495 1 6 0548 0537 0526 0516 1 5 0668 0655 0643 0630 0618 0606 1 4 0808 0793 0778 0764 0749 0735 0885 1 3 0968 0951 0934 0918 0901 1 2 1151 1131 1112 1093 1075 1056 JASA INL JAMA JARI Print Dor Area under a normal curve to the left of z page 2 5199 5596 Table of Areas to the Left of z When Is Positive 00 01 02 03 04 05 0 0 5000 5040 5080 5120 5160 0 1 5398 5438 5478 5517 5557 5948 5987 0 2 5793 5832 5871 5910 0 3 6179 6217 6255 6293 6331 6368 0 4 6554 6591 6628 6664 6700 6736 7088 0 5 6915 6950 6985 7019 7054 7257 7291 7324 7357 7389 7422 0 6 0 7 7611 7642 7673 7704 7734 7580 0 8 7881 7910 7939 1901 8186 8159 0 9 8438 1 0 8413 8643 8665 8212 6212 8461 8686 11 8888 8869 1 1 8643 99 10 8849 1 2 1 3 1 4 1 5 1 6 200 1 7 2 1 8 1 9 2 0 2 1 2 2 0903 22 06 07 08 09 5239 5279 5319 5359 5636 5675 5714 5753 6103 6026 6064 6141 6443 6406 6480 6517 6772 6808 6844 6879 124 7224 7123 7157 7190 7454 7486 7517 7549 7823 7852 7764 7794 8051 8078 106 8133 7967 7995 8023 8264 8289 8315 8238 O 8554 8485 8508 8531 Hoston Petan 8729 8770 8749 ore S S 8962 some 9131 9147 9162 9177 8340 ocam 8389 8365 8577 8599 8621 PETO 8830 8790 8810 8708 8907 8925 8944 8980 8997 9015 8901 0022 90 49 2117 0167 arm 9032 9192 9049 9066 9082 9207 CU SAN 9279 pin 9319 9292 9306 9418 9429 9441 9406 9394 9525 9535 9545 9515 9608 9616 9625 9633 O 9099 9192 9207 9222 9236 9251 9222 201 9332 9382 9345 9332 9357 9370 9505 9495 9484 9452 9463 9474 9591 9599 9564 9573 9582 9554 TOP 9664 9678 9656 9649 9671 9641 SPORT 9738 9744 9726 9732 9713 9719 9793 9788 9798 9783 9772 9778 9834 9838 9842 9826 9830 9821 9878 9881 9875 9861 9864 9868 9871 www 9686 1 9750 9803 9846 nonc nono BANK nnnA Print 9115 SID 9265 Done 9693 9699 9706 9756 9761 9767 9808 9812 9817 9850 9854 9857 9887 9884 9890 DALE 2017 2016

From the 12 male and 10 female sales representatives for an insurance company a team of 4 men and 4 women will be selected to attend a national conference on insurance fraud In how many ways can the team of 8 be selected In how many ways can the team of 8 representatives be selected

Sophia bought a puppy and has been tracking its weight at the end of each month since it was born She was told by the dog s breeder that the dog should have an adult weight somewhere between 45 and 50 pounds End of Month Answer 2 Points 1 2 3 4 5 6 7 8 9 10 11 12 Weight in pounds 2 5 8 12 16 22 26 30 33 38 43 49 The linear function w 1 4 271 4 06 models the weight of the puppy after r months By this model what is the interpolated weight of the dog after 4 5 months Round your answer to the nearest pound Keypad Keyboard Shortcuts

11 5 1 Show that the following functions are harmonic and find its har monic conjugates a x y c sinhrsing b xy 3x y y d e cos 2ry f Solution a Set u r y x y 1 2y 2r Au 0 thus is the function u x y is harmonic Cauchy Riemann give us Thus we have that thus b Set e tan y r x 0 x x y v u 2y v x y 2xy g y vy 2r g y v 2r u x y xy 3x y y g y 0 g y C v x y 2xy C 6y y 6y thus is the function u r y is harmonic Cauchy Riemann give us u y 6ry u x 3x 3y 52 u x 3x 3y v x y 3ry 9 y t 6ry g y Vy U y 6zy Thus we have that g x y g y C 2 Au 0

Show that if v is a harmonic conjugate for u then u is a harmonic conjugate for u Solution If f 2 u x y iv r y is analytic then if 2 v x y iu x y is analytic Thus u is a harmonic conjugate of v

61 0 2 Points Match the express Amount o

A study is to be conducted with four horror films to determine which causes more nightmares The researcher grouped the 500 participants into groups easily scared moderately scared hardly scared and randomly selected 40 participants from each group What type of sampling method was used O Simple random sample O Census Cluster sample Stratified sample

Question 2 of 3 Current Attempt in Progress Information regarding Cheyenne Corp is provided as follows Net income Dividends on preferred stock Dividends on common stock Weighted average number of common shares outstanding Common stockholders equity beginning of year Common stockholders equity end of year

That is Newton s Second Law Give the units and derive the final unit

Name the type of sampling study Joey could not find out how to break the student into groups so he just surveyed every single student in the school QUESTION 2 Name the type of sampling Alyssa took lists of all freshmen sophomore juniors and seniors then then randomly selected 25 students from each list QUESTION 3 Name the type of sampling Ashley got a list of all the students in the school and used a random number generator to select the students to be surveyed QUESTION 4

Implement a financial simulation model for a new product proposal and determine a distribution of profits using the provided discrete distributions for the unit cost demand and fixed costs Price is fixed at 1 000 Simulate this model for 50 trials and a production quantity of 140 What is the average profit Click here to view the discrete distributions Click here to view a sample of 50 simulation trial results Set up a lookup table for the unit cost Type integers or decimals Do not round Use ascending order Unit Cost Probability Lower Limit Upper Limit 400 0 25 0 0 25 600 0 35 0 25 0 60 700 0 20 0 60 0 80 800 0 20 0 80 1 Set up a lookup table for the demand Type integers or decimals Do not round Use ascending order Demand Probability Lower Limit Upper Limit 120 0 25 140 0 55 160 0 20 fo 400 600 700 800 1 120 140 160 Simulation Results 42 000 20 000 1 000 47 000 42 000 9 000 9 000 19 000 14 000 19 000 42 000 29 000 39 000 3 000 17 000 27 000 19 000 19 000 3 000 19 000 Print 11 000 8 000 11 000 0 000 19 000 6 000 28 000 22 000 19 000 29 000 29 000 22 000 22 000 22 000 22 000 13 000 11 000 34 000 8 000 3 000 22 000 Done 6 000 13 000 22 000 19 000 27 000 17 000 17 000 13 000 6 000 1 X Piscrete Distributions Unit Cost Probability 0 25 0 35 0 20 0 20 400 600 700 800 Demand 120 140 160 Probability 0 25 0 55 0 20 Fixed Costs Probability 0 25 0 50 0 25 45 000 50 000 55 000

Show that the sequence pn converges linearly i e with order a 1 to p 0 Show that the sequence Pn converges quadratically i e with order a 2 to p 0

Let f x x 2x x 3 Verify using algebraic manipulations that if f p then each of the following four functions have a fixed point at p 91 x 3 x 2x 4 1 2 2 3 93 x 92 x 94 x x 3 241 2 2 2 3x 2x 3 4x 4x 1

The productivity of a certain country with the utilization of x units of labor and y units of capital is given approximately by the function f x y 100x0 67 0 33 A Find fx x y and f x y B If the country is now using 500 units of labor and 200 units of capital find the marginal productivity of labor and the marginal productivity of capital C For the greatest increase in the country s productivity should the government encourage increased use of labor or increased use of capital A f x y

At the beginning of an experime her sample has decaved to 14 2

PAGE 10 OF 13 5 POINTS 21 ASSUME THAT THE WAITING TIMES FOR CUSTOMERS AT A POPULAR RESTAURANT BEFORE BEING SEATED ARE NORMALLY DISTRIBUTED WITH A MEAN OF 16 MINUTES AND STANDARD DEVIAITON OF 4 MINUTES A FIND THE PERCENT OF CUSTOMERS WHO WAIT FOR AT LEAST 14 MINUTES BEFORE BEING SEATED B FIND THE PERCENT OF CUSTOMERS WHO WAIT BETWEEN 12 AND 24 MINUTES BEFORE BEING SEATED C FIND THE PERCENT OF CUSTOMERS WHO WAIT AT LEAST 21 MINUTES BEFORE BEING SEATED D IN A RANDOM SAMPLE OF 1000 CUSTOMERS HOW MANY WAIT 18 MINUTES OR MORE BEFORE BEING SEATED E IN A RANDOM SAMPLE OF 500 CUSTOMERS HOW MANY WAIT LESS THAN 9 MINUTES BEFORE BEING SEATED

5 POINTS 16 USE THE FREQUENCY DISTRIBUTIO A THE TOTAL NUMBER OF OBSE

1 np 2 n 1 p 3 N N NAME THE PROCEDURE If no N is given in the problem use 1000000 2 The conditions are met to use a 1 Proportion Z Test 6 p p which is 2 T TEST STATISTIC The symbol and value of the random variable on this problem are as follows Leave this answer as a fraction which is 2 P 1 P n Z which is 2 The formula set up of the test statistic is as follows Leave any values that were given as fractions as fractions O OBTAIN THE P VALUE o Final answer for the test statistic from technology Round to 2 decimal places OF 1

The table below shows the number of hours per day 11 patients suffered from headaches before and after 7 weeks of soft tissue therapy At a 0 01 is there enough evidence to conclude that soft tissue therapy helps to reduce the length of time patients suffer from headaches Assume the samples are random and dependent and the population is normally distributed Patient 1 2 3 4 5 6 7 8 9 10 11 Daily headache hours before 3 3 2 1 4 3 1 9 1 8 1 7 2 3 1 6 3 8 2 2 1 9 Daily headache hours after 2 8 2 5 1 8 1 2 1 3 1 2 2 0 1 5 1 9 1 7 2 2 The claim is The therapy helps to reduce the length of time patients suffer from headaches Find the standardized test statistic Type an integer or a decimal Round to three decimal places as needed Decide whether to reject or fail to reject the null hypothesis Choose the correct answer below O Reject the null hypothesis OFail to reject the null hypothesis 0

Homework Not everyone pays the same price for the same model of a car The figure illustrates a normal distribution for the prices paid for a particular model of a new car The mean is 22 000 and the standard deviation is 2000 Use the 68 95 99 7 Rule to find what percentage of buyers paid between 18 000 and 22 000 Number of Car Buyers Question 7 12 4 13 99 7 95 68 16 18 20 22 24 26 28 Price of a Model of a New Car Thousands The percentage of buyers who paid between 18 000 and 22 000 is Type an exact answer

interval Graph f and show the region R f x x x 4 1 5 The area is Round to the nearest hundredth as needed Choose the correct graph below OA 50 25 OB Ay 50 25 O C All graphs shown in a 2 6 0 5 by 25 50 5 viewing window 50 25

A matrix A is given along with an iterate x5 7 2 3 6 249 X5 6 1 6 247 A Use these data to approximate a dominant eigenvector whose first component is 1 and a corresponding dominant eigenvalue Use three decimal plac

2 Calculate the mass flow and the annulus area at the rotor outlet for an axial compressor stage The flow enters the rotor without swirl at a Mach number of 0 4 at a stagnation pressure of 200 kPa and a stagnation temperature of 370 K in an annulus of area 0 17 m The axial velocity is constant across the rotor but the flow leaves at 30 6 degrees to the axial direction The stagnation pressure at the rotor outlet is 230 kPa and the stagnation to stagnation polytropic efficiency to this point is 0 94 Use properties of air as k 1 4and Cp 1008 9 J Kg K

Ryan believes that his mother s houseplants would grow taller if she watered with rainwater instead of tap water State the null and alternative hypothesis The true mean height of houseplants watered with tap water is the same as or greater than the true mean height of houseplants watered with rainwater The true mean height of houseplants watered with tap water is less than the true mean height of houseplants watered with rainwater

Which of the following propositions is equivalent to the given implication P q Op q O p q Opvq

Identify the type of proposition given P F O Conjunction O Contingency O Tautology Contradiction

6 The probability that Yuri will score a point on a free throw is 0 3 Yuri attempts two consecutive free throws Part A What is the probability that he scores points on both free throws Part B What is the probability that he scores a point on the first free throw and misses the second

Determine the truth value for the statement when p is false q is true and r is false pv r pvq Choose the correct answer below The statement is true The statement is false

Let p and q represent the following statements p 2 10 12 q 7x3 21 Determine the truth value for the statement pv q Choose the correct truth value below Opv q is true pv qis false

8 Half of a class took Form A of a test and half took Form B Of the students took Form B 39 passed What is the probability that a student randomly selected from the class took Form B and did not pass 9 Three fourths of a research team worked in a lab while the other one fourth of the team worked near a pond Of the researchers who worked near the pond 14 collected insects What is the probability that a randomly selected researcher worked near the pond and collected insects

The mean weight of all kangaroos is less than 200 pounds State the null and alternative hypothesis P2200 P200 For Blank 1

Consider a cable TV company that has a fixed cost of 100 million and a marginal cost of 5 per subscriber The company is regulated with an average cost pricing policy The first two columns of the following table show five points on the initial demand curve For example at a price of 27 the quantity demanded is 3 million subscribers For each 1 reduction in price the number of subscribers increases by 1 million The regulated price is

M Homepage Sp23 21 3 Points x y W Assignment 12 Find the intersection points of the pair of ellipses 100x 25y 100 y2 x y DETAILS 1 1 smaller x value larger x value Sketch the graphs of the pair of equations on the same coordinate axes y 3 3 Launch Meeting 1 3 2 Homepage M Speech 5 y

Summarize the Bill of Rights as these rights are seen to protect the U S citizens They are also protected and guaranteed thanks to them being implemented into the U S Constitution Your summary should be AT

uncertain and the manager estimates that the actual cash flow will be normally distributed with a mean of 9 000 and a standard deviation of 400 The discount rate is set at 5 and assumed to remain constant over the next five years The company evaluates capital investments using net present value How risky is this investment Develop and run a simulation model to answer this question using 50 trials Click the icon to view a sample of 50 simulation trial results is un Say the values of the mean of the cash flow distribution the standard deviation of the cash flow distribution the initial investment and the discount rate are entered in cells B3 B4 B5 and B6 respectively Then for the Monte Carlo simulation the cash flow for an individual year is randomly generated using the Excel formula NORM INV RAND B B If the randomly generated cash flows for the five years are in cells B9 C9 D9 E9 and F9 then the Excel formula for the net present value is B NPV BB Type whole numbers Simulation Results 89 65 1 579 93 174 45 717 02 784 65 3 057 49 1 786 30 1 781 27 1 180 61 2 604 18 901 40 2 344 31 685 61 1 899 89 1 205 22 3 069 45 1 195 65 774 76 68 69 913 51 1 552 81 1 966 66 1 827 60 1 261 51 131 44 695 02 827 36 253 69 954 05 714 76 942 82 818 66 413 88 960 97 1 228 96 433 41 2 041 97 1 349 45 458 31 14 83 697 51 1 071 15 1 512 50 264 67 1 708 88 X

p 11 Quiz 5 ts n ferences TB MC Qu 11 64 Static Llewelyn Company purchased Llewelyn Company purchased 1 000 shares of Its own 10 par value comm treasury stock Multiple Choice

A pipe with a radius of R 1 8m flows partially full as shown What is the approximate hydraulic radius R 70

5 Reserves Loans Securities Property Assets Liabilities Net Worth 60 Checkable Deposits 100 Stock Shares 25 100 150 135 5 Refer to the accompanying consolidated balance sheet for the commercial banking system Assume the required reserve ratio is 12 percent All figures are in billions of dollars The maximum amount by which the commercial banking system can expand the supply of money by lending is A 350 billion B 250 billion C 450 billion D 600 billion

10 Spring olistically competitive firm sells a partic and marginal revenue in the table bel

ion 4 ess pays 68 for a car seat and wants a 24 markup for o ers think the car seats are ugly so they are not selling Mar Find selling price

A single serve coffee maker is programmed to dispense 20 ounces per cup of coffee Each month a quality control representative from the manufacturer takes a random sample of 15 cups of coffee from the coffee maker and carefully measures each pour If the average pour of the sample is found to be significantly different than 20 ounces then the machine is sent back to the manufacturer for repair The mean of a recent sample of 15 cups of coffee was found to be 19 66 ounces Use the critical value method to test the hypothesis that the mean volume of coffee dispensed by this machine is different than 20 ounces using a 0 005 Assume that the distribution of all cups of coffee dispensed from the coffee maker is known to be approximately normally distributed with a standard deviation of 0 45 ounces State the null and alternative hypothesis for this test Ho H Determine if this test is left tailed right tailed or two tailed left tailed two tailed Oright tailed Should the standard normal 2 distribution or Student s t distribution be used for this test The standard normal 2 distribution should be used The Student s t distribution should be used Determine the critical value s for this hypothesis test Round the solution s to two decimal places If more than one critical value exists enter the solutions using a comma separated list Determine the test statistic Round the solution to two decimal places Determine the appropriate conclusion for this hypothesis test The sample data do not provide sufficient evidence to reject the alternative hypothesis that the mean pour of coffee dispensed by the coffee maker is different from 20 ounces and thus we conclude that the coffee maker needs to be serviced by the manufacturer The sample data do not provide sufficient evidence to reject the null hypothesis that the mean pour of coffee dispensed by the coffee maker is 20 ounces and thus we conclude that the coffee maker does not need to be serviced by the manufacturer The sample data provide sufficient evidence to reject the null hypothesis that the mean pour of coffee dispensed by the coffee maker is 20 ounces and thus we conclude that the coffee maker needs to be serviced by the manufacturer The sample data provide sufficient evidence to reject the alternative hypothesis that the mean pour of coffee dispensed by the coffee maker is significantly different than 20 ounces and thus we conclude that the coffee maker does not need to be serviced by the manufacturer

Marissa and Kendra are 2 years apart in age Their ages are two consecutive even integers Kendra is the younger of the two If Marissa s age is added to twice Kendra s age the result is 26 How old is each girl Kendra is years old while Marissa is

According to a 2018 report the mean amount of data used by all smartphone users with unlimited data plans was 4 87 GB per month A company would like to determine if the mean amount of data used per month by smartphone user is different that it was in 2018 In order to investigate the issue random sample of 550 smartphone users was selected Determine the null and alternative hypotheses Ho HA A Type I error in the context of this problem would be Select an answer A Type II error in the context of this problem would be Select an answer

12 1 An element in plane stress on the fuselage of an airplane figure part a is subjected to compressive stresses of magnitude 42 MPa in the horizontal direction and tensile stresses of magnitude 9 5 MPa in the vertical direction see figure part b Also shear stresses of magnitude 15 5 MPa act in the directions shown Determine the stresses acting on an element oriented at a clockwise angle of 40 from the horizontal Show these stresses on a sketch of an element oriented at this angle a 9 5 MPa T b 42 MPa 15 5 MPa

6 62 WP Air at 200 kPa 52 C and a velocity of 355 m s enters an insulated duct of varying cross sectional area The air exits at 100 kPa 82 C At the inlet the cross sectional area is 6 57 cm Assuming the ideal gas model for the air determine a the exit velocity in m s b the rate of entropy production within the duct in kW K