Mathematical Induction Questions and Answers

A company has the following products in its ending inventory Compute lower of cost or market for inventory applied separately to each product Cost per Market per Unit Unit 734 704 534 574 684 709 Product Quantity Product A 10 15 20 Product B Product C Multiple Choice 29 030 28 730 1 952 29 830

A rigid bar ACE is supported by three vertical wires and is initially horizontal as shown in the figure Then a force P is applied at the center of the bar All wires are made from the same material with modulus of elasticity E 200 GPa and have the same cross sectional area A 10 mm You may assume that the deformations are small and that the stresses are within the elastic range for this problem 1 5 m B A 1 0 m D C P 1 0 m F A E 2 0 m Figure 3 1 Rigid bar supported by three vertical wires a Find the normal stresses and the axial displacements in the wires if P 15 kN b Knowing that AB is the critical wire and its yield stress is oy maximum P that can be applied 1500 MPa find the

Which number of simulation trials would be likely to produce results that a closest to those predicted by probability theory O A 50 OB 70 O C 40 O D 60

For an election with four candidates A B C and D we have the following preference schedule Number of voters 15 11 9 6 2 A CD B C B B C D D C D B C B DAAAA 1st choice 2nd choice 3rd choice 4th choice 8 Since there is no majority winner use the Instant Runoff Voting IRV method to determine a winner Which candidate wins the election A A B B C C D D E none of these 8

Find an equation for the line whose graph is sketched y 1 0 1 3 X

The point slope form of the equation of the line with slope 3 passing through the point 1 2 is

Refer to the figure below D E 0000 4GH G G H C 144 F D y 1 E 1 Select the points that lie in Quadrant I Select all that apply A B A H B Select the points that lie in Quadrant III Select all that apply DA X

Three rollers with diameter of 5 inches each radius 2 5 inches are placed on the ground Two rollers diameter 4 inches radius 2 inches each are placed on top and a final 3 inch diameter roller is placed on top See diagram below What is the overall height of this stack Points A B C D E and F are all the centres of their respective circles NOTE A D and F are NOT in a line A F B E C h overall height Round your FINAL answer to the nearest hundredth of an inch Be sure to 7

to provide for uidelines dictate t ft What is the curve ne highway 10 h with a 6 f the curve is 35 3 49 You are asked to design a horizontal curve with a 40 degree central angle A 40 for a two lane road with 11 ft lanes The design speed is 70 mi h and superelevation is limited to 0 06 ft ft Give the radius degree of curvature and length of curve that you would recommend

Manually execute one iteration of the secant method using the initial approximations 1 and x 0 0 to ascertain a solution of tan x 0 1 where x is expressed in radians Following this single iteration provide the precise values of your solution estimate x 1 its estimated relative error and express the tolerance in function as a decimal floating point number in engineering notation with 7 mantissa digits

In a fishing lodge brochure the lodge advertises that 75 of its guests catch northern pike over 20 pounds Suppose that last summer 63 out of a random sample of 78 guests did in fact catch northern pike weighing over 20 pounds Does this indicate that the population proportion of guests who catch pike over 20 pounds is different from 75 either higher or lower Use a 0 05 a What is the level of significance 0 05 USE SALT State the null and alternate hypotheses Enter for as needed Ho P 0 75 H b What sampling distribution will you use Do you think the sample size is sufficiently large Explain We ll use the Student s t because the sample size is not sufficiently large since np 5 and ng 5 O We ll use the standard normal because the sample size is sufficiently large since np 5 and ng 5 We ll use the Student s t because the sample size is sufficiently large since np 5 and nq 5 O We ll use the standard normal because the sample size is not sufficiently large since np 5 and nq 5 Use the value of the sample test statistic to find the corresponding z value Round your answer to two decimal places X c Find the P value of the test statistic Round your answer to four decimal places X 3 Sketch the sampling distribution and show the area corresponding to the P value 2 1 0 1 3 2 1 0 1 2 2 3 3 O x 3 2 1 3 2 1 0 0 1 1 2 2 3 O 3 Q

10 Manny a single taxpayer earns 66 800 per year in taxable income and an additional 12 180 per year in city of Boston bonds If Manny earns an additional 36 800 in taxable income in 2023 what is his marginal tax rate on this income Use tax rate schedule Note Do not round intermediate calculations Round your final answer to two decimal places 00 30 03 Multiple Choice 15 20 percent 22 00 percent 22 45 percent 24 00 percent A

Describe the additive inverse of a vector in the vector space C The additive inverse of f x is f x The additive inverse of f x is f x The additive inverse of f x is f y The additive inverse of f x is f y O The additive inverse of f x is f x The additive inverse of f x is f y

The piston of a steam engine is 50 cm in diameter and the maximum steam gauge pressure is 1 4 MPa If the design stress for the piston rod is 68 MPa its cross sectional area m should be most nearly P 1 4 MPa 50 cm rod

Jigwill bha pic P 16 Jlju 1 00 jo pjall p If f x 2x 3 and g x is a function such that fog x 4x 13 then g x 2x 5 a o g x 2x 5 b O None CO g x x 5 x 5 d O g x x 5 e O

The monod growth function is given by R N TAN ION O a 5 8 O b 5 16 O c 15 32 O d 5 10 then R 3 a

Price 12 8 15 5 3 65 2 D PERPEe 220 400 Supply Demand Quantity ne market depicted above suppose a price floor holds the price at 8 15 ulate producer surplus for this situation Show your answer as a decimal e g

A study of parental empathy for sensitivity cues and baby temperament higher scores mean more empathy was performed Let x be a random variable that represents the score of a mother on an empathy test as regards her baby Let x be the empathy score of a father A random sample of 38 mothers gave a sample mean of x 68 36 Another random sample of 38 fathers gave X 58 70 Assume that a 10 99 and 10 88 a What distribution standard normal or Student s t should be used to construct a confidence interval for Explain A Student s t should be used because o and are known A standard normal should be used because and are known A standard normal should be used because o and are unknown A Student s t should be used because and are unknown b Let be the population mean of x and let 2 be the population mean of x Find a 99 confidence interval for Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to two decimal places

How much does a sleeping bag cost Let s say you want a sleeping bag that should keep you warm in temperatures from 20 F to 45 F A random sample of prices for sleeping bags in this temperature range is given below Assume that the population of x values has an approximately normal distribution 60 105 90 115 120 70 60 30 23 100 110 95 105 60 110 120 95 90 60 70 LUSE SALT a Use a calculator with mean and sample standard deviation keys to find the sample mean price x in dollars and sample standard deviation s in dollars Round your standard deviation to four decimal places X S b Using the given data as representative of the population of prices of all sleeping bags find a 90 confidence interval for the mean priceu in dollars of all sleeping bags Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to two decimal places

or cell bre his may be an advance less such as Overproduction in the body can be gout leukemia or lymphoma Over a period of months an adult male patient has taken seven blood tests for uric acid The mean concentration was X 5 43 mg dl The distribution of uric acid in healthy adult males can be assumed to be normal with o 1 87 mg dl a Find the margin of error for a 95 confidence interval for the population mean concentration of uric acid in mg dl in this patient s blood Round your answer to two decimal places mg dl Find a 95 confidence interval for the population mean concentration of uric acid in mg dl in this patient s blood Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to two decimal places mg dl b What conditions are necessary for your calculations Select all that apply O uniform distribution of uric acid O is unknown On is large normal distribution of uric acid O is known c Interpret your results in the context of this problem We are 95 confident that the true uric acid level for this patient falls within this interval The probability that this interval contains the true average uric acid level for this patient is 0 95 We are 5 confident that the true uric acid level for this patient falls within this interval The probability that this interval contains the true average uric acid level for this patient is 0 05 d Find the sample size necessary for a 95 confidence level with maximal margin of error E 1 02 for the mean concentration of uric acid in this patient s blood Round your answer up to the nearest whole number blood tests

How profitable are different sectors of the stock market One way to answer such a question is to examine profit as a percentage of stockholder equity A random sample of 30 retail stocks was studied for x1 profit as a percentage of stockholder equity The result was x1 13 8 A random sample of 36 utility gas and electric stocks was studied for x2 profit as a percentage of stockholder equity The result was x2 10 6 Assume that 1 4 4 and 2 3 1 Let u1 represent the population mean profit as a percentage of stockholder equity for retail stocks and let 2 represent the population mean profit as a percentage of stockholder equity for utility stocks Find a 95 confidence interval for u1 u2 in Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to one decimal place

The Wind Mountain archaeological site is located in southwestern New Mexico Wind Mountain was home to an ancient culture of prehistoric Native Americans called Anasazi Suppose that a random sample of excavations at Wind Mountain gave the following depths in centimeters from present day surface grade to the location of significant archaeological artifacts 86 46 119 79 74 54 66 61 66 96 89 71 76 66 69 USE SALT a Use a calculator with mean and sample standard deviation keys to find the sample mean x and sample standard deviation s in cm Round your answers to four decimal places cm S cm b Compute a 95 confidence interval for the mean depth in cm at which archaeological artifacts from the Wind Mountain excavation site can be found Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to one decimal place

A study recorded the following weights of adult grey wolves from two regions in Old Mexico Chihuahua region x variable in pounds 86 75 91 70 79 80 68 71 74 64 LAUSE SALT a Use a calculator with mean and standard deviation keys to calculate x and s in pounds Round your answers to four decimal places Durango region variable in pounds 68 72 79 68 77 89 62 55 68 68 59 63 66 58 54 71 59 67 52 lb lb Use a calculator with mean and standard deviation keys to calculate x and s in pounds Round your answers to four decimal places lb lb c Let be the mean weight of the population of all grey wolves in the Chihuahua region Let be the mean weight of the population of all grey wolves in the Durango region Find an 85 confidence interval for in pounds Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to two decimal places

me runs per gave the following data for home run percentages percentage is X a S Home run percentages of a sample of 43 professional baseball players 1 6 2 3 1 2 6 4 2 3 0 0 1 8 LUSE SALT 1 9 2 4 0 0 1 8 3 1 3 7 3 2 1 6 4 1 0 0 1 2 hes at bat A andom sample of 43 proressional baseball players 1 7 1 3 2 1 2 7 1 4 4 0 2 1 3 3 1 3 1 5 2 7 2 7 2 5 6 4 1 8 2 7 a Use a calculator with mean and standard deviation keys to find x and s Round your answers to four decimal places puto 00 confidence int 2 0 1 9 1 3 2 6 N al for the pon Istion b Compute a 90 confidence interval for the population mean of home run percentages for all professional baseball players Hint If you use the Student s t distribution table be sure to use the closest d f that is smaller Enter your answer in the form lower limit to upper limit Include the word to Round your answers to two decimal places 0 0 4 1 2 9 1 8 2 2 porcentages for all professional all players

Clarkson University surveyed alumni to learn more about what they think of Clarkson One part of the survey asked respondents to indicate whether their overall experience at Clarkson fell short of expectations met expectations or surpassed expectations The results showed that 3 of the respondents did provide a response 24 said that their experience fell short of expectations and 65 of the respondents said that their experience met expectations Round your answers to two decimal places a If we chose an alumnus at random what is the probability that the alumnus would say their experience surpassed expectations b If we chose an alumnus at random what is the probability that the alumnus would say their experience met or surpassed expectations

Clarice goes to a local home improvement store to purchase new carpet and to have the new carpet installed in a room Clarice says the room is approximately 400 square feet Installers arrive and after taking measurements determine that the room is 378 square feet a Compute the absolute error Simplify your answer completely AE Interpret the result The square footage of Clarice s carpet was increased by this amount Clarice s approximation was off by this much relative to the measured square footage of the room Clarice s approximation had this percent error Clarice s approximation was this many square feet off of the measured square footage of the room This is the ratio of Clarice s approximation to the measured square footage of the room b Compute the relative error Round to three decimal places Simplify your answer completely RE Interpret the result The square footage of Clarice s carpet was increased by this amount Clarice s approximation was off by this much relative to the measured square footage of the room Clarice s approximation had this percent error Clarice s approximation was this many square feet off of the measured square footage of the room This is the ratio of Clarice s approximation to the measured square footage of the room

The estimated and actual values are given Compute the absolute error Simplify your answer completely ve 7 and v 5 AE

Find A Begin by finding A 1 and then evaluate its determinant Verify your result by finding A and then applying the formula A1 1 A A 0 1 1 A 9 1 9 1 9 6

Compute each of the following derivatives a 2x 8 b X dx 18 c 5 x 8 7 dx