# Mathematical Induction Questions and Answers

Math - Others

Mathematical InductionAli is a Lead Engineer working on a new oil rig drilling project The project is located outskirts of Kuwait and has no cellular phone service Ali has a two way radio that allows him to transmit messages to other Engineers on the ground His device has a range of 8 miles in all directions The other Engineers have similar devices that can pick up Ali s messages when they are in range of his two way radio On a particular day Ali is in the project head office at the center of the project His co worker Mahmoud is doing a survey of the land by driving along a straight road through the project area The road that Mahmoud is on starts 12 miles west and 12 miles south of the project s head office and ends 14 miles north and 8 miles east of the project s head office A Construct a model on a coordinate plane of the scenario described B Approximately how many miles of road will Mahmoud be able to receive Ali s messages C Suppose that Mahmoud drives at an average rate of 14 miles per hour If Mahmoud starts his trip at 9 A M at what time should Ali expect him to first be able to receive his messages

Math - Others

Mathematical InductionEnter an ordering on the atomic subformulae of the following formula P P V Q Enter an ordering

Math - Others

Mathematical Inductionapter 4 Compression Members 4 9 5 A column for a multistory building is fabricated from ASTM A588 plates as shown in Figure P4 9 5 Compute the nominal axial compressive strength based on flexural buckling do not consider torsional buckling Assume that the components of the cross section are connected in such a way that the section is fully effective my 2 3 2 8 12 1 1

Math - Others

Mathematical Induction2 7 A 3400 lb car is traveling in third gear overall gear reduction ratio of 2 5 to 1 on a level road at its top speed of 130 mi h The air density is 0 00206 slugs ft The car has a frontal area of 19 8 ft a drag coefficient of 0 28 a wheel radius of 12 6 inches a drive axle slippage of 3 and a drivetrain efficiency of 88 At this vehicle speed what torque is the engine producing and what is the engine speed in revolutions per minute

Math - Others

Mathematical Induction25 to 69 beats per minute Let x be a random variable that represents the resting heart rate for an adult horse Assume that x has a distribution that is approximately normal USE SALT a The empirical rule indicates that for a symmetric and bell shaped distribution approximately 95 of the data lies within two standard deviations of the mean 95 20 Therefore a 95 range of data values extending from 4 20 to 20 is often used for commonly occurring data values Note that the interval from 20 to 20 is 40 in length This leads to a rule of thumb for estimating the standard deviation from a 95 range of data values 20 Estimating the standard deviation For a symmetric bell shaped distribution standard deviation range high value low value where it is estimated that about 95 of the commonly occurring data values fall into this range Use this rule of thumb to estimate the standard deviation of x distribution in beats per minute 11 beats per minute b What is the probability that the heart rate is less than 29 beats per minute Round your answer to four decimal places 0 0505 c What is the probability that the heart rate is greater than 61 beats per minute Round your answer to four decimal places 0 10156 d What is the probability that the heart rate is between 29 and 61 beats per minute Round your answer to four decimal places e A horse whose resting heart rate is in the upper 10 of the probability distribution of heart rates may have a secondary infection or illness that needs to be treated What is the heart rate corresponding to the upper 10 cutoff point of the probability distribution Round your answer to the nearest whole number

Math - Others

Mathematical InductionWhich of the following is the correct way to declare a pointer O int ptr O int ptr O Pointer ptr O All of the above is correct O none of the above is correct

Math - Others

Mathematical InductionQuestion 2 Which of the following give the value stored at the address pointed to by ptr Optr ptr val ptr

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Mathematical InductionEvaluate the function f x x 6x for the given value of x Simplify your answer f x h

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Mathematical InductionMake an appropriate substitution and solve the equation 2 7 2 7 72 0 The solution set is 3

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Mathematical InductionTawana owns and operates a sole proprietorship and has a 37 percent marginal tax rate She provides her son Jonathon 17 000 a year for college expenses Jonathon works as a pizza delivery person every fall and has a marginal tax rate of 15 percent Required a What could Tawana do to reduce her family tax burden b How much pretax income does it currently take Tawana to generate the 17 000 after taxes given to Jonathon c If Jonathon worked for his mother s sole proprietorship what salary would she have to pay him to generate 17 000 after taxes ignoring any Social Security Medicare or self employment tax issues d How much money would the strategy in part c save Complete this question by entering your answers in the tabs below Required A Required B Answer is not complete Required C Required D How much money would the strategy in part c save

Math - Others

Mathematical Inductionin pounds lbs We will treat a subset of this dataset as a representative sample of realized values for our random variable The first five rows of the data look like this Weight in lbs 4 9 12 0 9 2 9 5 6 1 Import the dataset into SALT for analyzing After you have clicked the tab for your selected topic and read the problem answer the questions below a Create a histogram in SALT to determine if the distribution of our sample is mound shaped and symmetric with no outliers When a data s distribution is mound shaped and at least roughly symmetric with no outliers a normal distribution can be used to model the variable s behavior USE SALT Since the histogram for our sample is mound shaped and is O at least roughly symmetric with no outliers the normal distribution can be used to approximate the behavior for this random variable b Locate the sample mean and standard deviation for our variable Round your answers to four decimal places X X S c Draw the normal distribution with a mean of x and a standard deviation of s on SALT s Distribution Calculators page Round your answers to two decimal places The random variable value that is predicted to be one standard deviation above the mean is The random variable value that is predicted to be two standard deviations below the mean is The random variable that is predicted to have a z score of 3 00 is X x x x d Use the Probability and Z Score sections on the left panel and radio buttons on the right panel to answer the following questions Remember to convert the percentage to a proportion before entering the value into SALT Round your answers to four decimal places Approximately 2 8 of values for our random variable are predicted to be larger than what value Approximately 90 of values for our random variable are expected predicted to be centered around the mean with a lower value of X and an upper value of The Z scores for these two values are Z X and z e How well is the normal distribution modeling the random variable represented by our sample data Use SALT s data filters and Descriptive Statistics page to answer the following questions In part d you found the boundary values where the normal model predicts the middle 90 of data values are located Use the filters on the Dataset page to filter out observations that are outside of this range then return to the Descriptive Statistics page to locate the number of sample values within this region There are sample values within this region Remove the filter and return to the Descriptive Statistics page There are values in the entire sample Use these two counts to determine the actual proportion of sample values within this region Rounded to three decimal places the proportion of sample values within this middle region is How different are the actual and predicted proportions Subtract the predicted proportion from the actual proportion and take the absolute value of the result to determine how different they are Calculate the following quantity difference in proportions actual proportion predicted proportion Also in part d you found the boundary value that the normal model predicts 2 8 of values are larger than Enter this value into SALT s data filter and determine the number of sample values that meet this criteria There are sample values within this region Use this count and the size of the sample to determine the actual proportion of sample values within this region Rounded to three decimal places the proportion of sample values within this region is How different are the actual and predicted proportions Subtract the predicted proportion from the actual proportion and take the absolute value of the result to determine how different they are Calculate the following quantity difference in proportions actual proportion predicted proportion

Math - Others

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

Math - Others

Mathematical InductionRequired information NOTE This is a multi part question Once an answer is submitted you will be unable to return to th Show that each of these conditional statements is a tautology by using truth tables Complete the truth table given below for the conditional statement p A p q q p p q og p p q T q Click to select T P q T Click to select FT Click to select K The given conditional Click to select Click to select True False F Click to select Click to select Click to select Click to select statement is not a tautology 4

Math - Others

Mathematical Inductionp T Required information NOTE This is a multi part question Once an answer is submitted you will be unable to return to this part Complete the truth table given below to verify the associative laws T T T F F F F q T T F F T T F F r T F T F T F T F pv q T T T T T T F F p V q V r T T Click to select Click to select Click to select Click to select q Vr T T T F T T T F PV qVr T T T T Click to select Click to select Click to select Click to select

Math - Others

Mathematical InductionGiven that x is a normal variable with mean 49 and standard deviation 6 3 find the following probabilities Round your answers to four decimal places LUSE SALT a P x 60 b c P x 50 X X P 50 x 60

Math - Others

Mathematical InductionThe second dose of the COVID 19 vaccine is more likely to produce side effects than the first The time between receiving the shot and the onset of side effects is called the lag time Suppose according to one study the lag times among the subjects that reported side effects from a second dose of the vaccine were normally distributed with a mean of 13 hours with a standard deviation of 4 hours Use the empirical rule to answer the following a What is the probability that a person selected at random from among those that experienced side effects from their second dose of the vaccine had a lag time of less than 9 hours b What is the probability that a person selected at random from among those that experienced side effects from their second dose of the vaccine had a lag time between 13 and 21 hours c Estimate a range of lag times in hours centered about the mean that should include about 95 of all lag times for those experiencing side effects between and hours

Math - Others

Mathematical Induction8 Calculate the mean median mode and range of the set 1 3 7 29 12 15 5 4KC Mean Mode 9 Provide an example of the following Explain your reasoning 2C Depreciating asset Median Range Appreciating asset

Math - Others

Mathematical InductionDetermine whether each statement is true or false If a statement is true give a reason or cite an appropriate statement from the text If a statement is false provide an example that shows the statement is not true in all cases or cite an appropriate statement from the tem a To find the determinant of a triangular matrix add the entries on the main diagonal O True the determinant of a triangular matrix is equal to the order of the matrix which is equal to the sum of the entries in the main diagonal False the determinant of a triangular matrix is equal to the product of the entries in the main diagonal which may not be equal to the sum of the entries in the main diagonal O True the determinant of a triangular matrix is equal to the product of the entries in the main diagonal which is equal to the sum of the entries in the main diagonal O False the determinant of a triangular matrix is equal to the number of nonzero entries in the main diagonal which may not be equal to the sum of the entries in the main diagonal O False the determinant of a triangular matrix is equal to the order of the matrix which may not be equal to the sum of the entries in the main diagonal b To find the determinant of a matrix expand by cofactors in any row or column O False to find the determinant of a matrix expand by cofactors in any row but not in any column O False to find the determinant of a matrix expand by cofactors in only the first column O False to find the determinant of a matrix expand by cofactors in only the first row O True to find the determinant of a matrix expand by cofactors in any row or column False to find the determinant of a matrix expand by cofactors in any column but not in any row X c When expanding by cofactors you need not evaluate the cofactors of zero entries O True in a cofactor expansion each cofactor gets multiplied by the corresponding entry If this entry is zero the product will be zero True in a cofactor expansion each cofactor gets multiplied by the corresponding entry If this entry is zero the product will be one O False in a cofactor expansion each cofactor gets multiplied by the corresponding entry If this entry is zero the product will be zero O True in a cofactor expansion each cofactor gets multiplied by the corresponding entry If this entry is zero the product will be equal to the cofactor O False in a cofactor expansion each cofactor gets multiplied by the corresponding entry If this entry is zero the product will be equal to the cofactor X

Math - Others

Mathematical InductionUse the table to express the following Babylonian numeral as a Hindu Arabic numeral V V V V V vvv V V V V v 0 points Babylonian numerals Hindu Arabic numerals Points 0 of V 1 10

Math - Others

Mathematical InductionWrite Matlab scripts that determine the zero state responses of the following systems by solving differential equations in the time domain 1 dy t dt 2y t 15u t

Math - Others

Mathematical Induction7 A glass is in the shape of a rectangular based prism 4A 2 2 a How much water is needed to fill the glass to the nearest cubic centimeters 10 cm 5 cm 4 cm b How much more water would I need if I wanted to double the length and the width of the base

Math - Others

Mathematical InductionFind the sum difference or product Simplify your answer completely 2x 3x 1 3x 5x 5 Your answer cannot be understood or graded More Information

Math - Others

Mathematical InductionFactor the expression completely This type of expression arises in calculus when using the Product Rule x1 2 9x 4 1 2 2x1 2 9x 4 1 2

Math - Others

Mathematical InductionAccording 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

Math - Others

Mathematical InductionDeja and Aniyah each planted a tree at the same time Deja s tree is 1 foot tall and grows 2 feet per year feet per year Aniyah s tree is 4 feet tall and grows 1 2 Name 4 1 Write a system of equations to represent this situation Use x for the number of years since they planted the tree and y for the tree s height in feet 1 ft 4 ft 4 2 The solution to a system of equations for this situation is 2 5 Explain what the solution says about the trees

Math - Others

Mathematical InductionShenise is a star player for her women s basketball team She has injured her ankle and it is doubtful that sh will be able to play in an upcoming game If Shenise can play the coach estimates that the team will score 78 points If Shenise is not able to play the coach estimates that they will score 62 points The team doctor estimates that there is a 70 chance Shenise will play Determine the number of points the team can expect to score It is expected that the team will score points Round to the nearest whole number as needed www

Math - Others

Mathematical Inductionimits Continuity Course Packet on indetermi x x 9 X 81 X 81 Evaluate lim If an answer does not exist enter DNE

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Mathematical InductionIf there are five pears in a bowl in how many ways can there be one pear that is ripe and four pears that are unripe There are ways for this to occur Type a whole number

Math - Others

Mathematical InductionWatch the video and then solve the problem given below Click here to watch the video A salesman has to travel to different cities Assume the numbers listed are the costs in hundreds of dollars for the salesman to transport materials and travel to the city Find the cost of the path for AECDBA Enter the cost for his path traveled E 165 302 205 D 185 340 320 500 360 200 305 C B

Math - Others

Mathematical InductionIn a sales effectiveness seminar a group of sales representatives tried two approaches to selling a customer a new automobile the aggressive approach and the passive approach For 1 160 customers the following record was kept Sale Aggressive 263 Passive 413 No Sale Row Total P S Pa 317 Column Total 676 484 167 580 P Pa and S 580 Suppose a customer is selected at random from the 1 160 participating customers Let us use the following notation for events A aggressive approach Pa passive approach S sale N no sale So P A is the probability that an aggressive approach was used and so on 1 160 a Compute P S P SIA and P S Pa Enter your answers as fractions P S X P S A Enter an exact value instead of a rounded value x Enter an exact value instead of a rounded value b Are the events S sale and Pa passive approach independent Explain Yes P S P S Pa No The two events cannot occur together Yes The two events can occur together No P S P S Pa c Compute P A and S and P Pa and S Enter your answers as fractions P A and S x Enter an exact value instead of a rounded value d Compute P N and P NI A Enter your answers as fractions P N P N A Enter an exact value instead of a rounded value e Are the events N no sale and A aggressive approach independent Explain No The two events cannot occur together Yes P N P N A Yes The two events can occur together No P N P N A f Compute P A or S Enter your answer as a fraction

Math - Others

Mathematical InductionWrite each number in scientific notation a 69 800 000 b c d x 10 7 300 000 000 x 10 0 0000028535 x 10 0 0000001581

Math - Others

Mathematical InductionComplete the following tables Round your answers to three decimal places 1 n n 1 2 5 10 100 21 n What about the nth root of n What happens to the nth root of 2 as n gets large As n gets larger 21 n decreases to 1 As n gets larger 21 n increases to 1 As n gets larger 21 n does not change As n gets larger 1 2 1 n decreases to 1 As n gets larger 1 2 1 n increases to 1 As n gets larger 1 2 1 n does not change 1 2 5 10 100 Construct a similar table for n n What happens to the nth root of n as n gets large As n gets larger n n decreases As n gets larger n n increases As n gets larger n n does not change

Math - Others

Mathematical InductionPut each fractional expression into standard form by rationalizing the denominator S a 2 1 2t b c 1 3 5 X X

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Mathematical InductionWrite each number in decimal notation 3 19 x 107 a b c CHY 2 757 x 107 2 670 x 10 8

Math - Others

Mathematical Induction15 A plane needs to travel to a location 1550 km away at a direction N30 E The plane flies at a velocity of 625 km hr and there is a wind of 80 km hr at a direction N10 W a What heading should the pilot take to arrive at the destination A 3 b How long will it take T 2

Math - Others

Mathematical InductionSometimes probability statements are expressed in terms of odds The odds in favor of an event A are the following ratio P A P A P not A P AC For instance if P A 0 60 then P AC 0 40 and the odds in favor of A are 0 60 6 3 0 40 4 a Show that if we are given the odds in favor of event A as n m the probability of event A is given by the following e n M n 1 P A P A Hint Solve the following equation for P A P A 1 P A n n m n nP A 77 n m n n written as 3 to 2 or 3 2 2 P A P A P A 1 P A P A P A nP A b A telemarketing supervisor tells a new worker that the odds of making a sale on a single call are 2 to 19 What is the probability of a successful call Round your answer to two decimal places A sports announcer says that the odds a basketball player will make a free throw shot 5 to 3 What is the probability the

Math - Others

Mathematical InductionShow that the matrix is invertible and find its inverse 8 A 1 A si sin 8 cos e cos 0 sin 0

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Mathematical InductionShow that AB and BA are not equal for the given matrices 1 A 4 6 3 B 03 1 6 AB DA 20

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Mathematical InductionFactor each completely 9 2p 3p 5 11 2n 9n 18 13 4n 5n 6 15 6a a 2 10 3x 14x 8 12 3k 17k 20 14 10x 9x 2 16 4r r 18

Math - Others

Mathematical InductionFind if possible A B A B 2A 2A B and B A If not possible enter IMPOSSIBLE in any single cell A 6 5 1 4 a A B 8 5 It b A B c 24 d 24 B B e B A 1 5 1 10 11 11 11 K

Math - Others

Mathematical InductionWrite the system of linear equations in the form Ax b and solve this matrix equation for x 3x 3 X2 31 2x1 x 6x X1 30 CHO X2 31

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Mathematical InductionUsing V 9 mV and given the voltage across an inductor L 10 mH as shown in Fig P6 25 determine the waveform for the inductor current during the time t1 t t2 where t1 4 ms and t2 19 ms Assuming the solution looks like iL t X t t1 Y t t1 C what is the initial condition of the current the constant C For your answer just put the magnitude of the initial value of the constant and in milliAmps there should only be a number in your answer v 1 mv A Figure P6 25 V Notes on entering solution t1 t2 Pay attention to the interval Enter your solution to 2 decimal points Only put the constant ex 200 t t1 50 t t1 1 is entered as 1 Do not include units in your answer 1 ms

Math - Others

Mathematical Inductionb The Monod growth function is given by R N Find 1 R 2 2 the saturation level 20 N 2 N

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Mathematical Inductionb Use a calculator to verify that Ex 149 6 Ex 3 220 10 y 244 Ey2 9 834 and Exy 5 290 7 Computer Round your answer to four decimal places r As x increases does the value of r imply that y should tend to increase or decrease Explain your answer Given our value of r y should tend to remain constant as x increases Given our value of r y should tend to increase as x increases Given our value of r y should tend to decrease as x increases Given our value of r we can not draw any conclusions for the behavior of y as x increases

Math - Others

Mathematical Inductionate the following and round the FINAL answer to 2 decimal places 800 1 005 1 0 005 a 150 000 1 0 0575 A footwear retailer sold 13 pair of b nach