Mathematical Induction Questions and Answers

13 05 20 2022 Minimise Z 4x 2x2 subject to using the big M method 20230 3x1 x 27 21 2 21 x 22 30 x1 x 0 023 05 20 202218b1393 877 2023 05 20

In inspection which procedure provides more information O gaging measurement

Show that n 0 AHC r 1 r 2 For the toolbar press ALT F10 PC or ALT FN F10 Mac 72 2 n 2

10 In the mid 1800s Border Ruffians had the goal to vote illegally for a a OA pro slavery government in Kansas O B pro slavery government in Missouri OC anti slavery government in Kansas O D anti slavery government in Missouri

q is inversely proportional to p3 When p 2 q 5 P 9 2 5 3 12

4 3 SI units A bridge to be fabricated of steel girders is designed to be 500 m long and 12 m wide at ambient temperature assumed 20 C Expansion joints will be provided to compensate for the change in length in the girders as the temperature varies Each expansion joint can compensate for a maximum of 20 mm of change in length From historical records it is estimated that the minimum and maximum temperatures in the region will be 35 C and 40 C respectively Determine a the minimum number of expansion joints required and b the length that each bridge section should be fabricated The coefficient of thermal expansion a 12 10 6V C for steel

23 determine the values of a for which the system has no solutions exactly one solution or nfinitely many solutions x 2y3z 3x y 4x y a 14 z 5z 4 2 a 2

3 2 SI Units During a tensile test the starting gage length 100 0 mm and the cross sectional area 150 mm During testing the following force and gage length data are collected 1 17 790 N at 100 2 mm 2 23 040 N at 103 5 mm 3 27 370 N at 110 5 mm 4 28 910 N at 122 0 mm 5 27 400 N at 130 0 mm and 6 20 460 N at 135 1 mm The final data point 6 occurred immediately prior to failure Yielding occurred at a load of 19 390 N 0 2 offset value and the maximum load 4 was 28 960 N a Plot the engineering stress strain curve Determine b yield strength c modulus of elasticity d tensile strength and e percent elongation

olve the system or show that it has no solution If there is no solution enter NO SOLUTION If there are an infinite number of solutions enter the general solution in terms of x where x is any real numbe 1 x y 2 5 4x 10y 6 x y 26 3 43 15 X

the kite below TN 12 JG 6 and GM 18 Find the perimeter of the kite Round answers to the tenths place TNG In the kite below TN 12 JG 6 and GM 18 Find the perimeter of the kite Round answers to the tenths place 11

Which of the following is the Central Limit Theorem As sample size increases the distribution of the population becomes normal All populations are normally distributed As sample size increases variance of the population and mean of the population are approximately equal O When sample size is sufficiently large the sampling distribution of approximated by a standard normal curve X OFF is well

Find the general solution to the given system of differential equations Consider all functions to be functions of t x 0 3 x y x y 0 0 z 0 3 z x y x t y t z t Find the specific solution that satisfies the initial conditions x t y t 9e 6 9e y z Z z t 3e 6 X 3e 6 X

Use a numerical integration command on a graphing calculator Find the future value at 4 5 interest compounded continuously for 5 years of the continuous income stream with the rate of flow function f t 200t 3 000 The future value of the income stream at 4 5 compounded continuously at the end of 5 years is Round to the nearest dollar as needed

The Weidmans want to save 30 000 in 4 years for a down payment on a house If they make monthly deposits in an account paying 12 compounded monthly what is the size of the payments t are required to meet their goal Round your answer to the nearest cent

Find an equation of the parabola with vertex 5 4 and focus 5 6 A B 1 0

sider the following 2 A 3 Find all eigenvalues of the matrix A Enter your answers as a comma separated list 1 X Give bases for each of the corresponding eigenspaces Enter sqrt n for n smaller 7 value span 5920 larger value span 1 sqrt 3 1 sqrt 3 1 Orthogonally diagonalize the matrix by finding an orthogonal matrix Q and a diagonal matrix D such that QTAQ D Enter each matrix in the form row 1 row 2 where each row is list D Q

3 4 points A fish farmer has 5000 catfish in his pond The number of catfish increases by 8 per month and the farmer harvests 300 catfish per month a Give t recursive formula for the catfish population an after n months Be sure to include ao b How many fish are in the pond after 6 months Round to the nearest whole number

Solve using simplex Minimize W 2y1 y2 3y3 Subject to Y1 y2 Y3 100 2y1 y2 50 With Y10 y2 0 y3 0 y2 100 y2 50 Oy2 300 y2 0

Find an equation of the ellipse that has center 3 3 a major axis of length 6 and endpoint of minor axis 3 5 N 00 0 0

Write each Mayan number as a base ten number a b c d

From a point on the ground a person notices that a 129 foot antenna on the top of a hill subtends an angle of 2 5 If the angle of elevation to the bottom of the antenna is 29 find the height of the hill

Theme William Golding says the theme of the book is an attempt to trace the defects of society to the defects of human nature Meaning the shape of society must depend on the ethical nature of the individual and not on any political system Describe how you think the following could be possible themes or lessons within the story Fear of the unknown Blindness Sight Good vs Evil

Classify each of the following as classical or empirical probability 14 According to the floor salesman the probability that a stovetop will need repairs during a five year period is 0 07 15 The probability of choosing five numbers from 1 30 that match the 8 numbers drawn in the local lottery is 0 00000004115

Caleb made the table below to show the number of hours he works and the amounts he earns over a four week period Hours Earnings in dollars 12 140 Caleb s Earnings 15 170 18 200 21 230 Which describes whether the relationship between the earnings and the number of hours represents a direct variation O He earns 20 more than 10 times the number of hours he works each week so the earnings vary directly with the hours The earnings increase by 30 for every increase of 3 hours so the earnings vary directly with the hours The ratios of earnings to hours are not the same each week so the earnings do not vary directly with the hours The earnings increase at a steady rate so the earnings do not vary directly with the hours

An electronic gadgets distributor distributes various brands of cell phones to retailers The data for the number of smartphones distributed in nine months Jan Sept are collected to make a box and whisker plot Read the plot and answer the questions TTTTT 20 30 40 Write the median for the above given plot What is the least number of smartphones distributed Write the third quartile from the given plot a b C 9 QUESTION 8 Tammy recorded the amount of time she spent on six activities over a twenty four hour period and drew a bar graph as follows Tammy s daily activities 8 7 Time in hours 6553 2 1 0 Sleep Sport 50 Activity What percentage of her time was spent playing sports About 8 School Washing Eating 60 TV

sing the histogram estimate the average age of a student who owns an ipod Show your work 800 600 400 200 0 H 14 15 16 17 18 Students That Own an iPod ALTEN F10 Mac

er Complete each phrase to state the meaning of the expression h 7 a number by 7

The rabbit population at the city park increases by 17 per year If there are intially 281 rabbits in the city park a Write a model for the population y in terms of years t y b Find the rabbit population in 16 years Round to the nearest whole rabbit c Estimate When the rabbit population reaches 39618 It will happen between year and year

Inman Products estimates its sales at 180 000 units in the first quarter and that sales will increase by 18 000 units each quarter over the year They have and desire a 25 ending inventory of finished goods Each unit sells for 25 40 of the sales are for cash 70 of the credit customers pay within the quarter The remainder is received in the quarter following sale

Gallow Industries prepared a fixed budget of 60 000 direct labor hours with estimated overhead costs of 300 000 for variable overhead and 90 000 for fixed overhead Gallow then prepared a flexible budget at 57 000 labor hours How much is total overhead costs at this level of activity

Determine the vertex the equation for the axis of symmetry and the x interce the quadratic function Use this information to graph the function f x 2x 16x 35

Use a truth table to determine whether the two statements are equivalent p q q p and q p Complete the truth table q p q q p q p T T F T PT FL LL F LL F Choose the correct answer below O The statements are equivalent O The statements are not equivalent

Consider the following linear transformation T R2 R2 defined by T Find the nullity of T nullity T 4x y x 4y Determine if the linear transformation is one to one O one to one O not one to one Determine if the linear transformation is onto O Onto because T is one to one and the domain and codomain have the same dimension Onto because T is not one to one and the kernel is nontrivial O Not onto because T is one to one and the domain and codomain have different dimens O Not onto because T is not one to one and the kernel is trivial

Which of the following is NOT an interest that affected the literature of Postmodernism Women s movement Protests against the Vietnam War Prohibition Civil Rights Movement

17 Calculate the number of grams of saturated fat that is needed for a client prescribed a 1500 calorie per day diet using the recommendation from the Dietary Guidelines for Americans 2020 2025 Make sure to find the percentage of calories and then convert to grams Show all work 8 points

According to the Keynesian macroeconomic model the level of intended investment check all that apply is determined by savings and the interest rate depends on the level of optimism or pessimism among investors is autonomous is determined by the inflation rate is a function of the unemployment rate is a function of the level of output and income

Statistics A sociologist chose 300 students at random from each of two schools and asked each student how many siblings he or she has The results are Number of siblings 0 1 2 3 4 Lincoln School 120 80 60 30 10 Washington School 140 110 30 10 10 shown in the table There are a total of 2 400 students at Lincoln School and 3 300 students at Washington school What is the median number of siblings for all the students surveyed A 0 B 1 C 2 D 3 WI

Write an equation of the circle with center 5 2 and diameter 12 x 5 y 2 144 3

Using the information provided in the given table determine how much monthly income would be necessary to budget for loan fees over the 9 month academic year Round your answer to the nearest cent if necessary Itranscript Estimated Cost of Local College Next Academic Year Budget Category University Fees Room Board Books Supplies Transportation Personal Health Insurance Loan Fees On Campus Student 9942 16 570 957 681 1256 1583 152

A resort plans to apportion 49 new toboggans among the four resorts based on the number of rooms in each resort as shown below Use the table to answer parts a through c Resort A Total D D 265 Number of rooms 93 637 a Determine the standard divisor B 137 C 142 Type an integer or decimal rounded to the nearest hundredth as needed

Choose the correct answer below COLLA OA The median of a data set is the data item in the middle of the ordered se To find the median first arrange the data items in order from smallest to largest If the number of data items is odd th median is the data item in the middle of the list If the number of data items is even the median does not exist OB The median of a data set is the sum of the data items divided by the number of data items To find the median first arrange the data items in order from smallest to largest If the number of dat items is odd the median is the data item in the middle of the list If the number of data items is even the median does not exist OC The median of a data set is the sum of the data items divided by the number of data items To find the median first arrange the data items in order from smallest to largest If the number of dat items is odd the median is the data item in the middle of the list If the number of data items is even the median is the mean of the two middle data items O D The median of a data set is the data item in the middle of the ordered set To find the median first arrange the data items in order from smallest to largest If the number of data items is odd the median is the data item in the middle of the list If the number of data items is even the median is the mean of the two middle data items

Choose the correct answer below A A frequency distribution is a type of data presentation The first column contains the first part of each data item The second column contains the second part of each data B A frequency distribution is a graph in which a circle is divided into parts whose sizes express the percentages of a sample that fall into particular classes C A frequency distribution is a method in which each data item is assigned to a class The data are then counted according to which class they appear in D A frequency distribution is a type of data presentation The data values are listed in one column The adjacent column indicates the number of times each value occurs

What is a population Choose the correct answer below OA A population is the set of all the properties that can be assigned to any people or objects in a given sample OB A population is a set of data OC A population is the set containing all the people or objects whose properties are to be described and analyzed by the data c OD A population is a group that exhibits characteristics typical of those possessed by the target sample What is a sample Choose the correct answer below OA A sample is the set of all the properties that can be assigned to any people or objects in a given population B A sample contains one or many populations OC A sample is obtained in such a way that every element in the population has an equal chance of being selected OD A sample is a subset or subgroup of the population

The systolic blood pressures of 40 women have a mean of 110 8 mm Hg and a standard deviation of 17 1 mm Hg The highest systolic blood pressure measurement in this sample is 181 mm Hg In this context is a systolic blood pressure of 181 mm Hg unusual Why or why not Choose the correct answer below BOD A Yes because it differs from the mean by more than one standard deviation B No because it does not differ from the mean by more than two standard deviations OC No because it does not differ from the mean by more than one standard deviation D Yes because it differs from the mean by more than two standard deviations

Problem 1 Given the quadratic function y 2 x 1 2 8 Find a The vertex b The axis of the symmetry c Sketch the graph

17 The slope and the y intercept for y 6x 1 are 6 and 1 b 6 and 1 b c 4 d 18 Points E 1 9 and F 2 3 are on a line What is the slope of the line c 4 6 and 1 6 and 1 d 4

Multiple Choice Knowledge Understanding 20 Identify the choice that best completes the statement or answers the question 1 Which one of the following graphs represents the equation y 2 x 1 1 VA YA a C b A N 4 2 0 2 4 VA 4 2 0 d 41 24 ON 4 20 4 44 2 LA 20 4 2

Graphs What is the period of the graph of y 5 sin x 1 2 01 1 2 N T O 2 2x 4

Question Sine Graphs What is the amplitude of the graph y sin 2x 6 3 01 2 3 6

K Among fatal plane crashes that occurred during the past 55 years 138 were due to pilot error 68 were due to other human error 113 were due to weather 459 were due to mechanical problems and 556 were due to sabotage Construct the relative frequency distribution What is the most serious threat to aviation safety and can anything be done about it Complete the relative frequency distribution below Relative Cause Frequency Pilot error Other human error Weather Mechanical problems Sabotage Round to one decimal place as needed