Linear Algebra Questions and Answers

What type of study uses a sample to draw a conclusion about the population that the sample was drawn from Designed experminet Analytical study Observational study Enumerative study

The linear model relating hurricanes wind speed to their central pressure is given as Max Wind speed 955 27 0 897x Central Pressure Use this model to make a prediction Hurricane Katrina had a central pressure measured at 940 millibars a What is the predicted Max Wind speed b Given the Katrina s actual wind speed of 110 knots what is the difference between the actual Wind speed and the predicted windspeed a 112 09 b 2 09 Oa 0 897 b 955 27 Oa 110 09 b 20 Oa 135 b 20 03

Given the demand curve p 38 q2 and the supply curve p 6 q2 find the producer surplus when the market is in equilibrium Round your answer to 3 decimal places Part 1 The producer surplus is the total amount gained by producers by selling at the current price rather than the price they would have been willing to accept It is the area between the supply curve and the horizontal line p To begin our problem we need to find the equilibrium price p and quantity q In equilibrium supply demand So we have to solve the equation for q This will give us the value for q Og 4 22 38 q 6 q

Q8 Suppose f z u x y iv x y is an analytic function where u x y 4xy 4x y x is a harmonic function no need to prove Answer the following questions while clearly mentioning any theorems and or properties that you use to obtain the answers 15pts a Find a harmonic conjugate v x y of u x y b Find f z satisfying f 1 i 1 4i c Calculate f zo for zo 4e 4 60 2 2 3i

Triangle ABC is a scaled copy of t longest side of ABC Side DE measures 8 cm and is the fo 1 Triangle ABC is a scaled copy of triangle DEF with what scale fader 2 Triangle DEF is a scaled copy of triangle ABC with what scale factor 5 The diagram shows two intersecting lines Find the missing angle measures 15 102 De B

c 7 x x d x 3x 11

A metal warehouse whose dimensions are shown below feeas paint The front and back of the warehouse each have z rolup doors measuring zo i by 31 ft each The side of the warehouse facing the parking lot has an entry door measuring 54 in by 80 in The other side of the warehouse has no window or door Use the given information to answer the questions Each tab shows a different view of the warehouse a Assuming the roof and doors require no paint what is the area in square feet that needs paint Do not round any intermediate computations and give your answer as a whole number 0 2 0 ft b The paint to be used is sold in cans Each can contains enough paint to cover 640 ft Assume there is no paint yet and partial cans cannot be bought How many cans will need to be bought in order to paint the warehouse cans c What is the total cost of the paint needed for the warehouse if each can costs 38 50 0 Conversion facts for length 1 foot ft 12 inches in 1 yard yd 3 feet ft 1 yard yd 36 inches in Front right view Back left view K 35 ft

Find an equation for the line that passes through the point P 0 2 and has a slope 3

A custom guitar shop sells two types of guitars electric and acoustic The creation process of each guitar is broken into three parts building the base guitar applying the finish paint and adding accessories The time requirements in days and the total days available for each phase of the creation process are shown in the below Electric Acoustic Total days Base guitar creation 6 4 564 Applying the Adding finish paint accessories 2 2 202 5 340 If they profit 900 from each electric guitar and 700 from each acoustic guitar how many of each guitar type should be made to maximize the shop s profit What is the shop s maximum profit in dollars The maximum profit is when X X electric guitars and Xacoustic guitars are made Determine if the shop has any leftover time in days for each task entering 0 if no time is leftover

Which of the three main types of studies is shown in each example below Explain your reasoning Study 1 A fund manager studies whether the values of her clients investments increase decrease or stay the same based on applying her normal investment strategy or using a more aggressive strategy Study 2 An investment company polls randomly selected business school students about which industry they would most likely invest their money in Study 3 A firm is considering a new website design An intern determines how long each visitor stays on the site using the new design and then using the old design

Public Domain OA A OB Oc B Business Cycle C Which part of the cycle represents a period of contraction Assessments E

The Arctic Lion s Mane Jellyfish is one of the largest known animals Its tentacles can be as long as 120 feet Find how this length compares to your height Round your height to the nearest foot 120 feet is times as long as feet

Question 16 A random variable has the probability density TOR 2 0 1 5 1 0 0 5 0 0 0 0 0 5 X What is the mean value of a variable with this distribution B 0 500 C 0 667 A 0 25 1 0 D 1 00 1 5

1 Find the Fourier transform of following 15 points a s t 5 a real positive b e atu t c e 1 j2 u t Where u t is unit step signal defined as u t 1 for 0 and u t 0 for

9 1 point When simplified and written with positive exponents the expression 27x x 125x becomes d 5 an b sa 5 WIT 9 1 WIT

4 The graph of y tan x is stretched verticaly by a factor of 4 and compressed horizontally to have a period of What is the equation of the new graph

an wants to measure the height of a nearby tower He places a 9 ft pole in the shadow of the tower so that the shadow of the pole is exactly covered by shadow of the tower The total length of the tower s shadow is 175 ft and the pole casts a shadow that is 5 75 ft long How tall is the tower Round your wer to the nearest foot The figure is not drawn to scale Shadow of pole Pole Shadow of tower Sun Tower 0 ft X S

Eyan wants to measure the width of a river He marks off two right triangles as shown in the figure The base of the larger triangle has a length of 57 m and he base of the smaller triangle has a length of 34 m The height of the smaller triangle is 17 9 m How wide is the river Round your answer to the nearest meter The figure is not drawn to scale 17 9 m U River 34 m 57 m m X

Accounting equation The total assets and total liabilities in millions of ABC Corporation and XYZ Corporation follow Assets ABC XYZ 19 947 19 349 8 777 9 288 Liabilities Determine the stockholders equity of each company ABC Corporation stockholders equity XYZ Corporation stockholders equity million million

Exercise 6 6 5 First prove that all degree at most 2 functions P 2 f x ax bx cla b c R is a vector space Then find a basis for this vector space Next consider P to be the set of all polynomials of all degrees can you imagine basis set If you can you have found your first infinite dimensional basis

An Environmental Code of Ethics 1 Use knowledge and skill for the enhancement and protection of the environment 2 Hold paramount the health safety and welfare of the environment 3 Perform services only in areas of personal expertise 4 Be honest and impartial in serving the public your employers your clients and the environment 5 Issue public statements only in an objective and truthful manner

5 5 Vertical Intercept Horizontal Intercept 25 25 y Vertical Intercept x 5 X 25 5 5 Vertical Intercept Horizontal Intercept 100 100 y 100 Vertical Intercept Horizontal Intercent 5 x 100 X q

2 0 t0s te R is a subspace of R by using only the definit 2 subspace Then explain why we know this is true by some theorem we discussed Exercise 6 6 3 Show that the plane P s

Increasing the down payment on a mortgage reduces both the size of the monthly payments and the total interest paid Calculate a the reduction in the monthly payment by increasing the down payment by the amount specified and b the amount saved on interest over the life of the loan Assume the mortgage is for 30 years and use the amortization table to find the monthly payments Increase in Down payment 15 000 Click the icon to view a table of monthly payments on a 1 000 loan Amount of Loan Interest Rate Down Payment 162 000 38 000 5 a The monthly payment will be reduced by 80 55 when the down payment is increased by 15 000 Round to the nearest cent as needed b Increasing the down payment by 15 000 saved Round to the nearest cent as needed CIL on interest over the life of the loan Monthly Payment on a 1 000 loan Annual Interest Rate 4 5 6 8 10 Number of Years for the Loan 4 20 10 22 58 10 12 23 03 10 61 6 06 6 60 11 10 7 16 12 13 8 36 13 22 9 65 3 29 53 29 97 30 42 23 49 31 34 24 41 32 27 25 36 30 4 77 5 37 6 00 7 34 8 78 X

Complete parts a and b below a If 10 000 is invested at 5 compounded annually find the future value in 10 years Simplify your answer Round to the nearest cent as needed www

Let S 1 2 8 Also let A and B be the following sets Compute the following A B Gils A a b c E SXSXS a b c are all different B a b c ESXSXS ab b c

Simplify the matrix expression as much as possible A C B I AB

ve 2xy 1 dx 2x y dy 0

The energy used in a 100 kilometres car trip is about 15 kWh Assuming that the energy content of the fuel is 10 kWh litre and the efficiency of the engine is 33 how many litres of fuel are needed for a 100 kilometres car trip Choose the best alternative 5 litres 7 5 litres 10 litres O 15 litres

4 Find the determinant of the matrix A 2 2 3 1 0 1 4 5 1 4 5 49 O None of the other options is correct 51

2 x 6 5x b

Q1 Shannon s Brewery currently boasts a customer base of 1 750 customers that frequent the brewhouse on average twice per month and spend 31 per visit Shannon s current variable cost of goods sold is 50 of sales The customer retention rate per month is 0 75 based on data collected from its website and an analysis of credit card receipts Its current cost of capital for borrowing and investing is about 12 per year or 1 per month What is Shannon s approximate CLV for its average customer Compute your answer to the nearest penny

1 to 109 1768 Section S 37 55 41 92 92 Lines a b c and d intersect as shown Part A Which lines are parallel Use a theorem or property to justify your answer Part B Find the values of x y and z Explain how you found aggh

a A cyclist travels down a hill in a straight line with constant acceleration She starts with speed 1 5 m s and finishes with speed 9 5 m s The length of the hill is 22 m Show your working i Find the time taken ii Find the acceleration of the cyclist

f A die is rolled twice Let all the elementary events in 2 i j i j 1 2 6 be assigned the same probability Let A be the event that the first throw shows a number 2 and B the event that the second throw shows at least 5 Find An B and P AUB Explain your answer

Using matrices and determinants solve the following system if possible Show your working If not possible show why not x 2y 3z 1 f x 2x z 0 3x 4y 4z 2

e If Show that A A 2 4 7 A 12 2

The Sun River beverage company is a regional producer of teas exotic juices and energy drinks With an interest in healthier lifestyles there has been an increase in demand for its sugar free formulation The final packing operation requires 13 tasks Sun River bottles Its sugar free product 5 hours a day 5 days a week Each week there is a demand for 2 500 bottles of this product TASK ANASANA 6 9 10 12 13 PERFORMANCE TIME TASK MUST MINUTES FOLLOW 0 2 0 2 0 3 0 1 0 2 0 2 0 3 0 1 0 1 0 1 0 2 0 1 INNNAT 96 3 4 5 7 18 11 12 Using the above data solve the assembly line balancing problem and calculate the efficiency of your solution Use the longest task time for your decision criteria Enter your answer as a percentage rounded to 1 decimal place

20 2x x 2

Use the graph to find all the solutions of x x 3 0 ya 10 X x 2 x 1 O SE

Solve for X X x X 5

9 9x 5 7x 547 9 54 2 X 74 15x 21 7x 13 6x 32 14x 7 110x 69 355 18 8x 9 74 7 9 3x 18 6x 4 32 20 7x 329 11 999 172 10

The Pappas family has two cats Zeus and Athena Together they weigh nine pounds Zeus weighs 5 pounds less than Athena How much does Athena weigh Write an algebraic equation that represents the situation Use a for your variable Athena

Kyle paid 984 for a set containing a TV and a TV stand The salesperson informed her that separately the TV was worth 1 1 2 times as much as the TV stand How much would each item cost separately TV Round to the nearest cent Price Price

Simplify the algebraic expression 6x 4 22x

Sparkle Cleaners uses of a jug of window cleaner in 3 weeks How much window cleaner do they use in 1 week Simplify your answer and write it as a proper fraction mixed number or whole number

Price dollars per arrow 150 28 2288 228 140 1 30 120 110 100 90 80 Using the point plotting tool interpret the demand schedule to plot five points on Oliver and Malcolm s combined demand curve Then use the straight line tool to draw the demand curve that connects them Use a single line not multiple segments To refer to the graphing tutorial for this question type please click here 50 588 88 40 30 10 0 8 arrow 30 OF g 140 90 60 30 0 AND 100 week 0 20 40 60 80 66 85 8 Market demand arrows per week arrows per week 0 30 40 50 60

The Hawks played the Elks in a basketball game Based on the information to the right complete the scoreboard showing the number of points scored by each team during each quarter and the final score of the game Fill in the table below using the information given Quarters 3 Teams 1 Hawks 2 4 Final Score a The Hawks scored 15 points in the first quarter b The Hawks were behind by 2 points at the end of the first quarter c The Elks scored 8 more points in the second quarter than they did in the first quarter d The Hawks scored 5 fewer points than the Elks in the second e The Elks outscored the Hawks by 3 points in the fourth quarter f The Hawks scored a total of 115 points in the game quarter g The Hawks scored twice as many points in the third quarter as the Elks did in the first quarter h The Elks scored as many points in the third quarter as the Hawks did in the firs two quarters combined

3 1 point Find a parametric representation for the intersection of the surface x 4y 4 with the plane 2y z 4

Identify the attractors and state what type of attractor If no attractor state corresponding equilibrium or oscillation type Draw an approximate time series graph for one of the variables ii 0 5 V 0 5 0 5 0 5 X