Math - Others Questions

he probability of an event that cannot occur is

ch outcome of an experiment has the same chance of occurring as any other outcome the outcomes are ch outcome of an experiment has the same chance of occurring as any other outcome the outcomes are likely outcomes likely outcomes

he correct choice that completes the sentence below ity determined through a study of the possible outcomes that can occur for a given experiment is called

with an appropriate word phrase or symbol s bability determined by the relative frequency of occurrence of an event or actual observations of an experiment is called GIETS bability determined by the relative frequency of occurrence of an event or actual observations of an experiment is called probability probab

The possible results of an experiment are ca

I in the blank with an appropriate word phrase or symbol s subcollection of the outcomes of an experiment is called a n subcollection of the outcomes of an experiment is called a n

N N No No Cape Y Yes Tie Y Yes No Smoke Yes Bad Good Good Bad Based on this decision tree in what class does Batgirl belong Y 181

The first matrix is 1 x 2 and the second matrix is 2 x 2 The product of these two matrices is a Step 2 Multiply the row of the 1 x 2 matrix with the first column of the 2 x 2 matrix 5 8 40 7 9 63 40 63 Step 3 Multiply the row of the 1 x 2 matrix with the second column of the 2 x 2 matrix 5 10 50 7 11 77 63 50 Step 4 Construct the product matrix 40 6 77 50 77 X 2 matrix

P x 300x 3 300 Step 4 P 343 300 343 99600 343 99 600 That is if 343 items are produced and sold the total profit is 99600 c How many items must be sold to avoid losing money 3 300 The manufacturer makes money if the profit is positive x 3 3 300 0 300x 99 600 So to avoid losing money the manufacturer must produce and sell the break even quantity which is the number of items that results in a profit equal to 0 We can find the break even quantity by solving the equation P x positive and loses money if the profit is negative Step 5 To find the break even quantity substitute 300x 3 300 for P x in the equation P x 0 and solve for x Since the equation is linear isolate x on the left side of the equation P x 0 negative When the manufacturer breaks even the profit is

Multiply the matrices 2 245 6 7 8

Tutorial Exercise Multiply the matrices 8 10 57 91 11 Step 1 xir x The product of these two matrices is a matrix

A system of linear equations and a reduced matrix for the system are given 2 x 4y 2z 2 2x y 2 x 4y 2z 3 1 0 01 Naa 9 0 0 000 1 a Use the reduced matrix to find the general solution of the system if one exists If there is no solution enter NO SOLUTION If there are infinitely many solutions expre terms of z as in Example 3 x y z b If multiple solutions exist find two specific solutions Enter your answers as a comma separated list of ordered triples If there is no solution enter NO SOLUTION x y z

Tutorial Exercise Determine whether the function s vertex is a maximum point or a minimum point and find the coordinates of this point Find the zeros if any exist and sketch the graph of the function y x Step 1 First write the function in general form y ax bx c Since a y 0 the parabola opens downward O The vertex is a maximum point The vertex is a minimum point downward So is the vertex a maximum or a minimum able to come back to Step 2 The coordinates of the vertex of a quadratic function of the form y ax2 bx care Use the values of a and b to determine the x coordinate of the vertex

Use the indicated row operation to change matrix A where 1 5 1 9 A 6 1 5 7 55 Add 7 times row 1 to row 3 of matrix A and place the result in row 3 to get 0 in row 3 column

Tutorial Exercise An augmented matrix for a system of linear equations in x y and z is given Find the solution of the system 1 1 3 3 0 4 19 0 360 Step 1 The solution of the system can be found using the Gauss Jordan elimination Recall that when using Gauss Jordan elimination the end goal is to obtain an identity matrix for the coefficient matrix by using elementary row operations Notice column 1 already has a 1 and then 2 zeros So next we focus on obtaining a 1 in row 2 column 2 This can be achieved by adding row 3 to row 2 and putting the result in row 2 1 1 3 37 1 1 3 3 0 4 19 0 0 3 60 0 3

Multiply the matrices 57 68 24

Part 4 The following is a balance sheet of the Gamma bank in millions of dollars Assets Required reserves 8 Excess reserves 17 Treasury bills 30 Commercial Loans 37 Mortgage 8 X Liabilities Checkable Deposits 80 CB Loans 13 Common Stock 5 Bad debt provision 2 1 What is the non risk based capital requirement of Gamma Bank Does it comply with Basel 3 standard 5 points 2 What is the Tier 1 capital ratio 5 points 3 The bank makes a loan commitment of 15 million to a commercial customer and discovers 1 million bad loans that should write off from the balance sheet Calculate the bank s Tier 1 capital ratio before and after the agreement 5 points Note Show all the details of balance sheet analysis 4 In what capitalization capital risk category would the bank be placed before and after the operation and why 5 points

2 36 Determine the reactions at the supports A and B Assume the support at B is a roller C is a fixed connected joint 15 k 4 ft 10 k 4 ft C 7 k ft 10 ft B

8 Use the quadratic formula to solve each of the following for x Use two decimal places where necessary K 5 3x 5x 1 0

solve the following homogeneous systems of differential equations Y 10 10 9 4 2 Y

15 Two boats at location P and Q are being tracked by a satellite located at R Using the information in the diagram find the distance between the two boats PQ to the nearest kilometre A 5 P 10km 107 15km

14 Ted hit a baseball The height h of the ball above ground in metres at any time t in seconds is given by the equation h 5t 20t 1 Complete the square and express h in the form h a t p q Then use your answer to answer the questions below A 10 a Determine the maximum height reached by the ball b How long does it take the ball to reach its maximum height c From what height above the ground did Ted hit the ball

17 Determine an equation if the given base graph has been transformed as follows K 6 a y cos x stretched vertically by a factor of 4 translated 60 to the left and 5 units downward b y sinx compressed vertically by a factor of and 5 5 units upward translated 120 to the right

7 For the parabola defined by the quadratic function y 3 x 4 15 determine the following K 5 a Does it have a maximum or minimum value b What is the maximum minimum y value c For what x value does the maximum minimum value occur d What are the co ordinates of the vertex e What is the equation of the axis of symmetry

5 Use exponent laws to simplify 16m 2m n 5n 10mn K 4

10 Frank s parents invested 4000 by opening an account in his name when he was fist born The account paid interest at 5 a compounded semi annually A 3 a How much could Frank withdraw on his sixteenth birthday b How much of the withdrawal is interest

11 A pine tree casts a 31 meter shadow when the angle of elevation from the ground to the top of the tree is 40 Find the height of the pine tree to two decimal places Include a diagram A 4

6 Given the trigonometric function y 3sin x 60 1 Draw a sketch then graph A 5 I I 1 1

ecessar 8 Use the quadratic formula to solve each of the following for x Use two decimal places where neces K 5 3x 5x 1 0

Given g x 5x 4x determine each of the following K 5 g 2 b g x 3

6 Factor and simplify and state restrictions x 9x 18 10xy x 2x 15 5x 25x K 5

2 Rewrite the term w in exponential form K 1 3 Factor fully K 1 x 81

1 Factor each of the following K 3 a x 7x 12 b 3x 14x 8

The adjacency matrix below defines a directed graph with vertices A B C D E F G H 1 Write down the strong connected components as sets of vertices separated by commas and enclosed by braces 2 Give an example of one edge we can add to make it a strong connected graph Hint we recommend drawing the graph on your scrap paper 000 0 1 0 1 0 000 00000 100 0 0 0 000 0 1 01 O O O 1 101 00 O

The following information pertains to the inventory of Parvin Company during Year 2 Beginning Inventory Purchased Purchased 400 units 30 2 000 units 35 600 units 38 January 1 April 1 October 1 During Year 2 Parvin sold 2 700 units of inventory at 90 per unit and incurred 41 500 of operating expenses Parvin currently uses the FIFO method but is considering a change to LIFO All transactions are cash transactions Assume a 30 percent income tax rate Parvin started the period with cash of 75 000 inventory of 12 000 common stock of 50 000 and retained earnings of 37 000 Determine the cash flow from operating activities under FIFO and LIFO Amounts to be deducted should be indicated with minus sign

2 12 Classify each of the frames as statically determinate or indeterminate If indeterminate specify the degree of indeterminacy All internal joints are fixed connected a b c

Amy is taking out a mortgage for 158 000 to buy a new house and is deciding between the offers from two lenders She wants to know which one would be the better deal over the life of the mortgage loan and by how much Answer each part Do not round intermediate computations and round your answers to the nearest cent If necessary refer to the list of financial formulas a A bank has offered her a 15 year mortgage loan at an annual interest rate of 3 4 Find the monthly payment 0 b An online lending company has offered her a 40 year mortgage loan at an annual interest rate of 3 4 Find the monthly payment 0 c Suppose Amy pays the monthly payment each month for the full term Which lender s mortgage loan would have the lowest total amount to pay off and by how much Bank The total amount paid would be less than to the online lending company Online lending company

Sec 2 2 2 5 2 11 Classify each of the structures as statically determinate or indeterminate If indeterminate specify the degree of indeterminacy a b d

m s The total distance traveled before stopping can be I be determined from the use of the fundamental forms Each student is required to work the problem on paper make a graph of the position vs time velocity vs time and the acceleration vs time using the Excel software and individually submit their own work Homework format specified in the Homework Submission Guide First Name or Initial GIVEN FIND SOLUTION Middle Name s or Initial s 1 2 3 Actual Date of your Submission 4 Course Number Homework Submission Due Free Body Diagrams Other Graphical Tools Work should be Neat Date MM DD REQUIRED HOMEWORK FORMAT Homework Submission Instructions Staple papers in upper left corner of the page Repeat title format given above for each page For better problem illustration or solution determination use or draw Diagrams Problem Number Page Number Total Number o Pages

2 4 Solve Prob 2 3 with a 10 ft b 15 fi

Cylinder a Cylinder b Rectangular block c Rectangular block d Rectangular block e 1 cm 1 89 Average 2 20 3 81 3 78 3 62 True density 2 cm Standard deviation 2 59 3 09 Density statistics for five objects Coefficient of variation CV 2 32 2 22 2 12 3 cm N A N A 1 19 1 12 1 09 8 198 13 813 Complete the following table with the statistics for your density calculations Report Table ME 4 Calculation of Density statistics 12 341 11 489 9 561 cm Table view List view Density g cm 1 168

When a cold drink is taken from a refrigerator its temperature is 5 C After 25 minutes in a 20 C room its temperature has increased to 10 C Round your answers to two decimal places a What is the temperature of the drink in C after 35 minutes C b After how many minutes will its temperature reach 17 C min

3 Bob is planning to take a tram to his destination Three different trams run at the same time but they appear to go different speeds One of them reaches its top spe almost immediately while the other two seem to start out slower and then become faster The distance 3 that each tram travels in a given time is represented by the following functions y 2x 1 2 1 y y 22 a If y represents the distance the tram travels what does a represent b On a separate piece of paper make a table of values and or graph each function Describe the shape of each graph and explain what about the function s equation causes it to have this shape c How many intersections are there and where are they How do you know Explain what each intersection represents d Which tram would be best for Bob Explain why e True or False Exponential functions will always eventually grow faster than polynomial functions Explain your answer 6

Mate 8 8 5 compounded continuously Complete parts A and B below Click the icon to view the derivatives of exponential and logarithmic functions A Find the instantaneous rate of change of the amount in the account after 2 year s Round to two decimal places as needed B Find the instantaneous rate of change of the amount in the account at the time the amount is equal to 12 500 Round to two decimal places as needed

Find the linear approximation L x of the function f x 1 x at a 0 L x 1 X Use L x to approximate the numbers 0 9 and 0 99 Round your answers to four decimal places V0 9 0 9334 X 0 99 0 9933 X Use technology to graph f and the tangent line in the same viewing window y 2 2 5 10 15 2 1 y 1

Interpreting Venn diagram cardinalities with 2 sets for a real A college radio station surveyed 410 incoming freshmen to see how many like rap music and how many like classical music The Venn diagram below shows the results Each number gives the number of freshmen who fall into that Venn diagram category All freshmen in the survey Like rap 33 113 Like classical 22 242 a How many of the freshmen like classical music freshmen b How many of the freshmen like rap music or classical music or both freshmen c How many of the freshmen do not like both rap music and classical music freshmen

www awu aleks com alekscgi x ist exe 1o u IgNslla7j8P3H lis SdZFdonGg9pin SETS Interpreting Venn diagram cardinalities with 2 sets for a real Try Again Your answer is incorrect A drug trial had 424 participants A survey was taken to determine how many had nausea as a side effect and how many had anxiety as a side effect The Venn diagram below shows the results Each number gives the number of participants who fall into that Venn diagram category All participants in the survey Had Had anxiety a How many of the participants had nausea 21 participants By again neither nausea nor anxiety Angella 6 S

1 You are going to send a probe to explore a shipwreck in the ocean The probe will not work when the temperature is below 0 5 C The temperature varies inversely with depth at depths greater than 900 meters At a depth of 3700 meters the temperature is 1 2 C a Create an equation to model temperature Which type of equation will you create b What is the constant of variation c If the depth is 5000 meters what is the temperature d If the temperature is 2 7 C what is the depth e How deep can the probe go before it won t work

If A a b c d and B c d e f g then n A U B n a b c d e f g 7 n A 4 n B 5 and n An B n c d 2 Since 7 4 5 2 this suggests that n AUB n A n B n An B Use Venn diagrams to justify thi arbitrary finite sets A and B OA OB O C O D n AUB n AUB n AUB n AUB A A B A A B O O B n AUB B n ANB n ANB n ANB CALE

By using the definition of a subspace determine if the following is a subspace of appropriate R File Preview 21 12 T3 TA ER 321 22 6x4 0 and x3 0