Math - Others Questions

A board game uses the shown to the right Two cards are selected 14 at random from this deck Determine the probability that neither card shows a 1 or a 4 both with and without replacement 12 N R 3 23 R 4 10 5 2 3 4 5 2 3 4 5 Determine the probability that neither card shows a 1 or a 4 with replacement Type an integer or a simplified fraction

bability of selecting a bird or an even number is ninteger or a simplified fraction a 7 X P 3 30 2 37 12 2 37

board game uses the deck of 20 cards own to the right Two cards are selected at 1 ndom from this deck Calculate the obability that both cards selected have a both with and without replacement 2 3 X3 4 5 1 2 3 4 5 X 5 2 45 LI wo cards are to be selected with replacement Determine the probability that both cards selected have a one on integer or a simplified fraction

K If P A or B 0 8 P A 0 4 and P A and B 0 15 find F P B Simplify your answer Type an integer or a decimal

the blank ability problems that require obtaining a favorable outcome in each of the given events are mability problems that require obtaining a favorable outcome in each of the given events are probability problems probability pro

P A and B Simplify your answer Type an integer or a decimal

Experiments done without replacement will result in

or two events A and B if the occurrence of either event in no way affects the probability of the occurrence of the other event then the two events are considered to be GILD or two events A and B if the occurrence of either event in no way affects the probability of the occurrence of the other event then the two events are considered to be events ev

indicated probability nd B 0 4 P A 0 6 and 5 find P A or B P A or B Simplify your a

Experiments done with replacement will result in Experiments done with replacement will result in events events

ne formula for finding the probability of event A or event B is P A or B

obability problems that contain the words and or or are considered obability problems that contain the words and or or are considered probability problems probability pro

Extra Credit A chemist has 14 quarts of a solution that has 24 acid and another solution which has 18 acid How much of the second solution should he use to end up with a solution that has 20 acid A

Annuity payments Calvin Johnson has a 4 500 debt balance on his Visa card that charges 12 9 percent APR compounded monthly In 2009 Calvin s minimum monthly payment is 2 percent of his debt balance which is 90 How many months round up will it take Calvin Johnson to pay off his credit card if he pays the current minimum payment of 90 at the end of each month In 2010 as the result of a federal mandate the minimum monthly payment on credit cards rose to 3 percent If Calvin made monthly payments of 135 at the end of each month how long would it take to pay off his credit card a If Calvin made monthly payments of 90 at the end of each month how long would it take to pay off his credit card months Round up to the nearest unit b If Calvin made monthly payments of 135 at the end of each month how long would it take to pay off his credit card months Round up to the nearest unit GEOED

You have taken a loan of 75 000 00 for 23 years at 5 8 compounded quarterly Fill in the table below Round all answers to 2 decimal places Payment number Payment amount Principal Amount Interest 0 1 N DL S S Balance 75 000 00

Saving for retirement future value of an annuity Selma and Patty Bouvier are twins and both work at the Springfield DMV Selma and Patty Bouvier decide to save for retirement which is 35 years away They ll both receive an annual return of 7 percent on the nvestment over the next 35 years Selma invests 2 000 per year at the end of each year only for the first 10 years of the 35 year period for a total of 20 000 saved Patty doesn t start saving for 10 years and then saves 2 000 per year at the end of each year for remaining 25 years for a total of 50 000 saved How much will each of them have when they retire a How much will Selma have when she retires Round to the nearest cent b How much will Patty have when she retires Round to the nearest cent This question 2 point s possible REED

This question 2 point s possible Comprehensive Problem Suppose that you are in the fall of your senior year and are faced with the choice of either getting a job when you graduate or going to law school Of course your choice is not purely financial However to make an informed decision you would to know the financial implications of the two alternatives Let s assume that your alternatives are as follows If you take the get a job route you expect to start off with a salary of 45 000 per year There is no way to predict what will happen in the future your best guess is that your salary will grow at 5 percent per year until you retire in 43 years As a law student you will be payin 25 000 per year tuition for each of the 3 years you are in graduate school However you can then expect a job with a starting salary of 80 000 per year Moreover you expect your salary to grow by 9 percent per year until you retire 36 years later Clearly your total expected lifetime salary will be higher if you become a lawyer However the additional future salary is not free You will be paying 25 000 in tuition at the beginning of each of the 3 years of law school In addition you will be giving up a little more than 141 000 in lost income over the three years of law school 45 000 the first year 47 250 the second year and 49 613 the third year a To start your analysis of whether to go to law school calculate the present value of the future earnings that you will realize by going directly to work assume a discount rate of 10 percent b What is the present value today of your future earnings if you decide to attend law school assuming a discount rate of 10 percent Remember that you will be in law school for 3 years before you start to work as a lawyer Hint assume that you are paid at the end of eac year so that your first salary payment if you decide to go to law school occurs 4 years from now c If you pay your law school tuition at the beginning of each year what is the present value of your tuition assuming a discount rate of 10 percent a What is the present value of the future earnings that you will realize by going directly to work assuming a discount rate of 10 percent Round to the nearest cent b What is the present value today of your future earnings if you decide to attend law school assuming a discount rate of 10 percent Round to the nearest cent CITY Submit qu c If you pay your law school tuition at the beginning of each year what is the present value of your tuition assuming a discount rate of 10 percent Round to the nearest cent

This question 2 point s possible Submit quiz Comprehensive problem Over the past few years Microsoft founder Bill Gates net worth has fluctuated between 20 billion and 130 billion In early 2006 it was about 26 billion after he reduced his stake in Microsoft from 21 percent to around 14 percent by moving billions into his charitable foundation Let s see what Bill Gates can do with his money in the following problems GIOCCE a Manhattan s native tribe sold Manhattan Island to Peter Minuit for 24 in 1626 Now 387 years later in 2013 Bill Gates wants to buy the island from the current natives How much would Bill have to pay for Manhattan if the current natives want a 6 percent annual return on the original 24 purchase price b Bill Gates decides to pass on Manhattan and instead plans to buy the city of Seattle Washington for 60 billion in 10 years How much would Bill have to invest today at 9 percent compounded annually in order to purchase Seattle in 10 years c Now assume Bill Gates only wants to invest half his net worth today 13 billion in order to buy Seattle for 60 billion in 10 years What annual rate of return would he have to earn in order to complete his purchase in 10 years d Instead of buying and running large cities Bill Gates is considering quitting the rigors of the business world and retiring to work on his golf game To fund his retirement Bill would invest his 20 billion fortune in safe investments with an expected annual rate of return of 8 percent He also wants to make 40 equal annual withdrawals from this retirement fund beginning a year from today running his retirement fund to 0 at the end of 40 years How much can his annual withdrawal be in this case a The amount Bill would have to pay for Manhattan if the current natives wanted a 6 percent annual return on the original 24 purchase price after 387 years is billion Round to two decimal places b The amount Bill would have to invest at 9 percent compounded annually in order to purchase Seattle for 60 billion in 10 years is S billion Round to two decimal places c If Bill Gates only wants to invest half his net worth today 13 billion in order to buy Seattle for 60 billion in 10 years the annual rate of return he would have to earn in order to complete his purchase in 10 years is Round to two decimal places d If Bill invests his 20 billion fortune in safe investments with an expected annual rate of return of 8 percent and he also wants to make 40 equal annual withdrawals from this retirement fund beginning a year from today the amount of his annual withdrawal in this case would be billion per year Round to two decimal places

all orders that used Paypal all orders under 100 all orders that were over 100 and used a credit card Click the icon to view the sales transactions East West North West South West West West South South East North West West East West Transactions data use Excel s filtering capability to extract Paypal Credit Credit Paypal Credit Paypal Credit Paypal Paypal Paypal Credit Paypal Credit Paypal Paypal Paypal Web Web Web Email Web Email Web Web Web Email Web Web Web Web Web Web r Book Book DVD Book DVD DVD Book DVD DVD Book DVD DVD Book DVD DVD Book Sale Transactions Region East West North West South West East West West South South East North East West West East West Payment Source Paypal Web Credit Web Credit Web Email Web Email Web Web Web Web Email Web Web Web Web Web Paypal Credit Paypal Credit Credit Paypal Paypal Paypal Credit Paypal Credit Credit Paypal Paypal Paypal Web Web Amount 20 43 17 19 24 54 24 94 14 79 18 13 184 18 23 24 17 66 24 55 24 86 21 97 20 24 150 06 20 21 22 76 19 66 21 88 Product Book Book DVD Book DVD DVD Book Book DVD DVD Book DVD DVD DVD Book DVD DVD Book 10

This question 2 point s possible Present value of complex cash flows You have an opportunity to make an investment that will pay 200 at the end of the first year 300 at the end of the second year 200 at the end of the third year 400 at the end of the fourth year and 300 at the end of the fifth year a Find the present value if the interest rate is 8 percent Hint You can simply bring each cash flow back to the present and then add them up Another way to work this problem is to either use the NPV function in Excel or to use your CF key on a financial calculator but you ll want to check your calculator s manual before you use this key Keep in mind that with the NPV function in Excel there is no initial outlay That is all this function does is bring all the future cash flows back to the present With a financial calculator you should keep in mind that CF is the initial outlay or cash flow at time 0 and because there is no cash flow at time 0 CF 0 b What would happen to the present value of this stream of cash flows if the interest rate were zero percent a What is the present value of the investment if the interest rate is 8 percent Round to the nearest cent b What is the present value of the investment if the interest rate is zero percent Round to the nearest dollar Submit quiz

resent value of complex cash flows How much do you have to deposit today so that beginning 11 years from now you can withdraw 15 000 a year for the next 8 years periods 11 through 18 plus an additional amount of 30 000 in the last year period 18 Assume a erest rate of 8 percent he amount of money you have to deposit today is Round to the nearest cent This question 2 point s possible GELEB

Question 20 of 20 a If the annual discount rate is 11 percent the present value of the annuity due is S b If the annual discount rate is 16 percent the present value of the annuity due is S Present value of an annuity due Determine the present value of an annuity due of 1 000 per year for 25 years discounted back to the present at an annual rate of 11 percent What would be the present value of this annuity due if it were discou percent Round to the nearest cent Round to the nearest cent This quiz 40 point s possible This question 2 point s possible GEXED G

Recently a certain bank offered a 5 year CD that earns 2 07 compounded continuous Use the given information to answer the questions a If 10 000 is invested in this CD how much will it be worth in 5 years approximately Round to the nearest cent b How long will it take for the account to be worth 35 000 approximately years Round to two decimal places as needed

a How much must you deposit annually to accumulate this amount Round to the nearest cent b If you decide to make a large lump sum deposit today instead of the annual deposits how large should the lump sum deposit be Round to the nearest cent c If you deposit 15 000 received at the end of five years in the bank what will the amount grow to by the end of year 16 S Round to the nearest cent Comprehensive problem You would like to have 56 000 in 16 years To accumulate this amount you plan to deposit an equal sum in the bank each year that will earn 9 percent interest compounded annually Your first payment will be made at the end of the ye a How much must you deposit annually to accumulate this amount b If you decide to make a large lump sum deposit today instead of the annual deposits how large should this lump sum deposit be Assume you can earn 9 percent on this deposit c At the end of five years you will receive 15 000 and deposit this in the bank toward your goal of 56 000 at the end of year 16 In addition to the lump sum deposit how much must you deposit in equal annual amounts beginning in year 1 to reach your goal A assume you can earn 9 percent on your deposits In addition to the lump sum deposit how much must you deposit in equal annual amounts beginning in year 1 to reach your goal Round to the nearest cent This question 2 point s possible BLOOD Q Sub

Led to Checkpoint 6 1 Future value of an annuity Imagine that Homer Simpson actually invested the 120 000 he earned providing Mr Burns entertainment 7 years ago at 8 percent annual interest and that he starts investing an additional 1 900 a year today and eginning of each year for 20 years at the same 8 percent annual rate How much money will Homer have 20 years from today amount of money Homer will have 20 years from now is S Round to the nearest cent GILB

he following graph of g x Write a formula for g x that describes the transformations performed on the basic function wer S 1012 59 13 101 Enable Zoom Pan

An outboard motor has an initial price of 1 250 A service contract costs 300 for the first year and increases 130 per year thereafter The total cost of the outboard motor in dollars after n years is given by C n 1 250 250n 50n where n 1 Complete parts A through C A Write an expression for the average cost per year C n for n years C n B Graph the average cost function found in part A Choose the correct graph below OB OA Ay 4 500 0 0 n 20 G Ay 4 500 0 0 n 20 O C 4 500 Ay 0 n 20 OD 4 500 Ay 0 0 C When is the average cost per year minimum This time is frequently referred to as the replacement time for this piece of equipment The average cost per year is minimum after years n 20 LV

This question 2 point s possible Present value of a growing perpetuity What is the present value of a perpetual stream of cash flows that pays 10 000 at the end of year one and then grows at a rate of 4 per year indefinitely The rate of interest used to discount the cash flows is 12 The present value of the growing perpetuity is Round to the nearest cent GCCCB

Evaluate f 3 where f x is the piecewise function graphed below f 3 2

Add 9900000000 and 299000000using only Egyptian notation Write your answer as simply as possible Choose the correct sum below OA 9999200000 OB 9999990000 O C 999920000 OD 999990000

Use the histogram below to answer the questions Annual Car Insurance Premiums for Students Number of students 06 650 854 803 701 752 905 Price 625 675 676 726 727 777 778 828 829 879 880 930 956 1007 Second class 676 726 c How many students have an annual car insurance premium in the class with a class mark of 752 There are 7 students who have an annual car insurance premium in the class with a class mark of 75 d What is the class mark of the modal class The class mark of the modal class is 803 e Construct a frequency distribution from this histogram Number of Students 78 GOOD 6 2

formula to determine the periodic deposit b How much of the financial goal comes from deposits and how much comes from interest Periodic Deposit at the end of each year 7 compounded annually Click the icon to view some finance formulas Rate KIDD Time 18 years Financial Goal 160 000 a The periodic deposit is Do not round until the final answer Then round up to the nearest dollar as needed

Use the accompanying frequency polygon to answer the following questions a How many people sent five e mail messages b How many people sent six or fewer e mail messages c How many people were included in the survey d Construct a frequency distribution from the frequency polygon e Construct a histogram from the frequency distribution in part d umber of Peopl e Construct a histogram from the frequency distribution in part d OA OB OPEYNO 6 7 Number of E mail Messages Sent 8 9 10 Number of People Number of E mail Messages Sent SEDINO CITR Number of People Number of E mail Messages Sent per Day M Number of Messages Der Type whole numbers O C Number of People OPOTNO Number of E mail Messages Sent of MT 10 odb C

a How many homes were included in the survey b In how many homes were five televisions observed c What is the modal class d How many televisions were observed e Construct a frequency distribution from this histogram There were 3 homes where five televisions were observed Type a whole number The modal class is 2 Type a whole number 1 There were 85 observed televisions Type a whole number Construct a frequency distribution from this histogram Televisions per home Number of Homes 0 1 00 III COTTE Number of Homes 565476 Televisions per Home Number of Televisions

F Use the accompanying frequency polygon to answer the following questions a How many people sent five e mail messages b How many people sent six or fewer e mail messages c How many people were included in the survey d Construct a frequency distribution from the frequency polygon e Construct a histogram from the frequency distribution in part d a There were 6 people who sent five e mail messages Type a whole number b There were 17 people who sent six or fewer e mail messages Type a whole number c There were people included in the survey Type a whole number CELLD Number of People Number of E mail Messages Sent per Day Number of Messages Sert 88 Q C

graph to the right the percentage of that cost for tuition fees room board and computer costs Determine in dollars for each category of tuition and fees is 4910 90 to the nearest cent as needed of room is 5416 50 o the nearest cent as needed of board is o the nearest cent as needed to Abend a Pub Tution Room Board Compu DE

Express the following equation as a function y f x 3xy 4y 1

Illustrate the addition or subtraction using Place Value Cards 4 94 99 5 74 258 6 821 230 662

traveled 12 102 At a given instant the jet plane has a speed of 400 ft s and an acceleration of 70 ft s acting in the direction shown Determine the rate of increase in the plane s speed and the radius of curvature p of the path 400 ft s 60 a 70 ft s P

You deposit 3000 in an account earning 3 interest compounded monthly How much will you have in the account in 5 years

Extra Practice Add or Subtract using your Units Strips and Mats then draw a diagram showing the steps 22 1 19 52 2 28 400

Cost to attend a public university in a recent year is 14 444 The circle graph to the right is the percentage of that cost for tuition fees room board and computer costs Determine most in dollars for each category cost of tuition and fees is nd to the nearest cent as needed COE Cost to Attend a Publ Tution Room Board Compu 000

12 101 A car moves along a circular track of radius 250 ft such that its speed for a short period of time 0 t 4 s is v 3 t t ft s where t is in seconds Determine the magnitude of its acceleration when t 3 s How far has it traveled in t 3 s

Marying table shows the ticket sales of the 15 highest grossing movies of all time adjusted for inflation in millions of dollars Construct a frequency distribution with a first class of 877 996 p Construct a histogram Construct a frequency polygon Construct a frequency distribution with a first class of 877 996 Sales million 5 Number of Movies 877 996 OND BOC DE em Cam 1785 1156 943 Ticket sales in millions of dollars 1233 982 902 1629 1136 912 1235 1117 906

8 67 32 9 237 96 Use the Instructional Algorithm for addition or subtraction to perform the operation 10 15 44 11 54 958 12 592 426 13 719 493 14 56 38 15 664 26

Number of students m 2 2 Annual Car Insurance Premiums for Students 650 701 752 803 854 905 956 1007 a How many students were surveyed There were students who were surveyed

na frequency distribution another name for the midpoint of a class is the class na frequency distribution another name for the midpoint of a class is the class

as that are often used to compare parts of one or more components of the whole to the whole are called pie charts or

graph with observed values on its horizontal scale and frequencies on its vertical scale and that uses bars to indicate frequency is called a graph with observed values on its horizontal scale and frequencies on its vertical scale and that uses bars to indicate frequency is called a

frequency distribution the class with the greatest frequency is call the