Math - Others Questions

Starting at age 30 you deposit 2000 a year into an IRA account for retirement Treat the yearly deposits into the account as continuous income stream If money in the account earns 6 compounded continuously how much will be in the account 35 years later when you retire at age 65 How much of the final amount is interest What is the value of the IRA when you turn 65 Round to the nearest dollar as needed

Find the consumers surplus and the producers surplus at the equlibrium level for the given price demand and price supply equations Include a graph that identifies the consumers surplus and the producers surplus Round all values to the nearest integer p D x 36 0 06x p S x 11 0 04x The value of x at equilibrium is 250 The value of p at equilibrium is 21 The consumers surplus at equilibrium is 1875 The producers surplus at equilibrium is 4

Starting at age 35 you deposit 2000 a year into an IRA account for retirement Treat the yearly deposits into the account as a continuous income stream If money in the account earns 6 compounded continuously how much will be in the account 30 years later when you retire at age 65 How much of the final amount is interest What is the value of the IRA when you turn 65 Round to the nearest dollar as needed

An investor is presented with a choice of two investments an established furniture store and a new book store Each choice requires the same initial investment and each produces a continuous income stream of 4 compounded continuously The rate of flow of income from the furniture store is f t 14 000 and the rate of flow of income from the book store is expected to be g t 12 000 0 05t Compare the future values of these investments to determine which is the better choice over the next 4 years The future value of the furniture store is Round to the nearest dollar as needed SCOXS

A random variable is defined as a process or variable with a numerical outcome Which of the following are random variables a The amount of snow in inches that will fall next winter in Aspen Co b The job of a randomly picked person that is taking the subway c The number of movies that will be released next week by your local movie theater Oc only a and c Ob and c Ob only O a b and c O a only

For the proprablility distribution table below x x l 0 1 2 3 4 P x 0 1 0 18 0 12 0 14 0 46 0000 Find the mean Round to two decimal places Find the standard deviation Round to three decimal places xP x 00000 x P x 00000

Fill out the black to make the given table below a probability distribution x 0 1 2 3 4 P x 0 04 0 16 0 43

Determine whether this table represents a probability distribution P x X 0 2 2 4 0 18 0 1 0 14 0 86 Yes because P x is 100 O No because P x is not 100 No because x has negative O No because x 0 No because P x has negative

For the proprablility distribution table below P x 0 05 0 1 2 3 X 4 0 1 2 3 4 Find the mean Round to two decimal places 0 08 x 0 2 0 09 0 58 x Find the standard deviation Round to three decimal places xP x x P x

You save 5 000 per year for the 40 years you are working years 1 40 How much can you withdraw in equal amounts for the 35 years you are retired years 41 75 if the interest rate is 12 O 5 714 28 109 584 49 469 140 15

The demand for a new computer game can be modeled by p x 55 6 Inx for 0x800 where p x is the price consumers will pay in dollars and x is the number of games sold in thousands Recall that total revenue is given by R x x p x Complete parts a through c below a Find R x R x 55x 6x In x b Find the marginal revenue R x R x 49 6 In x c How many units will be sold if the price that consumers are willing to pay is 50 The number of units that will be sold is Round to the nearest whole number as needed

Listen Complete the truth table for the given statement by filling in the required columns PAq P T T F TITI F 1 9 T F TF T F P T T F F P 9 T F T F PAq wp F F T T PAq F T T F

Complete the truth table for the given statement by filling in the required columns p q P T T F F LL O 1 9 T FT F FL P T T F LL L p ST T FT L p q p F F T T p q F T T F

30 A park ranger at point A observes a fire in the direction N25 26 E Another ranger at point B 4 miles due east of A sites the same fire at N58 34 W Determine the distance from point B to the fire Round answer to two decimal places 4 08 miles O 3 43 miles O 3 63 miles O 1 73 miles 2 05 miles

An office machine is purchased for 7300 Assume that its salvage value V in dollars depreciates according to a method called double declining balance by 30 each year and is given by V t 7300 0 70 where t is the time in years after purchase a Find V 3 and explain its meaning b Find V 3 and explain its meaning c When will the salvage value of the office machine be half of the purchase price a V 3 to the nearest cent as needed

The demand for a new computer game can be modeled by p x 55 6 In x for 0 x 800 where p x is the price consumers will pay in dollars and x is the number of games sold in thousands Recall that total revenue is given by R x x p x Complete parts a through c below a Find R x R x

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11 8 At present Solartech Skateboards is considering expanding its product line to include gas powered skateboards however it is questionable how well they will be received by skateboarders You expect to be able to sell 10 000 of these products per year for 4 years The gas skateboards would sell for 100 each and have a variable cost of 40 each Regardless of how many you sell the annual fixed costs associated with production would be 160 000 In addition there would be a 1 million initial investment associated with the purchase of new production equipment which will be depreciated evenly over 4 years i e every year 25 or 250 000 is depreciated This project will require a one time initial investment of 50 000 in net working capital and working capital investment will be recovered when the project is shut down Finally assume that the firm s marginal tax rate is 21 percent and the investors require 10 return Questions a Construct Operating Cash Flows b Construct Investment Cash Flows c Calculate the Free Cash Flows d Evaluate the project using NPV and IRR methods

Violent crimes include rape robbery assault and homicide The following is a summary of the violent crime rate violent crimes per 100 000 population for all states of a country in a certain year Complete parts a through d Q 271 8 Q 388 5 Q 529 7 a Provide an interpretation of these results Choose the correct answer below OA 25 of the states have a violent crime rate that is 271 8 crimes per 100 000 population or more 50 of the states have a violent crime rate that is 388 5 crimes per 100 000 population or more 75 of the states have a violent crime rate that is 529 7 crimes per 100 000 population or more O B 25 of the states have a violent crime rate that is 271 8 crimes per 100 000 population or less 50 of the states have a violent crime rate that is 388 5 crimes per 100 000 population or less 75 of the states have a violent crime rate that is 529 7 crimes per 100 000 population or less OC 75 of the states have a violent crime rate that is 271 8 crimes per 100 000 population or less 50 of the states have a violent crime rate that is 388 5 crimes per 100 000 population or less 25 of the states have a violent crime rate that is 529 7 crimes per 100 000 population or less b Determine and interpret the interquartile range The interquartile range is crimes per 100 000 population Type an integer or a decimal Interpret the interquartile range Choose the correct answer below OA The middle 50 of all observations have a range of 116 7 crimes per 100 000 population OB All observations have a range of 257 9 crimes per 100 000 population OC The middle 25 of all observations have a range of 257 9 crimes per 100 000 population OD The middle 50 of all observations have a range of 257 9 crimes per 100 000 population c The violent crime rate in a certain state of the country in that year was 1 679 Would this be an outlier The lower fence is crimes per 100 000 population The upper fence is crimes per 100 000 population Round to two decimal places as needed The violent crime rate in n nortain state of the counter in that varume 1 670 Would this he an outlin

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K The following table shows the number of cell phone subscriptions in a country in billions for selected years x after 2005 2006 1 4 X y 2005 0 5 O C 2007 4 1 2008 7 6 2009 9 1 a Find a function C x that models the data where x is years after 2005 b Predict the number of cell phone subscriptions in 2012 a Select the correct choice below and fill in the answer boxes within your choice Round to two decimal places as needed OA The best model for the data is an exponential function and is given by f x B The best model for the data is a logarithmic function and is given by f x Inx 2010 10 0 The best model for the data is a logistic function and is given by f x Point

cautious and decide to save more of their income of saving and investment according to neoclassical economics the interest rate will decrease saving and investment will decrease the interest rate will decrease saving and Investment will increase the interest rate will increase saving and investment will decrease the interest rate will increase saving and investment will increase Question 50 2 points Saved 4 Listen Suppose there are 20 million part time workers and 100 million full time workers in an economy 3 million of the part time workers switch to full time work with no change in the labor force participation rate As a result the official unemployment rate will fall the size of the labor force will increase official unemployment rate will rise official unemployment rate will remain unchanged

D x is the price in dollars per unit that consumers are willing to pay for x units of an item and S x is the price in dollars per unit that producers are willing to accept for x units Find a the equilibrium point b the consumer surplus a the equilibrium point and c the producer surplus at the equilibrium point D x 2000 20x S x 950 15x a What are the coordinates of the equilibrium point Type an ordered pair

Heavier birds tend to have larger wings than smaller birds For one species of bird the table lists the area A of the bird s wing in square inches if the bird weighs w pounds w lb 2 6 10 14 18 A w in 2 150 340 475 590 695 a Find a function that models the data b Graph A and the data c What weight corresponds to a wing area of 550 square inches a To find the function R x first plot the data Use a graphing utility to draw a scatter plot of the data Use the viewing window 0 20 2 by 0 700 50 Choose the correct graph below OA OB OO Q 5 Q O C O D 5

Tutorial Exercise The probability that an 80 year old male in the U S will die within one year is approximately 0 069941 If an insurance company sells a one year 13 000 life insurance policy to such a person for 432 what is the company s expectation Part 1 of 3 Let S be the event that the person dies within one year Then P S 0 069941 Submit Skip you cannot come back In this case the company has to pay out 13 000 Since the company charged 432 for this policy the company s actual loss is 506 264

Tutorial Exercise The probability that an 80 year old male in the U S will die within one year is approximately 0 069941 If an insurance company sells a one year 13 000 life insurance policy to such a person for 432 what is the company s expectation Part 1 of 3 Let S be the event that the person dies within one year Then P S 0 069941 Submit Skip you cannot come back In this case the Fompany has to pay out 13 000 Since the company charged 432 for this policy the company s actual loss is X

Exercise a Part 1 of 2 The total number of candies is the odds of getting a green M M Let E be the event of getting a green M M Because there are 6 green M M s there are 6 Exercise b 15 11 6 14 5 11 63 Part 2 of 2 Write the odds in favor of E in fractional form 2 19 2 19 Part 1 of 2 the probability of getting green M M Because there are 63 M M s in the bag there are 63 elements in the sample space green M M There are 6 green M M s so there are 6 favorable outcomes leaving 57 57 unfavorable outcomes X elements in E

skipped part A snack size bag of M Ms candies contains 15 red candies 11 blue 6 green 14 brown 6 orange and 11 yellow If a candy is randomly picked from the bag compute the following Exercise a the odds of getting a green M M Part 1 of 2 The total number of candies is 15 11 6 14 6 11 63 Part 2 of 2 part of the question you will not receive any points for the skipped part and you will not be able to come back to the 63 Let E be the event of getting a green M M Because there are 6 green M M s there are 6 Write the odds in favor of E in fractional form 6 favorable outcomes leaving 57 unfavorable outcomes

ics does NOT argue the market system has the self adjusting mechanism that fixes unemployment and recession in the long run as long as wages prices and interest rates are flexible government regulation is generally good for the overall economy GDP is determined by supply factors such as resources and technology not aggregate demand raising minimum wage generally creates unemployment

What is NOT the example for the group not in labor force discouraged workers overqualified employees stay at home parents

The long run aggregate supply LRAS curve O is a vertical line is a horizontal line Oslopes downward slopes upward

Real GDP has gone up although the living standard enjoyed by the average citizen Real GDP per capital has gone down Why there was greater nominal GDP growth there was greater population growth there was greater inflation there was greater investment

The population of a country was 5 235 million in 1990 The approximate growth rate of the country s population is given 0 01664t by f t 0 0871104e where t 0 corresponds to 1990 a Find a function that gives the population of the country in millions in yeart b Estimate the country s population in 2013 a What is the function F t F t Simplify your answer Use integers or decimals for any numbers in the expression Round to five decimal places as needed b In 2013 the population will be about million Type an integer or decimal rounded to three decimal places as needed

The rate at which people are becoming infected in person per day during the outbreak of a disease was approximated by the function mentioned below where x is in days and x 0 corresponds to the start of the outbreak Complete parts a and b below f x 6xe X a Find the function F x that gives total number of people who have become infected by day x given that 12 people choice were infected when x 0 Select the correct choice below and fill in the answer box to complete your O A To find F x evaluate the antiderivative of f x Therefore F x Type an exact answer B To find F x evaluate the derivative of f x Therefore F x Type an exact answer b Find the total number of people who have become infected by the end of 2 weeks The total number of people who have become infected with the disease by the end of 2 weeks is Round to the nearest whole number as needed Do not round until final answer

Does n 1 1 1 2n 4 converge absolutely converge conditionally or diverge

Does 3 converge absolutely converge conditionally or diverge n5 T F1

A marginal revenue function MR x in dollars is given below Use numerical integration on a graphing calculator or computer to find the total revenue over the given range MR x 160 1 5e 0 7x 15 0 x 300 The total revenue over the given range is approximately Round to the nearest cent as needed

16 y sin x 5 cos x

9 Alex kicked a soccer ball from the ground to Dzeps standing 30 ft away If the maximum height the ball reached was 12ft write a quadratic equation to model the path of the ball written in factored form factored form g a x p x

7 Write the equation for the following function in vertex form 9 2 8 8 2 3 2 0 5 0 1 2 3 Aos x 2 11 65 y a x 1 b 0

Consider the following quadratic function y 6x Select the correct t a The function has a vertical stretch by 6 bThe function has a vertical stretch by 6 c The function has a shift down 6 d The function has a shift right 6 X

5 The domain for the quadratic y 8x 7 is a x ER bix Rx 7 X x c y E Rly 2 7 d x E RI x 8

4 The quadratic y x 6 x 8 passes through which of the following points 6 X 6 11 10 2 1 5

Bae is willing to pay up to 160 for a particular pair of boots She can buy the boots for 120 The marginal cost of producing the boots is 70 Which of these is TRUE regarding the economic surplus associated with her purchase of the boots Consumer surplus is 90 and producer surplus is 120 Consumer surplus and producer surplus are the same Consumer surplus is 50 and producer surplus is 40 Consumer surplus is 40 and producer surplus is 50

Figure The Market for Green Tea The figure shows the market for green tea In the green tea market the pretax equilibrium price is 3 and the pretax equilibrium quantity is 20 cups A tax charged on suppliers is levied on each cup of green tea shifting the supply curve upward What is the tax rate Price per tea 4 00 3 00 2 25 1 75 O SI 2 50 O 1 75 0 50 15 20 New supply Old supply Demand Cups of tea per month

figure Market for Printed Houses Consider the market for environmentally friendly three dimensional printed houses that is hown in the figure The government wants to encourage buyers to buy such houses and places a price ceiling on the market a 200 000 per house The market quantity sold after implementation of the price ceiling is houses Price per house 400 000 300 000 200 000 100 000 200 000 N00 000 400 000 300 000 100 000 200 000 Supply 400 000 Demand Quantity of houses

Strategies used by entrepreneurs to overcome barriers to entry do NUI include O combatting customer lock in O finding ways to reduce costs O using regulatory strategies to the entrepreneur s advantage

The economist for the City of San Francisco uses ticket sales data to estimate that the absolute value of the price elasticity of demand for the city s public transportation system is 0 4 The city council proposes a 5 increase in the price of a transit ticket to increase educational funding If the proposition passes the change in quantity demand for transit tickets will be revenue from ticket sales will and total O 5 fall 2 fall 2 rise O 5 rise

Table Nike and Reebok Advertising Game Use Table Nike and Reebok Advertising Game The sneaker industry is dominated by Nike and Reebok and each firm spends a lot of money on advertising Suppose each firm is considering a costly television commercial during the World Series The table shows the payoff matrix of profits that each firm would receive from its advertising decision given the advertising decision of its rival Profits in each cell of the payoff matrix are given as Nike Reebok If each firm independently decides whether to advertise the Nash equilibrium is for Nike and Reebok during the World Series Nike and Reebok Advertising Game Reebok advertises Reebok does not advertise Nike advertises 800 700 1 500 600 not to advertise to advertise not to advertise not to advertise Nike does not advertise 650 900 1 000 800

Prove the given identity tan x sec x csc x cot x Choose the correct proof below OA tan x sec xcsc x sin x 1 1 cos x cos x sin x sin x cos x 1 sinx sin x cos x 2 COS cot x O C tan x sec xcsc x sin x COS X 1 sin x sin x cos x COS X sin x cos x cot x OB O D tan x sec x sin x cos x sin x cos x 1 sin X sin x cos x cos x cot x tan x sec X 1 cos sin x cos X 1 sinx sin x cos x 2 COS X sin x cos x cot x