Basic Math Questions and Answers

3 When measuring a nation s standard of living of the following the best measure is A nominal GDP B market GDP C real GDP per capita D nominal GDP per capita

Figure 37 Price level LRAS SRAS SRASO SRAS LRAS H G ADO Real GDP 37 The economy s initial aggregate demand AD and aggregate supply SRAS and LRAS curves are illustrated in Figure 37 Which of the following is true a The profits of business firms are higher at I than J b H is a point of long run equilibrium c Downward pressure on prices occurs at point G d Point F is consistent with long run equilibrium

Use the following to answer question 29 Figure An Increase in Aggregate Demand Price level P3 P P LRAS SRAS Y Yp Y SRAS AD Real GDP AD 29 Figure An Increase in Aggregate Demand Because of the pressures existing at the short run equilibrium at Y and P A the SRAS will shift to the right B the SRAS curve will shift to the left C unemployment will decrease D LRAS will shift to the right

Use the following to answer questions 31 32 Figure AD AS Model II Aggregate price level P LRAS Y potential output SRAS AD Real GDP 31 Figure AD AS Model II If the price level increases which of the following will take place A SRAS curve will shift to the left B SRAS curve will shift to the right C AD curve will shift to the left D None of the answer choices provided will take place 32 Figure AD AS Model II As the size of the labor force increases over time which of the following will take place A LRAS will shift to the right B LRAS will shift to the left C AD curve will shift to the left DY 4D curve will shift to the right

34 If the economy grew at a 3 rate this year and average prices grew would be better off this year compared with last year A 3 B faster than 3 C slower than 3 D faster than 10 people

33 If the economy is at equilibrium above potential output A there is a recessionary gap and expansionary fiscal policy is appropriate B there is an inflationary gap and contractionary fiscal policy is appropriate C there is a recessionary gap and contractionary fiscal policy is appropriate D there is an inflationary gap and expansionary fiscal policy is appropriate

Figure 38 Price level b B C LRAS C D C E SRASO B Real GDP AD 38 The economy s short run SRAS and long run LRAS aggregate supply curves are shown in Figure 38 along with three alternative aggregate demand curves and the accompanying equilibrium points At which point will resource prices naturally tend to increase a A AD ADO

6 Consider the parametric curve given the equations r t t 23t 1 and y t 1 23t 6 How many units of distance are covered by the point P t x t y t between t 0 and t 6 11

Which of the following correctly defines respiration rate The number of breaths a person takes during a 45 second period while at rest O The number of breaths a person takes during a one minute period while active O The number of breaths a person takes during a 45 second period while active O The number of breaths a person takes during a one minute period while at rest

Starting at age 30 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 eams 6 compounded continuously how much will be in the account 36 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 238872 Round to the nearest dollar as needed How much of the future value is interest Round to the nearest dollar as needed

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

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

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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

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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

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

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

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

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

Verify the identity csct 1 cott O A Choose the sequence of steps below that verifies the identity OB O C B O D cott csct 1 csct 1 csct 1 csct 1 csc t 1 cott cott csct 1 cott csct 1 csct 1 cott csct 1 cott csct 1 cott csct 1 cott csct 1 cott csct 1 cott csct 1 csct 1 csct 1 csct 1 csc t 1 cott csct 1 csc t 1 cott csct 1 cott csct 1 csct 1 csc t 1 csct 1 cott csct 1 cot t cott csct 1 cot t cott csct 1 cott csct 1 cot t cott csct 1 cott csct 1 cott csct 1 cott csct 1 cot t cott csct 1 cott csct 1 csct 1 cott cott csct 1

Express the given expression in its simplest form with only positive exponents 4z 2 Z 2 Question 5 of 2 3 Simplify your answer Type exponential notation with positive exponents

25y Question 3 of 20 Simplify by taking roots of the numerator and denominator Assume that all expressions under the radicals represent positive numbers 25y7 11 This test 65 poin This question 4 p

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Simplify 3a 2 302 2 0 3a Simplify your answer Use positive exponents only Use integers or fractions for any numbers in the expression

Simplify by taking roots of the numerator and denominator Assume that all expressions under the radicals represent positive numbers 16y 10

Verify the identity tanxesc x tanx cotx Choose the sequence of steps below that verifies the identity tanx csc x tanx tanx csc x 1 1 cotx tanx csc x tanx tanx csc x 1 O A OB cot x O C cotx tanx csc x tanx tan x 1 csc x 1 O D tanxesc x tanx c c x cotx 2x Question 12 of 20 cot x cotx cotx cotx cotx cotx

Verify the identity sect 1 tant tant sect 1 Choose the sequence of steps below that verifies the identity O A B OC O D sect 1 sect 1 sect 1 tant tant sect 1 sect 1 sect 1 tant sect 1 tant sect 1 tant sect 1 tant sect 1 sect 1 sect 1 tant sect 1 sect 1 sec t 1 tant sect 1 sec t 1 tant sect 1 sec t 1 tant sect 1 tant sect 1 sect 1 sect 1 ec t 1 tant sect 1 tant sect 1 tan t tant sect 1 tan tant sect 1 tan t tant sect 1 tan t tant sect 1 tant sect 1 tant sect 1 tant sect 1 tan t sect 1

An engineer deposits 1500 per month into an account that pays interest at 6 per year compounded quarterly 4 times a year How much will be in the account at the end of 5years Assume no interperiod compounding 5 points O a 6 061 Ob 22 750 O c 88 978 Od 104 056

1 5 pts Solve the following trigonometric equation algebraically Give the exact solutions in the interval 0 27 Don t forget to show all of your work 2 cos x cosx 1 0

A company had the following situation last year Gross sales 15 890 000 Expenses 11 700 000 They purchased a machine that cost 2 000 000 that they intend to depreciate over 5 years using MACRS what was their before tax income a 3 680 000 O b 3 790 000 O c 3 987 000 O d 4 190 000

A company had a before tax profit if 2 500 000 what was their after tax profit O a 850 000 Ob 1 250 000 O c 1 650 000 O d 2 000 000

Rubrics 01 marks for solving each question 01x 4 4 marks 5 1 P 1 12 18 6 iii f x 5x5 8 x 6x 6 marks ii f t iv i Question 6 Find x so that 06 Marks Rubrics 03 marks for solving each question 03 x 2 2014 8t t t f x 8x4 2x2 9 7x 9x5 3 4 log281 log 128 loga 4 loga x 4 7 2 t

Given that ZQ ZS and ZQRT STR prove that AQTR ASRT T Statement Q 25 ZQRT STR AUTREASRT S Given Reason Reflexive Property

Q13 Part B Solve the following polynomials and state if the operation is closed multiplication addition or subtraction a 3x2 2 2x 3 b 5x 2x 3 2x x 5 c 6x 5x 3x 2x 5x 7 4x 3x 2 Q14 Use the Graph Provided to determine What Type of Parallelogram TUNE is whe T 0 10 U 4 2 N 2 1 and E 6 7

The National Sleep Foundation surveyed representative samples of adults in six different countries to ask questions about sleeping habits Each person in a representative sample of 250 adults in each of these countries was asked how much sleep they get on a typical work night For the United States the sample mean was 391 minutes and for Mexico the sample mean was 426 minutes MY NOTES The report also gave data for representative samples of 250 adults in Canada and 250 adults in England The sample mean amount of sleep on a work night was 423 minutes for the Canada sample and 409 minutes for the England sample Suppose that the sample standard deviations were 34 minutes for the Canada sample and 43 minutes for the England sample USE SALT minutes PRACTICE ANOTHER a Construct a 95 confidence interval estimate of the difference in the mean amount of sleep in minutes on a work night for adults in Canada and adults in England Use Canada England Use technology to calculate your critical value Enter your answer using interval notation Round your numerical values to three decimal places Interpret the interval There is a 95 chance that the sample difference in the mean amount of sleep on a work night for adults studied in Canada and adults studied in England falls within this interval We are 95 confident that the true difference in the mean amount of sleep on a work night for adults in Canada and adults in England falls within this interval There is a 95 chance that the true difference in the mean amount of sleep on a work night for adults in Canada and adults in England falls directly in the middle of this interval We are 95 confident that the sample difference in the mean amount of sleep on a work night for the adults studied in Canada and adults studied in England falls within this interval There is a 95 chance that the sample difference in the mean amount of sleep on a work night for adults studied in Canada and adults studied in England falls directly in the middle of this interval 0 b Based on the confidence interval from part a would you conclude that there is evidence of a difference in the mean amount of sleep on a work night for the two countries Explain why or why not The confidence interval allows us contained in the confidence interval to conclude that there is evidence of a difference in the mean amount of sleep on a work night for the two countries because zero is not 0

one is done for you Qu hora es 1 do the picture below and write what time it is in Spanish for each one The first 2 1 1152 13 2 Son las siete menos cuarto de la ma ana 3 45 Y

The amounts in millions of dollars grossed by movies in categories with PG PG 13 and R ratings we obtain the analysis of variance results from statistical software below Use a 0 05 significance level to test the claim that PG movies PG 13 movies and R movies have the same mean gross amount Amount Grosses By Movies Sum of df Squares Between Groups Within Groups Total 84801 867 255396 1 2 32 340198 0 34 Mean F Sig Squares 42400 933 5 313 010 7981 129 O We cannot come to any conclusions because the F distribution in this case is skewed to the right There is not sufficient evidence to warrant rejection of the claim that PG movies PG 13 movies and R movies have the same mean gross amount

Write the symbolic statement using words p We will go to the movies q It will rain on Saturday p q 1 We will not go to the movies if and only if it will not rain on Saturday 2 If we don t go to the movies then it will rain on Saturday 3 We will not go to the movies if and only if it will rain on Saturday 4 We will go to the movies if and only if it will not rain on Saturday

James and Susan wish to have 10 000 available for their wedding in 2 years How much money should they set aside now at 6 compounded monthly in order to reach their financial goal Use one of the formulas below to solve the problem Future Value A P 1 nxt Present Value P 5000 00 8871 86 9419 05 10 616 78 2 1 1 108

If f x 7 5 and g x 14 determine where f x g x Express your answer using interval notation 16 2 O 00 12 U 16 00 O 12 16 O 00 16 U 2 00

find the complex zeros of the quadratic function x 6x 13 F x 3 4i O 3 4i 3 2i 0 3 2i

Factor completely the given expression 4x 7 x 6 4x 7 4 2 07 4x 7 4x 1 07 4x 7 4x 1 The polynomial is prime O 4x 7 28x 7 O 28x 7 4x 7

Find the real solutions of the equation 18x 9 x 4 5 3 5 O 4

the following quadratic Click the square near each correct factor Be sure to mark ALL correct answers f x 10x 21x 10 2x 5 2x 5 O 5 2 5m LD 21 Page 14 of 41

The graph of two functions f and g is illustrated below Use the graph to answer parts a through d 40 a f g 3 A B