Mathematical Induction Questions and Answers

Which of the lines on the given graph have a zero slope e GALLE b d Select all lines with a zero slope f b a C d e None of the lines have a zero slope

20 If the labor unions lose memberships and become less popular then A production costs will increase SRAS will shift to the left decreasing equilibrium GDP and increasing the aggregate price level B production costs will fall there will be a downward movement along SRAS equilibrium GDP will increase and aggregate price level will fall C production costs will not change AD will shift to the right increasing equilibrium GDP and aggregate price level D production costs will fall SRAS will shift to the right increasing equilibrium GDP and lowering the aggregate price level

2 Which of the following is NOT true regarding the aggregate demand curve A A rise in the price level lowers real wealth and results in a lower level of consumer spending B A rise in the price level increases the demand for money raises the interest rate and reduces investment spending C A fall in the price level will generally lead to a rise in the level of aggregate output demanded D A fall in the price level will reduce the demand for money raise the interest rate and increase investment spending

5 The SRAS curve is upward rising because A a higher aggregate price level leads to lower output as costs of production increase B a higher aggregate price level leads to higher output since most production costs are fixed in the short run a lower aggregate price level leads to higher output since production costs tend to fall in the short run D a lower aggregate price level leads to higher profit and higher productivity

K Identify the sequence as either arithmetic or geometric List the next two terms of the sequence 1 1 1 1 5 25 125 1 Is the sequence arithmetic or geometric 1 O A Arithmetic B Geometric List the next two terms in the sequence 1 1 1 5 25 125 Type integers or simplified fractions

Suppose that you decide to buy a car for 23 635 including taxes and license fees You saved 5000 for a down payment and can get a four year car loan at 6 16 Use PMT to find the monthly payment and the total interest for the loan The monthly payment is Round to the nearest cent as needed The total interest for the loan is Round to the nearest cent as needed PA nt LIC

The line graph to the right shows the average gasoline prices of a country from 1980 through 2005 Let p q and r represent the following simple statements p Prices peaked in 2000 q Prices remained steady from 1985 through 1990 r Prices were more than 3 00 per gallon in 2000 Write the symbolic statement pvr in words Then use the information given by the graph to determine the truth value of the statement Write the symbolic statement pvr in words Choose the correct sentence below OA Prices did not peak in 2000 or prices were more than 3 00 per gallon in 2000 OB Prices peaked in 2000 or were not more than 3 00 per gallon in 2000 OC Prices did not peak in 2000 or prices were not more than 3 00 per gallon in 2000 OD Prices peaked in 2000 or prices were more than 3 00 per gallon in 2000 Using the information given by the graph the truth value of pvr is 4 Average Price per Gallon unleaded regular Average Gasoline Prices 4 00 3 00 2 00 1 00 50 00 1980 1990 Year 2000

Find the intercepts and asymptates If an answer does equations if necessary F x 5x 6 x 2 y intercept vertical asymptote s horizontal asymptote Sketch a graph of the rational function 15 10 xn xx n 15 10 5 1 84 15 10 5 10 5 10 10 15 15 15 10 5 S PA 10 15 O 10 10 O State the domain and range Use a graphing device to confirm your answer Enter your answers using interval notation domain 15

Bonus Question Dr Blue analyzed the effect of consequences on the likelihood of reporting unethical behavior Participants completed a questionnaire measure of their likelihood to report unethical behaviors depicted in a series of short videos A higher score in the questionnaire indicates a greater likelihood of reporting unethical behavior in which they received a reward for reporting unethical behavior punishment for not reporting unethical behavior or no consequences at all The researcher found that the type of consequence significantly affected the likelihood participants would report unethical behaviors The mean likelihood of reporting unethical behavior scores for the three consequence conditions are listed below Completely interpret these results based on the evidence provided below No calculations are necessary 2 pts Reward for Reporting 12 5 Punishment for Not Reporting 10 5 No Consequences 5 5

The U S Fish and ife Service re ded the in 10 State Parks during the summer season last year 345 89 123 412 231 390 287 190 401 215 The mean of this data set is 268 needed The median of this data set is 28 needed Question 2 Low Lower Quartile Give the Five Number Summary for the number of Grizzly Bears in the previous question Median round to the nearest whole number as Upper Quartile round to the nearest whole number as 3 pts

Consider laminar boundary layer flow past the square plate arrangements in the figure below Compared to the friction drag on a single square how much larger is the drag of the four plates together as in configurations a and b

The main cross cable between towers of a coastal suspension bridge is 60 cm in diameter and 90 m long Estimate the total drag force on this cable in crosswind of 50 miles hour Is the flow laminar or turbulent Hint Use Fig 11 31 on page 595 of our textbook to find the drag coefficient S 400 200 100 60 40 20 10 6 4 2 1 0 6 0 4 0 2 0 1 0 06 10 1 24 CD R 100 101 102 Re Smooth cylinder 103 Smooth sphere 11 8 THE DRAG COEFFICIENT 104 Drag coefficients for a sphere and long cylinder Fig 11 31 105 Rough cylinder 106

President s Opponent s height cm height cm 183 172 183 176 188 168 190 190 175 170 189 169 186 192 180 179 23 24 Print President s Opponent s Di height cm height cm 188 194 170 173 181 169 182 169 Done 160 177 187 185 190 193 160 168 196 200 President s height ble for election heights Question 24 of 24 d data for the heights of a certain country s presidents and their main opponents in the election campaign Construct a scatterplot rrect graph below OB Opponents height 200 160 160 President s height 200 TT OC 200 160 160 This test 24 point s possible This question 1 point s possible Does there appear to be a correlation between the president s height and his opponent s height 200 President s height O D 200 Resume later Submit test 160 160 200 President s height Q O E

The line graph shows the goals per game average for a sporting series during the years shown During what year s shown was the average number of goals per game less than 2 6 During the year s the average number of goals per game was less than 2 6 Use a comma to separate answers as needed Ave of Goals per Game Goals per Game Average Q 3 8 3 2 2 6 2 1976 Submit test 1984 1992 2000 Year

Consider the concentration C in mg litre of a drug in the blood as a function of the amount of drug injected x in mg and the time since injection t in hours For 0 4 mg and t 0 hours we have C f x t 26xte 4 Calculate the following f 3 4 Give a practical interpretation of your answer Choose the best option f 3 4 is A the amount of a 4 mg dose in the blood 3 hours before injection B the change in concentration of a 4 mg dose in the blood 3 hours after injection C the concentration in the blood 4 hours after injection of a 3 mg dose D the half life of a 3 mg dose in the blood 4 hours after injection E the concentration in the blood 3 hours after injection of a 4 mg dose F the change in concentration of a 3 mg dose in the blood 4 hours after injection

Due Date 30 2023 1 The following data are given for a direct shear test conducted on dry silty sand Specimen dimensions 63 mm x 63 mm x 25 mm height Normal stress 105 kN m Shear force at failure 300 N a Determine the angle of friction b For a normal stress of 180 kN m what shear force is required to cause failure NOTE SL

The data represent the results for a test for a certain disease Assume one individual from the group is randomly selected Find the probability of getting someone who teste negative given that he or she had the disease The probability is approximately The individual actually had the disease Yes C No 142 6 Positive Negative Round to three decimal places as needed H 20 132

A radioactive material decays according to the function A t Age 0 0244t where Ao is the initial amount present and A is the amount present at time t in years Assume that a scientist of the radioactive material a What is the decay rate of the radioactive material b Graph the function using a graphing utility c How much radioactive material is left after 30 years d When will only 300 grams of the radioactive material be left e What is the half life of the radioactive material a The decay rate of the radioactive material is 2 44 Type an integer or a decimal b Graph the function Choose the correct graph below The graphing window is 0 800 100 by 0 1 0 25 A B c There will be about 192 4 gram s of the radioactive material left after 30 years Do not round until the final answer Then round to the nearest tenth as needed d In about year s only 300 grams of the radioactive material will be left Do not round until the final answer Then round to the nearest tenth as needed O C Points 3 of 5 d D Q

If the temperature is held constant the pressure of a gas in a container varies inversely as the volume of the container Assume that the gas pressure in a piston cylinder the container is 6 pounds per square inch when the volume of the cylinder is 130 cubic inches If the volume of the cylinder is reduced to 125 cubic inches what is the pressure of the gas pounds per square inch Round to two decimal places as needed GILB

There are 449 seats in a nation s House of Representatives The number of representatives per state is calculated using a statistical formula determined by law but allocation is roughly proportionate to population In 2010 the nation s population was estimated to be 308 6 million The state s population was estimated at 24 9 million How many representatives would you expect to be assigned to the state Suppose the state actually has 39 representatives Compare this with the expected number of representatives from the state The expected number of representatives in the state is Round to the nearest integer as needed

1 point An implicit equation for the plane passing through the points 0 1 1 3 3 3 and 2 1 5 is

The population of a fish farm in is modeled by the equation where t is time in years Part 1 What is the size of the initial population 500 help numbers Part 2 How long does it take to double the initial size of the population Round your answer to the nearest tenth 2 1 I fish 1995 years Part 3 What is the size of the population after 5 years Round to the nearest whole number fish P t 7500 2 13e 0 4t

lodine 123 is a radioactive isotope used in medicine to test the function of the thyroid gland Its half life is 13 1 hours A 575 microcurie uci dose of iodine 123 is administered to a patient The quantity Q left in the body after t hours is given by the equation Q 575 5 1 1173 Answer parts a through d CAVA www c Determine the rate of change of the quantity of iodine 123 at 1 day The rate of change of iodine 123 at 1 day Is 8 55 Ci hr Type an integer or decimal rounded to two decimal places as needed d Determine the rate of change of the quantity of iodine 123 at 3 days What do your answers say about the rate at which iodine decreases as time increases The rate of change of iodine 123 at 3 days is Ci hr Type an integer or decimal rounded to two decimal places as needed torr

A couple decides to have children until they have one boy and one girl but they will not have more thar three children Choose the correct sample space for this random experiment Os GGG GGB GBG GBB BBB BBG BGB BGG Os GGG GGB BBB BGG Os GB BG BBG GGB Os GB BG BBG GGB BBB GGG

Determine the distribution of the data pictured below Frequency 6 5 4 3 2 1 1 2 Uniform Bell shaped Skewed right Skewed left 3 data 4 5 6 Q

Parent Function x X 2 1 2 y x X 2 T 1 2 X

A water tank shown to the right is shaped like an inverted cone with height 4 m and base radius 1 m a If the tank is full how much work is required to pump the water to the level of the top of the tank and out of the tank Use 1000 kg m for the density of water and 9 8 m s for the acceleration due to gravity b Is it true that it takes half as much work to pump all the water out of the tank when it is filled to half its depth as when it is full Explain Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression Set up the integral that gives the work required to pump the water out of the tank Use increasing limits of integration Select the correct choice below and fill in the answer boxes to complete your choice Type exact answers 0 9800 16 4y y OB f dx dy nquired is approximately OFFSECED wort answer using as needed Coleor all Check answer

A statisican that is a sports enthusiast estimated the mean cost upper level NBA tickets They determined the mean cost to be between 52 and 78 L What is the sample mean X What is the margin of error E estion 4 6 points large airline wants to estimate the mean number of unoccupied seats per flight ow many flight records must they select to be 90 confident that their estimate is thin 0 5 unoccupied seats Assume o 4 3

Simplify the given expression The result will be one of sin x cos x tan x cotx secx or csc x cos x sec x cot x cos x sec x cot x I

Verify the identity 2 sin x sinx cot x csc x Choose the sequence of steps below that verifies the identity OA OB O C 2 sin x sinx cot x sinx cot x 1 2 sin x sinx cot x sinx 1 cot x 2 sin x sinx cot x sin x 1 cot x SO D sin x sin x cot x 1 cot x csc x 1 CSC X 1 CSC X 1 2 CSC X CSC X 2 CSC X CSC X 2 CSC X CSC X CSC X MIN

Which of the following is true about a weak positive correlation The points on the scatterplot fall into a broad swath that slopes downward The points on the scatterplot fall into a fairly tight line that slopes downward The points on the scatterplot fall into a broad swath that slopes upward The points on the scatterplot fall into a fairly tight line that slopes upward

Convert the angle 5T 4 Submit Question 5T 4 n from radians to degrees

Find the mean median and mode for the set of numbers If necessary round the mean to one decimal place 297 234 579 106 612 334 269 542 Find the mean Select the correct choice below and if necessary fill in the answer box to complete your choice A The mean is 371 6 Type a whole number or decimal rounded to one decimal place as needed Use a comma to separate answers as needed OB There is no mean Find the median Select the correct choice below and if necessary fill in the answer box to complete your choice OA The median is Type a whole number or decimal rounded to one decimal place as needed Use a comma to separate answers as needed B There is no median

0 10 pts 399 Details Express the equation in logarithmic form a e 3 is equivalent to In A B Then A and B b e C and D x is equivalent to In C D Then

Air enters the compressor of a gas turbine plant at ambient conditions of 100 kPa and 25 C with a low velocity and exits at 1 MPa and 347 C with a velocity of 90 m s The compressor is cooled at a rate of 1500 kJ min and the power input to the compressor is 250 0 KW Determine the mass flow rate of air through the compressor The inlet and exit enthalpies of air are 298 2 kJ kg and 628 07 kJ kg Round the final answer to three decimal places The mass flow rate of air is kg s

Steam enters an adiabatic turbine at 8 MPa and 500 C at a rate of 3 200 kg s and leaves at 10 kPa If the power output of the turbine is 2 5 MW determine the temperature of the steam at the turbine exit Neglect kinetic energy changes Use data from the steam tables The temperature of the steam at the turbine exit is C

A record club has found that the marginal profit P x in cents is given by P x 0 0006x 0 20x 43 9x for x 300 where x is the number of members currently enrolled in the club Approximate the total profit when 180 members are enrolled 6 by computing the sum P x Ax with Ax 30 i 1 The total profit when 180 members are enrolled is approximately Round to the nearest cent as needed Marginal profit in cents 16 000 P x 0 0006x3 0 20x2 43 9x 12 800 9 600 6 400 3 200 04 0 TIV V VI 100 200 Number of members 300

Question Attempt 1 of Unlimited The graph of the ellipse is given a Use the distance formula to find the distances d d d3 and d4 b Find the sum d d c Find the sum dz d4 d How do the sums from b and c compare e How do the sums of the distance from b and c relate to the length of the major axis Express numbers in exact simplest form Note that the points 0 4 and 0 4 represent the foci 3 0 d Tr 4 6 0 4 d 3 4

16 58 If the block at C is moving downward at 4 ft s determine the angular velocity of bar AB at the instant shown AR 2 ft B 3 ft 30 Prob 16 58 vc 4 ft s

16 1 The angular velocity of the disk is defined by w 5r 2 rad s where is in seconds Determine the magnitudes of the velocity and acceleration of point A on the disk when t 0 5 s 0 8 m Prob 16 1

16 20 The operation of reverse for a three speed utomotive transmission is illustrated schematically in the gure If the crank shaft G is turning with an angular speed f 60 rad s determine the angular speed of the drive shaft H Each of the gears rotates about a fixed axis Note that gears A nd B C and D E and F are in mesh The radii of each of hese gears are reported in the figure TA 90 mm Trc 30 mm TD 50 mm TE 70 mm TF 60 mm Prob 16 20 B G 60 rad s G 16

xi yi 1 14 2 4 3 2 Find the natural cubic spline to interpolate the three points given Do it by your hand

The envelopes of letters received by an office one morning were measured The widths in centimetres were as follows 23 8 15 3 20 5 15 4 19 2 20 0 24 7 12 8 9 7 18 9 24 4 13 1 15 9 12 2 20 6 6 9 20 0 11 3 10 0 16 1 Width 5 w 10 10 w 15 15 w 20 20 w 25 Click the tally column to tally off the data and complete the frequency table You can click the numbers above as you tally them to cross them off How many envelopes were measured altogether How many envelopes measured less than 20 cm How many envelopes measured 20 cm or more Tally Frequency 000 1 1 2

Directions for finding standard deviation on the calculator 1 Press Stat and choose Edit 2 Type in all the numbers in the list into L1 3 Press Stat arrow over to Calc and choose 1 Var Stats 4 Make sure L1 is in next to List can leave Freq List blank press Enter The standard deviation is a Ex 18 What is the five number summary of the data set The five number summary includes the minimum value first quartile median third quartile and maximum value same numbers from ex 1A 4 12 15 9 14 16 13 6 7 6 25 3 13 17 22 4 Minimum value First quartile Median Third quartile Maximum value

What is the future value after 15 years if you deposit 1 000 for your child s education and the interest is guaranteed at 1 9 compounded continuously Round your answer to the nearest cent

Solve for x If there is no solution enter NO SOLUTION 21x 9 3x 5 X Tutorial Did you use properties of equality to get the variabile terms

The price of a home is 270 000 The bank requires a 5 down payment The home is financed with a 20 year mortgage at 7 Payment 1 P O 11 nxt Find a down payment b amount of mortgage c monthly payment d total cost of interest over 20 years Round answers to the nearest cent a down payment 13 500 b amount of mortgage 256 500 c monthly payment 1988 64 d total cost of interest over 20 years 477273 60 a down payment 13 500 b amount of mortgage 256 500 c monthly payment 624 04 d total cost of interest over 20 years 477273 60

A die is rolled The set of equally likely outcomes is 1 2 3 4 5 6 Find the probability of getting a 6 O 1 6

6 A lab wants to compare two different drugs and whether patients felt side effects For Drug A out of a sample of 90 patients 18 felt some side effects For Drug B out of a sample of 100 patients 22 felt side effects At a 95 confidence level a 0 05 determine if there is a difference between the two drugs as far the proportion of patients who felt side effects Ho P P2 HA P1 P2 The null and alternative hypotheses a Compute the test statistic z score b What is the p value for the test statistic

What changes have been made to the Social Security program since its creation in 1935 Choose one or more A Social Security taxes as a percentage of income have increased over time B The number of workers per retiree has increased C The length of time that individuals collect Social Security benefits has gotten shorter D The length of time that individuals collect Social Security benefits has gotten longer E The number of workers per retiree has decreased