Basic Math Questions and Answers

At the beginning of a population study a city had 380 000 people Each year since the population has grown by 1 1 Lett be the number of years since start of the study Let y be the city s population Write an exponential function showing the relationship between y and t 0 0 0 8 08

If a store owner places Joe as manager and gives him a special nametag customers may assume that Joe has for the owner in that respect apparent authority ratification power special agency universal agency

A agent is authorized by the principal to handle a definite business transaction or to do a specific act special general secret O universal

An agent is under a duty to obey all instructions given by the third party all lawful instructions given by the principal all instructions given by the principal obedience is not an obligation of the agent

An indorsement for deposit only is Orestrictive qualified special O O Oblank

Find the mean median and modes of these sets of numbers 11 13 11 13 2 13 29 11 24 22 16 26 23 7 8 6 12 7 12 3 11 8 13 10 12 7 8 8 13 10 Mean 1000 Median Mode

Work out the range for each group of numbers 3 5 7 8 9 11 13 13 15 20 22 28 22 21 23 27 25 1 2 4 4 6 7 9 10 12 74 80 77 76 77 78 73 72 78 80

Find the modal golf score from this frequency table score 23456 freq 76456 modal score 2

Find the mode of each group of numbers 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 5 5 5

Here are the weekly staff wages from 2 small internet companies A 260 300 330 360 730 B 160 160 240 240 320 360 400 400 Calculate the means Calculate the medians mean A median A Which company has the higher wages on average mean B median B 4 2 1

In order to join a social and educational club for tall people women must be at least 5 ft 6 in tall Assuming that the heights of adult women are approximately normally distributed with mean 62 in and standard deviation 2 in what z score is required for membership in the club The Z score required for membership is Type an integer or a decimal CITE

LO4 5 Explain the idea behind the CAPM what is the beta LO4 5 Different classes of beta 0 0 1 1 cyclicality examples interpretation of beta Chapter 8 LO3 Be able to briefly explain each of the characteristics of common stock claim in income

Chapter 6

04 Diversification and portfolios what is it how does it work LO4 Systematic vs unsystematic risks What is it plus example

Given a mean standard deviation and a raw score find the corresponding z score Assume the distribution is normal mean 50 standard deviation 2 x 53 What is the corresponding z score Z

A machine fills bottles with 64 ounces of liquid The quality control manager determines that the fill levels are normally distributed with a mean of 64 ounces and a standard deviation of 0 42 ounce He has an engineering recalibration machine in attempt to lower the standard deviation After recalibration the quality control manager randomly selects 19 bottles from the line and determines that the standard deviation is 0 38 ounce Is there less variability in the filling machine Use a 0 1 The null and alternative hypothesis would be 0 Ho 0 38 Ho p 64 Ho o 0 42 Ho p 0 38 Ho o 64 H 00 38 H 64 H o 0 42 H 0 38 H 0 64 O The test is left tailed two tailed right tailed Based on a sample of 19 bottles The test statistic is The D value is to 2 decimals to 2 decimals

54 of students entering four year colleges receive a degree within six years Is this percent smaller than for students who play intramural sports 111 of the 221 students who played intramural sports received a degree within six years What can be concluded at the level of significance of a 0 01 Use the p value approach a For this study we should use z test for a population proportion b The null and alternative hypotheses would be Ho p H P V please enter a decimal Please enter a decimal

The following table lists the number of years of education past high school and the annual income of six people Determine the linear correlation coefficient for the data and also determine whether we can be 95 or 99 confident that there is significant linear correlation between the two variables Years of Education Past High School Annual Income in thousands of 1 25 3 34 2 36 4 35 5 43 6 54 Click the icon to view the table of critical values for the linear correlation coefficient The correlation coefficient between the two variables is r Round to four decimal places as needed Table of critical values n 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 05 950 878 811 754 707 666 632 602 576 553 532 514 497 482 468 456 444 01 999 959 917 875 834 798 765 735 708 684 661 641 623 606 590 575 561 X

5 Identify the correct statement for the quadratic y x a The vertex is 2 5 Alm b The optimal value is a minimum c The axis of symmetry is 2 d The y intercept is 5 Almay this X

9 For the following function f x 3x 18x 15 a Use the discriminant to describe the number of the roots 2 1 Discriminant formula 2 1 hac 5 O f x 3 x 18 x 1n 18 2 18 2 1 b 51 180 4 3 15 11 45 180 324 180

Distribution Date 11 02 2023 Due Date 11 06 2023 1 A soil element is shown in the figure below Determine the a Maximum and minimum principal stresses b Normal and shear stresses on the plane AB Use eqs 10 3 10 4 10 6 and 10 7 A 100 kN m 30 45 kN m 45 kN m B 60 kN m NOTE Show all the calculation steps

Consider the line with the equation 5y 2x 15 Give the equation of the line parallel to Line 1 which passes through 6 1 Give the equation of the line perpendicular to Line 1 which passes through 6 1 I

Question 39 Sketch a graph of the linear equation y 1 5 4 3 2 1 5 4 3 2 1 Clear All Draw 1 2 3 4 5 1 2 3 4 5

Question 55 When you dive below the surface of the water the pressure increases You can feel this in your ears when you dive to the bottom of a deep swimming pool or spring The function that describes this relationship is 29 P d 14 5 d where d is the depth in feet below the surface of the water and P is the pressure 66 in pounds per square inch PSI What is the pressure at the surface of the water Select the correct units from the second box Select an answer feet PSI At what deparne pressure exactly double the pressure at the surface of the water Select the correct units from the second box Select an answer What is the pressure at a depth of 99 feet Use function notation in the first box and give the answer in the second box Select the correct units from the third box Select an answer e What is the pressure at a depth of 132 feet Use function notation in the first box and give the answer in the second box Select the correct units from the third box Select an answer Which of the following is the graph of the function P d 200 180 160 140 120 100 80 60 40 20 no 40 80 120 160 200 240 280 320 200 180 160 140 120 100 80 60 40 20 40 20 40 80 120 160 200 240 280 320

Question 51 Write the equation for a line with the given characteristics If possible write the equation in slope intercept form 1 Passes through 12 20 and m 2

Question 49 Determine whether lines with the given slopes are parallel perpendicular or neither 1 a m 7 m 1 7 b mi The lines are neither parallel nor perpendicular The lines are parallel The lines are perpendicular 4 m 1 4 c m 7 m 7 The lines are parallel The lines are neither parallel nor perpendicular The lines are perpendicular The lines are parallel The lines are perpendicular The lines are neither parallel nor perpendicular

Question 38 1 Graph the equation y 3 5 4 3 2 1 5 4 3 2 1 1 2 3 4 X 3 1 1 2 3 4 5

FOL Homepage MA 7 6 5 4 3 2 1 6 5 4 m 2 2 Hy 2 3 4 4 69 7 6 5 30 2 3 456 S 7 69 43 2 7 6 5 4 3 2 1 2 3 4 FOL 5 Slides MAT 1 2 3 Y N 4 56 4 5 6 56 P X FOL 4 Slides MAT The equation of the line is The equation of the line is The equation of the line is C Apple iPhone 1

For the equation 3x 4y 12 a Complete the table X 0 y 0 I b Plot the two points you found in the table 6 5 4 3 LIL Draw 2 1 6 5 4 3 2 1 a A w NL 2 3 4 5 6 Dot 1 2 3 4 5 6

Question 41 x intercept 2 0 y intercept 0 2 Graph the line with the following intercepts then write the equation of the line in y mx b form 5 4 3 2 Clear All Draw 4 3 2 1 T 2 3 4 5 1 2 3 4 5

Question 45 Graph the line through the point 1 1 having slope m 3 8 7 6 S 4 3 2 8 7 6 54 3 2 1 19 14 3 4 S 6 1 8 1 2 3 4 5 6 7 8

Next question Y Consider the equation x 2y 4 First re writing the equation in the form y mx b in the box below Now find 5 solutions to the equation x 4 2 0 2 4 Get a similar question You can retry this question below Click on the Y Plot the 5 solutions found above and then graph the equation click on the icon below the coordinate chart to begin plotting the points and then icon below the coordinate chart to begin graphing the equation 12 HI

Next question Sketch a graph of 2x y 3 5 4 3 2 1 4 3 2 1 Clear All Draw X 1 2 3 Get a similar question M 2 3 4 5

For the equations below q is the total number of units produced per day by m employees of a manufacturer and p the price per unit at which the q units are sold Find the marginal revenue product for the given value of m q 2 400m m 40 p 0 1q 80 m 50 The marginal revenue product when m 50 is Type an integer or a decimal

You want to make a 55 alcohol solution You have 100 mL of 25 solution and plenty of 70 alcohol solution on hand How much of the 70 mixture do you need to make a 55 mixture To answer this question you are going to do two things A Write the equation to solve this problem using for the amount of 70 solution Enter your equation here B Now solve your equation Round to the nearest tenth The amount of 70 solution I need is mL Submit Question

The U S Weather Bureau has a station on Mauna Loa in Hawaii that has measured carbon dioxide levels since 1959 At that time there were 335 parts per million of carbon dioxide in the atmosphere In 2005 the figure was 392 parts per million Find the increase in carbon dioxide levels and the percent of increase Round to the nearest tenth of a percent Increase carbon dioxide levels Percent increase Question Help Video parts per million

Find the number s with the following property two times the sum of 8 and a number is 9 less than seven times the same number

Lena is asked about her age She answers as follows My age is 10 more than twice the age of my younger brother How old is her younger brother if Lena is 28 years old years Question Help Video Submit Question

Complete the passage to show the identity sin x sin x x 7 7 cos x Use appropriate sum formulas cos x

It is estimate that 48 of the general population wears glasses If a random group of 14 people are selected what is the probability that a 10 People will wear glasses b Over 10 people will wear glasses C What is the expected number of people wearing glasses in a group this size

Consider the graph G shown below h 9 a 5 e f Determine whether each of the following is a perfect matching and whether it is a partial matching a h b g e f a b c d e f g h OA Is a perfect matching B Is a perfect matching OB Is a partial matching DA Is a partial matching a b b c c d d e e f f g g h h a a c e f g h OC Is a perfect matching OC Is a partial matching OD Is a perfect matching OD Is a partial matching

1 point Answer each of the following questions about the graph C shown below 1 Let S Which of the following vertices are in N S A B 0 C 00 duex 835 F I H Us 1 None of the above 174 2 Let S Which of the following vertices are in N S A VI 1 DJ 0 By 0 07 H None of the above 108 t B C B 201 By 1 3 Let S Which of the following vertices are in N S A

1 point Answer each of the following questions about the graph G shown below US 5 U7 B 22 C V3 D V4 E V5 OF V6 OG 07 01 H U8 V6 V2 1 Let S v3 v6 Which of the following vertices are in N S A V1 None of the above CIT V3 RESS

1 point Answer each of the following questions about the graph shown below 1 Let S 16 Which of the following vertices are in N S A 4 OB Occ Dod Ee OF G None of the above 2 Let S c Which of the following vertices are in N S A a DB 6 C C Dod Ee ORI G None of the above a 3 Let S a f Which of the following vertices are in N S Aa

27 000 1 Le S Which of the following vertices are in N S A U V 0 17 H Us 1 None of the above 27 U C UJ 114 Dy 2 Let S Which of the following vertices are in N S DA D 1 17 18 G 17 B None of the above OB noth 04 16 3 Le 5 1 4 J Which of the following vertices are in N S A

1 point Consider the relations R R2 R3 R4 R5 on A 1 2 3 4 defined by R 1 2 2 1 R 2 2 2 3 2 4 3 2 3 3 3 4 R3 1 1 1 2 2 1 2 2 3 3 4 4 R4 1 2 2 3 3 4 R5 1 1 2 2 3 3 4 4 Determine which of the following statements are true Select all that apply A R is not symmetric B R is reflexive C R is symmetric D R4 is transitive E R is reflexive F R5 is transitive G R5 is not reflexive H R3 is reflexive I R is transitive J R3 is not transitive K R4 is symmetric L None of the above

Consider the graph G shown below V1 W1 V2 v W v W2 V3 W3 A Is a perfect matching A Is a partial matching V3 W V V w3 W C Is a perfect matching C Is a partial matching W2 V3 W3 Determine whether each of the following is a perfect matching and whether it is a partial matching V1 V2 V3 W W2 W3 B Is a perfect matching B Is a partial matching v W v2 W V3 W3 V W3 D Is a perfect matching D Is a partial matching

Consider the graph G shown below h 9 a b C e d f Determine whether each of the following is a perfect matching and whether it is a partial matching a h b g e f OA Is a perfect matching OA Is a partial matching a b b c c d d e e f f g g h h a OC Is a perfect matching OC Is a partial matching a b c d e f g B Is a perfect matchin B Is a partial matchin a c e f g h D Is a perfect matchin D Is a partial matchin

2 1 point For all Canadian mortgages interest is compounded annually 1 point The amortization period is the length of time needed to eliminate a debt 4 1 point The amortization period and the term of a mortgage are different 5 1 point A longer amortization period means smaller payments and less total interest paid 6 1 point To find the weekly mortgage payment divide the monthly mortgage payment by fo 7 1 point Semi monthly payments are usually paid on the 1st and the 15th of the month

18 1 point Consider this amortization table for the first six months of a 195000 mortgage amortized over 15 years How much debt is owed on the house at the end of six months Principal Paid S Interest Paid S Month 1 3 5 6 187615 594 87 598 53 602 21 605 93 609 64 613 41 b 191375 1200 13 1196 47 1192 79 1189 08 1185 82 1181 60 184230 d 180845