Questions

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DETAILS Let vec B 4 95m at 60 0 vec C and vec 4 have equal magnitudes The direction angle of vec C is larger than that of vec 4 by 25 0 Let vec 2 A vec B 27 9m and vec 2 B vec C 33 9m Find the magnitude in m and direction in degrees of vec A

cot theta square root 3 0

Question 9 Prove the following statements by Mathematical Induction a 3 6 9 3 1 15 pts b 1222 3 1 c y 5 1 2m 1

Find the length x to the nearest whole number 240 66 38

Solve the formula for the indicated variable B rw x for w The solution is w

Solve Clear fractions first 52 53 7 1 3 3 x 18 6 6 The solution is x Type an integer or a simplified fraction

Jerry left a 2 40 tip on a meal that cost 15 What percent of the meal s cost was the tip What was the total cost of the meal including the tip The tip was of the meal s cost The total cost of the meal including the tip was

Graph the polar equation Create a chart of many ordered pairs in polar form and plot the points to show your work r 4sin20

Solve using the multiplication principle Don t forget to perform a check 2 8 7x 35 The solution is x Simplify your answer Type an integer or a fraction

Solve for m ag q m The solution is m Simplify your answer

Determine whether 11 is a solution of the equation 5 x 1 50 Is 11 a solution O No Yes

Translate to an inequality Use the variable x for the price of the amusement park ticket The price of an amusement park ticket is no less than 20 The inequality is

What point on the line y 3x 10 is closest to the origin Let D be the distance between the two polots What is the objective function in terms of the x coordinat D Type an expression The interval of interest of the function is Simplify your answer Type your answer in interval notation The point on the line y 3x 10 closest to the origin is Type an ordered pair Simplify your answer Type Integers or simplified fractions

The monthly incomes for 12 randomly selected people each with a bachelor s degree in economics are shown on the right Complete parts a through c below Assume the population is normally distributed 4450 93 459 4455 89 4151 48 3727 53 4283 44 4527 81 4407 28 3946 27 4023 68 4221 55 a Find the sample mean x 4263 3 Round to one decimal place as needed b Find the sample standard deviation S Round to one decimal place as needed

B If DE 16x 3 EF 9x 11 and DF 52 find HG E D H

The polynomial of degree 5 P x has leading coefficient 1 has roots of multiplicity 2 at x 4 and x 0 and a root of multiplicity 1 at x 5 Find a possible formula for P x P x

Verify the identity cot csct csct sint To verify the identity start with the more complicated side and transform it to look like the other side Choose the correct transformations and transform the expression at each step cot 2 csct csct Do not simplify csct sint

Use the standard normal distribution or the t distribution to construct a 95 co interval for the population mean Justify your decision If neither distribution can be used explain why Interpret the results In a random sample of 12 mortgage institutions the mean interest rate was 3 62 and the standard deviation was 0 48 Assume the interest rates are normally distributed Which distribution should be used to construct the confidence interval OA Use a normal distribution because the interest rates are normally distributed and is known OB Use a t distribution because the interest rates are normally distributed and is known OC Use a normal distribution because n 30 and the interest rates are normally distributed D Use a t distribution because it is a random sample is unknown and the interest rates are normally distributed O E Cannot use the standard normal distribution or the t distribution because is unknown n 30 and the interest rates are not normally distributed Select the correct choice below and if necessary fill in any answer boxes to complete your choice A The 95 confidence interval is 5 28 7 12 Round to two decimal places as needed B Neither distribution can be used to construct the confidence interval

1 point A street light is at the top of a 13 5 ft tall pole A man 5 3 ft tall walks away from the pole with a speed of 5 0 feet sec along a straight path How fast is the tip of his shadow moving when he is 40 feet from the pole Your answer 1 962962 ft sec Hint Draw a picture and use similar triangles

EXAMPLE history past present ng 1 source geography clue 2 government goods civics 3 culture economics money 4 geography South America inquiry 5 ocean events river 6 money culture 7 citizenship rights customs ocean 8 history monarchy democracy 2 Complete the sentences Use correct capital letters 1 Culture 2 historian is the study of the physical features of Earth is the study of the rights and Words to us historian culture responsibilities of citizens geograp 3 90graphy is the study of money resources goods econom civic ever and services 4 A events 5 economics and way of life studies history includes information about customs In history class you study civics from the past

UNIT 1 EXAMPLE You hear I m Gia I study life science You write I m Gia I study 1 Hi I m Ben I study planets and the life 2 Hello I m Mrs Park In my class you learn about 3 I m Matt I study 4 Hi I m Amy You are in my 5 Good morning I m Mr Dunn Welcome to 6 Hello I m Mr Reed I teach 7 Hey I m Nate My class focuses on the Ea science sonsize to livi engin univ non appli phy things things science class 5 Listen Write yes or no D EXAMPLE You hear Science is a way to solve problems You write yes 1 2 3 science of s

3 1 2 2 Complete the sentences 4 1 Life science is the study of universe things 2 Scientists nprast things when they think about what is different 3 Earth and space scientists study our planet and the empor 4 Scientists ving Words to use universe contrast non living things when they think about what is the same 5 Physical science is the study of non living things living compare at the science steps in order Investigate together Discuss your ideas

Write an equation for the function graphed below 7 6 5 4 3 2 2 3 4 6

Divide Check your answer by showing that the product of the divisor and the quotient plus the remainder is the dividend 6y 2 2y 3 2y 2

Find the missing length in the simila triangles 16 Find the missing length in the similar triangles 18 6 12 15 9

Nolan Walker decided to buy a used snowmobile since his credit union was offering such low interest rates He borrowed 3 100 at 3 75 on December 26 2021 and paid it off February 21 2023 How much did he pay in interest Assume ordinary interest and no leap year Use Days in a year table Note Do not round intermediate calculations Round your answer to the nearest cent Interest paid

Translate the statement into a confidence interval Approximate the level of confidence In a survey of 3336 adults in a country 44 believe the economy is getting better Three weeks prior to this survey 56 believed that the economy was getting better The survey s margin of error is 1 Use the results from the newer survey The confidence interval for the proportion is D Round to three decimal places as needed

5 A city is planning a new children s park Two contractors are bidding for the project Contractor A will construct the playground for 2 500 000 and estimates annual maintenance to cost 100 000 Contractor B will construct the playground for 3 500 000 and annual maintenance will be 75 500 In both cases the contractors will maintain the park for 20 years The relevant rate of interest is 8 On the basis of NPV analysis which contractor would you recommend

On April 5 2022 Janeen Camoct took out an 10 25 loan for 31 000 The loan is due March 9 2023 Use ordinary interest to calculate the interest What total amount will Janeen pay on March 9 2023 Ignore leap year Use Days in a year table Note Do not round intermediate calculations Round your answer to the nearest cent Maturity value

es On April 5 2022 Janeen Camoct took out an 10 25 loan for 31 000 The loan is due March 9 2023 Janeen s terms are ordinary interest Sabrina Bowers took out the same loan as Janeen Sabrina s terms however are exact interest Ignore leap year Use Days in a year table a What is Sabrina s difference in interest Note Do not round intermediate calculations Round your answer to the nearest cent Difference b What will Sabrina pay on March 9 2023 Note Do not round intermediate calculations Round your answer to the nearest cent Amount

Question 4 Find the derivatives of the following functions a 7 pts f x log4 x 4x 1 10 e 10

In a random sample of 8 people the mean commute time to work was 33 5 minutes and the standard deviation was 7 4 minutes A 98 confidence interval using the t distribution was calculated to be 25 7 41 3 After researching commute times to work it was found that the population standard deviation is 8 8 minutes Find the margin of error and construct a 98 confidence interval using the standard normal distribution with the appropriate calculations for a standard deviation that is known Compare the results The margin of error of is Round to two decimal places as needed

Harold Hill borrowed 15 200 to pay for his child s education at Riverside Community College Harold must repay the loan at the end of 10 months in one payment with 4 interest a How much interest must Harold pay Note Do not round intermediate calculation Round your answer to the nearest cent Interest to pay b What is the maturity value Note Do not round intermediate calculation Round your answer to the nearest cent

Question 3 Find an equation of the tangent line to the given curve at the giver point sin xy x y at 0 0

Look at the graph 101 50 10 5 0 5 10 5 10 What is the equation of the horizontal asymptote

Nolan Walker decided to buy a used snowmobile since his credit union was offering such low interest rates He borrowed 3 100 at 3 75 on December 26 2021 and paid it off February 21 2023 How much did he pay in interest Assume ordinary interest and no leap year Use Days in a year table Note Do not round intermediate calculations Round your answer to the nearest cent Interact poid

Translate the statement into a confidence interval Approximate the level of confidence In a survey of 1069 adults in a country 74 said being able to speak the language is at the core of national identity The survey s margin of error is 3 7 The confidence interval for the proportion is CD Round to three decimal places as needed

8 A successful alumni of UNO wants to establish a scholarship that will pay 2 engineering students 4000 per semester per year assume the students can enroll for only 2 semesters a year If the university earns 6 on endowment accounts what amount must be deposited today by the alumni Hint first calculate the total amount that is required each year for 2 students for 2 semesters

On May 3 2020 Leven Corporation negotiated a short term loan of 630 000 The loan is due October 1 2020 and carries a 5 20 interest rate Use ordinary interest to calculate the interest What is the total amount Leven would pay on the maturity date Use Days in a year table Note Do not round intermediate calculations Round your answer to the nearest cent Maturity value

5 A machine costs 125 000 to purchase and will provide 15 000 per year in additional revenue for 10 years At the end of 10 years the machine can be sold for 35 000 What is the NPV of this machine if the relevant rate of interest is 6

1 How much must be deposited into a savings account in year 0 that pays 7 interest in order to make the following withdrawals Year Cash flow 0 1 0 2 3000 3 4000 4 2500 5 4500

The monthly incomes for 12 randomly 4450 93 4596 75 4366 68 selected people each with a bachelor s degree 4455 89 4151 48 3727 53 in economics are shown on the right Complete parts a through c below 4283 44 4527 81 4407 28 3946 27 4023 68 4221 55 Assume the population is normally distributed a Find the sample mean x Round to one decimal place as needed

In a random sample of 6 cell phones the mean full retail price was 547 90 and the standard deviation was 188 00 Further research suggests that the population mean is 433 06 Does the t value for the original sample fall between to 99 and to 99 Assume that the population of full retail prices for cell phones is normally distributed The t value of t fall between to 99 and to 99 because to 99 Round to two decimal places as needed

The grade point averages GPA for 12 randomly selected college 2 4 3 4 2 6 students are shown on the right Complete parts a through c below Assume the population is normally distributed 1 8 0 9 4 0 2 4 1 5 3 9 0 3 2 2 3 1 a Find the sample mean x Round to two decimal places as needed

14 A corporate bond is sold for 920 It pays interest of 60 every year and is valid for 10 years At the end of 10 years the bond issuer will redeem the bond for 1000 If you purchase the bond and hold it for the 10 years what would your rate of return be

10 Dorothy invested 250 000 in a rental property She earns net revenue of 50 000 per year from the property If she keeps the property for 10 years what is her rate of return Here assume the salvage value is 0

13 The owner of a corner lot is trying to decide between two alternate uses for the land His options are Fast food rest Gas station Initial cost 800 000 1 100 000 Y1 net benefit 150 000 190 000 Y2 net benefit 150 000 225 000 Y3 to Y10 150 000 275 000 The salvage value for both options is 0 at the end of 10 years The owner has an MARR of 15 for all projects Using IRR analysis which project would you recommend

7 A company is planning to purchase a new machine to meet increased demand Both options under consideration have useful lives of 10 years and no salvage value at the end Cash flows for both are as follows Annual maintenance Annual Machine Initial Cost costs income A 400 000 20 000 80 000 B 650 000 30 000 160 000 Use NPV analysis to determine which machine would be a better option Interest rate is 8 Hint first compute the net annual benefit annual cost annual income

12 Byron deposited 20 000 in a savings account 15 years ago He withdrew 85 000 today and closed the account Compute the rate of interest on the account