Basic Math Questions and Answers

Use the given vectors to find vw and v v v 71 5j w 10i 8j

Given v 2i and w 2i 3j find the angle between v and w

Let u 3i j v 4i 3j and w 2j Find the specified scalar or vector 5u 3v 4w

Given v 4i j and w 3i 2j find the angle between v and w What is the angle between yond w

u 2i j v 3i j w i 3j Find the specified scalar u v w

A Differentiate the given equation implicitly and then solve for y B Solve the given equation for y and then differentiate directly A What is the implicit differentiation of the given function 9 5y 0 B 9 5y 0 C 9x 5y 0 D 9 5y 0 B Solve the given equation for y y

An investor bought stock for 40 000 Ten years later the stock was sold for 60 000 If interest is compounded continuously what annual nominal rate of interest did the original 40 000 investment earn The annual nominal rate of interest earned is Round to two decimal places as needed

K Find for the function y 7 dy dx dy dx

Use implicit differentiation to find y and then evaluate y at the point 3 y 8x 8 0 y 0 Y 3 4 Simplify your answer

K dx expr that wi 1 In x 6 187 5 X 6 The missing expression is equation

At what nominal rate compounded continuously must money be invested to triple in 9 years A rate of is required for money to triple in 9 years Do not round until the final answer Then round to the nearest tenth

K Replace with an expression that will make the equation dx sta et 9 9 e The missing expression is

Find f x 10 f x In x 0 2 In x f x

Part 1 of 3 The vectors u and v have the same direction a Find u b Find v c Is u v Explain O Points 0 of 1 10 5 10 S UJ

A plane is flying at a speed of 360 miles per hour on a bearing of N65 E Its ground speed is 390 miles per hour an its true course given by the direction angle of the ground speed vector is 30 Find the speed in miles per hour ar the direction angle in degrees of the wind

A country with two states has 16 seats in the legislature The population of each state is given by State A B Total Population86 34277 312163 654 A third state is added with 5 additional seats as shown below State A B C Total Population 86 342 77 31253 792 217 446 Does the new states paradox occur using Hamilton s method of apportionment O Yes O No

A sample of 790 elementary school children is needed to obtain a 99 5 confidence interval with a margin of error of 0 05 Correct Answer 788 Part 2 3 Part 3 of 3 c If the educator wanted to estimate the proportion in the entire United States rather than in Colorado would the necessary size be larger smaller or about the same Explain The necessary sample size would be Choose one since it Choose one depend on the size of the population 2 Ella V Espa ol 8 E B M dla

Let u 7i 4j v 9i j and w 6i Find 2u 3v w

Find the magnitude v and the direction angle 0 for the given vector v v 4i 14j v

Find the unit vector that has the same direction as the vector v v 2i The unit vector that has the same direction as the vector v is Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Type

esort plans to apportion 50 new toboggans among the four resorts based on the number of rooms in each resort as shown below Determine each resort s apportionment using Adams s meth nt Some divisor between 13 and 14 will work Resort Number of rooms A 99 Resort lumber of rooms Allocated toboggans B 119 What is each resort s apportionment using Adams s method A 99 17 C D 150 282 B 119 150 D 282 Total 650 50 Total 650

Twenty members of the executive committee of the Student Senate must vote for a student representative for the college board of trustees from among three candidates Greenburg G Haskins H and Vazquez V The preference table follows Number of Votes First Second Third 9 V G H 6 4 1 G H H H V G V G V Another way to determine the winner if the plurality with elimination method is used is to eliminate the candidate with the most last place votes at each step Using the preference table given to the left determine the winner if the plurality with elimination method is used and the candidate with the most last place votes is eliminated at each step Choose the correct answer below OA There is no winner There is a tie between Vazquez and Greenburg B Haskins OC Greenburg OD Vazquez OE There is no winner There is a three way tie

A small country consists of seven states there are 198 seats in the legislature that need to be apportioned among the seven states and the population of each state is shown in the table A B C D E F G Population 1283 2374 2725 2155 1592 2511 2017 State Find the standard quota for state C Round your answer to two decimals A 44 42 B 40 34 C 36 81 OD 45 22

N 7 Leah wrote the equation x4 6 32 2 What number makes the equation true J Not here F 7 G 7 H 0 7

Find the standard divisor for the given situation Round your answer to two decimals A school district receives a grant to purchase 62 new computers to be apportioned among the 6 schools in the district based on the student population of each school The student populations a given in the following table School A B C DE F Population 314 211 197 243 279 325 A 19 24 B 20 06 C 25 31 OD 21 90

An appropriate 95 confidence interval for u has been calculated as 0 73 1 92 based on n 15 observations from a population with a Normal distribution If we wish to use this confidence interval to test the hypothesis Ho 0 against H 0 which of the following is a legitimate conclusion O Fail to reject Ho at 0 05 level of significance We cannot perform the required test since we do not know the value of the test statistic Fail to reject Ho at 0 10 level of significance Reject Ho at 0 10 level of significance Reject Ho at 0 05 level of significance Page 8 of 10

For testing Ho 10 vs H 10 the p value is computed to be 0 04 Based on this we can conclude Ho can be rejected at x Ho can be rejected at x 0 05 Ho cannot be rejected at x 0 01 All of the above 0 10

A major department store chain is interested in estimating the mean amount its credit card customers spent on their first visit to the chain s new store in the mall Fifteen credit card accounts were randomly sampled and analyzed with the following results sample mean 50 50 and sample standard deviation 20 Assuming the distribution of the amount spent on their first visit is normal what is the shape of the sampling distribution of the sample mean that will be used to create the desired confidence interval for population mean a standard normal distribution O at distribution with 15 degrees of freedom Oat distribution with 14 degrees of freedom approximately normal with a mean of 50 50

The average time it takes for a pesticide to kill a particular pest is 360 minutes A new ingredient is added to help speed up the effect of pesticide Let u denote the mean time for the pest to die after ingesting the pesticide An entomologist is conducting an experiment to verify if the new product works more quickly What are the null and the alternative hypotheses for the appropriate test of significance Ho 360 vs H 360 Ho X 360 vs H X 360 O Ho X 360 vs H X 360 Ho X 360 vs H X 360 Ho 360 vs H 360 Ho H 360 vs H 360 40

Confidence interval cannot be used for hypothesis testing when alternative hypothesis is one tailed True False

Consider these null and alternate hypotheses Ho 0 and Ha 0 If the null hypothesis is rejected at 1 level of significance then it will necessarily be rejected at 5 level of significance True False

can think of in a really interesting way a normal curve It shows the median salary as well as the 10th 25th 75th and 90th percentiles The website provides the following information about licensed practical nurses LPNs nationally Based on HR reported data a national average with a geographic differential 10 42 334 25 46 634 50 Median 51 357 Employers Find Surveys For This Job Employers Price Your Company Jobs Employees View your Salary 75 57 128 Didn t find your job Click View as table 90 62 383 You will complete the assignment with a file submission You may upload a picture file PDF Word file or Power Point A A normal distribution curve typically displays the mean in the middle This graph displays the median Does this matter Why or why not Answer this question with two complete

Use a calculator to solve the following equation for 8 on the interval 12 12 sin 0 56 Find all the correct answers Round to three decimal places

Find the area of the indicated region We suggest you graph the curves to check whether one is above the other or whether they cross and that you use technology to check your answer HINT Se Example 1 Between y x and y 2 for x in 1 1

Show that a complex valued function h 2 on a star shaped domain D is harmonic if and only if h 2 f 2 g 2 where 2 and g 2 are analytic on D Solution Write h u iw where u w are harmonic By the Theorem on page 83 both u and w have harmonic conjugate in D since D is star shaped so thus there are analytic such that u Rey w Rev u y p 2 w v v 2 gives Take h p p iv iv 9 iv p ip then h 2 f z g z 8 Ref x To show the oposite direction Assume that h z f z g 2 where f 2 and g z are analytic on D Then h Ref Reg i Im f Im g and from Cauchy Riemanns equations follows that f 6 i 9 p iv 0 Im f x y Reg x 0 Ref dy so h 2 is harmonic Img x y i Im f Im g x dx 8 Reg dy i i 2 8 Im f dy 02 Reg x y Ref x y i 3 Im g dy 2 Im f y x 8 Ref y x Im g y x Reg y x 0

Cyrus deposits 233 57 each month into an annuity account for his child s college fund in order to accumulate a future value of 60 000 in 16 years How much of the 60 000 will Cyrus ultimately deposit in the account and how much is interest earned Round your answers to the nearest cent if necessary Itranscript AnswerHow to enter your answer opens in new window Answered 2 Points Amount Cyrus will donorit 41815 11 Formulas Keypad Keyboard Shortcuts

invests 6 154 in a savings account with a fixed annua est rate of 8 compounded continuously What will the 10 6 54e 06 10

1 point The graph describes your height in meters after 1 minutes have elapsed during a ride on a ferris wheel You boarded the ferris wheel prior to time t 0 a How long does it take the ferris wheel to complete one full rotation Include units in your answer b What is the diameter of the ferris wheel Include units in your answer c What is your height at time t 0 Include units in your answer d What is the height of the loading platform Include units in your answer e What length of time does the graph show you riding the wheel Include units in your answer h n M t min Click on graph to enlarge

Suppose a closed economy with no government spending which in equilibrium is producing an output and income of 2350 Suppose also that the marginal propensity to consume is 0 75 and that if at full employment the economy would produce an output and income of 3150 By how much would the government need to cut taxes T to bring the economy to full employment round your answer to the nearest whole value Your Answer

Consider the initial value problem a Find the eigenvalues and eigenvectors for the coefficient matrix dx dt AL 4 2 x t b Solve the initial value problem Give your solution in real form 181 Use the phase plotter pplanem in MATLAB to answer the following question Counterclockwise direction and A x 0 21 1 Describe the traiectory 8

weight is motionless d 12 cm If the weight is disturbed it begins to bob up and down or oscillate Then d is a periodic function of 1 the time in seconds so d f t Consider the graph of d f t below which represents the distance of the weight from the ceiling at time t d cn in 19 1 include units in your answer c What is the closest the weight gets to the ceiling Include units in your answer t see a Based on the graph of d f t above which of the statements below correctly describes the motion of the weight as if bobs up and down d What is the furthest the weights gets from the ceiling Include units in your answer 2 A The weight starts closest to the ceiling and begins by stretching the spring down towards the floor B The weight starts closest to the floor and begins by bouncing up towards the ceiling C The spring starts at its average distance between the ceiling and floor and begins by stretching the spring down towards the floor D None of the above b How long does it take the weight to bounce completely up and down or down and up and return to its starting position

Identify the lower class limits upper class limits and class width for the given frequency distribution Also identify the number of individuals included in the summary ONCTEER Age yr when award was won 15 19 20 24 25 29 30 34 35 39 40 44 45 49 Identify the lower class limits 0 0 0 0 0 0 0 Type integers or decimals Do not round Use ascending order Identify the upper class limits 0 0 0 0 0 Type integers or decimals Do not round Use ascending order Identify the class width Frequency 27 NM2TSLA 34 13

Twenty five people in a survey were asked to give their current checking account balances Use the balances shown in the following list to complete the frequency distribution table 110 25 207 341 176 230 139 Class 198 499 583 Fill in the missing information Intervals Account Balances 0 99 115 290 434 295 360 Class 585 370 205 294 453 Frequency Number of People 495 288 454 123 151

The length of roadways in a small country is 9 58 x 104 kilometers What is the approximate length of these roadways in kilometers written in standard form The approximate length of the roadways written in standard form is kilometers

Suppose a closed economy generates 2000 output and income in equilibrium Suppose also that the government spends 400 and imposes a lump sum tax of 200 By how much is the government in deficit round your answer to the nearest whole value Your Answer

Itranscript Determine the annual percentage yield or the effective interest rate for 500 invested at 3 52 over 10 years compounded daily Round your answer to the nearest hundredth of a percent if necessary Answer 2 Points Keypad Keyboard Shortcuts

EMIU Write the fraction as a percent 2 13 2 0 153 Round to the nearest hundredth as need 13

120 in to feet 12 inches 1 foot 3 feet 1 yard 5280 feet 1 mile 120 in

The stopwatch at the finish of a race displayed a time of 6 3458 hours Round this time to the nearest hundredth of an hour The number 6 3458 hours rounded to the nearest hundredth is hours

Suppose a closed economy has an aggregate savings equal to 300 and intended investment equal to 450 By how much must the government be in surplus round your answer to the nearest whole value Your Answer