Sequences & Series Questions and Answers

Find the median for the following set of data 74 68 64 63 71 72 64 Provide your answer below

3 sin x 5x 1 similar integrand whose behaviour is known is 1 x 3 2 A converges OB diverges so we find that this in 3

Note Exercises preceded by an asterisk are of a more challenging natur 1 Given OO with OEI CD CD OC mCF Find E E F D

7 DFB Inc expects earnings next year of 4 22 per share and it plans to pay a 2 13 dividend to shareholders DFB will retain 2 09 per share of its earnings to reinvest in new projects that have an expected return of 15 2 per year Suppose DFB will maintain the same dividend payout rate retention rate and return on new investments in the future and will not change its number of outstanding shares Assume next dividend is due in one year a DFB s growth rate of earnings is Round to one decimal place b If DFB s equity cost of capital is 12 9 then DFB s stock price will be nearest cent Round to the c Suppose instead that DFB plans to pay a dividend of 3 13 per share next year and retained only 1 09 per share in earnings That is it chose to pay a higher dividend instead of reinvesting in as many new projects If DFB maintains this higher payout rate in the future what stock price would you estimate for the firm now DFB s stock price would be Round to the nearest cent Should DFB follow this new policy a No DFB should not raise dividends because companies should always reinvest as much as possible b Yes DFB should raise dividends because the return on new investments is lower than the cost of capital c Yes DFB should raise dividends because according to the dividend discount model doing so will always improve the share price d No DFB should not raise dividends because the projects are positive NPV

1 of Write the next four terms of the geometric sequence given the first term and the recursive formula If your term is not an integer type it as a decimal rounded to the nearest tenth a 486 and an 3 a2 a3 a4 an 1 Quiz navigation 1 Reggie Whitfie 3 4 5 2 Finish attempt

Write the expression as a single logarithm Express powers as factors log 3 x log 3x C log 3 x log 3x Type an exact answer Use integers or fractions for any numbers in the expression

If 4000 is borrowed at a rate of 6 75 interest per year compounded quarterly find the amount due at the end of the given number of years For each answer enter a number Round your answers to the nearest cent a 3 years b 5 years c 7 years

Use the present value table to complete Note Round the PV factor to 4 decimal places and final answer to the nearest cent Future Amount Desired 8 000 Length of Time 10 years Rate Compounded 8 semiannually Table Periods Rate Used P V Factor P V Amou

Use the graph to identify the a x intercept or state that there is no x intercept b y intercept or state that there is no y intercept a Select the correct choice below and fill in any answer boxes within your choice OA The x intercept is Type an integer OB There is no intercept Use the graph to identify the a x intercept or state that there is no x intercept b y intercept or state that there is no y intercept a Select the correct choice below and fill in any answer boxes within your choice OA The x intercept is Type an integer OB There is no x intercept Plot the intercepts to graph the equation 5x 4y 20 GILB Use the graphing tool to graph the equation Use the intercepts when drawing the line If only one intercept exists use it and another point to draw the line Click to GALLS 8 10 10 A

Question An account is opened with an initial deposit of 2 500 and earns 1 8 interest compounded semi annually What will the account be worth in 30 years Round your answer to the nearest cent Do NOT round until you have calculated the final answer answer below

Edgar accumulated 5 000 in credit card debt If the interest rate is 20 per year and he does not make any payments for 2 years how much will he owe on this debt in 2 years with monthly compounding Round your answer to the nearest cent Do NOT round until you calculate the final answer

4 Find two values of that satisfy the equation 050 2m sin 3 5 Find the exact value of each expression Write the answer as a single fraction Do not use a calculator

etermine if the following sequence by induction is convergent or divergent Check if it is bounded and if it is decreasin a a a 4 n 1 e a 1 1 A a2

order to determine her career path Priscilla randomly selects 100 actresses living in Hollywood and discovers that th verage income is 75 000 per year In fact one actress surveyed made 5 million dollars this year Why is this statistic misleading Select the correct answer below The data contain one or more outlier s The sample size is insufficient The sample is biased The computation of the statistic involves a calculation error

Sampling error best fits which of the following descriptions Select the correct answer below the natural variation that results from selecting a sample to represent a larger population O a method of selecting a sample that gives every member of the population an equal chance of being selected an issue that affects the reliability of sampling data other than natural variation O the situation in which not all members of the population are equally likely to be selected

d Based on the graph above determine the amplitude midline and period of the function Midline y S Amplitude

Given the following table of values compute f g 4 Do not include f g 4 in your answer Provide your answer below x 1 2 3 4 f x g x 14 4 9 3 6 1 5 2

23 A researcher asks a random sample of 300 people the following question Do you think that people who hurt defenseless animals should be punished Is this question biased Why or why not O A Biased The researcher is only asking 300 people which is not enough and he is leaving out lots of people O B Biased The wording of the question specifically the use of people who hurt defenseless animals makes it biased Not biased People who hurt defenseless animals should be punished Not biased This question is worded in a way to find out exactly what people O C D think

21 A theater has 50 seats in the first row and every row behind that one has 4 more seats than the one in front of it If the theater has 64 rows how many seats are in the theater O A 302 seats OB O C n 11264 seats 3648 seats 1097 core

24 Find the sum of the following series O A 261 B C n 1 D 106 63 107 3n 2

15 What is the sum of the first 7 terms of this series 3 1 1 3 A B C 4 333 4 498 4 872 D 5

8 In June Cory begins to save money for a video game and a TV he wants to buy in December He starts with 20 Each month he plans to save 10 more than the previous month How much money will he have at the end of December O A 154 31 O B O C 228 72 D 189 74 251 59

12 The University of Minnesota annually collects data from their graduate students to measure their experience in graduate school Which of the following survey questions would be considered the least biased O A How would you rate your experience working with your academic adviser Poor Fair Moderate Good Excellent B Given the influence your academic adviser has on your experience how would you rate your academic adviser Poor Fair Moderate Good Excellent O C The academic advisers at the University of Minnesota are well trained How would you rate your academic adviser Poor Fair Moderate Good Excellent D Do you agree that the academic advisers at the University of Minnesota are excellent in their jobs

What is the sum of the series 10 6 2 OA 15 658 B 6 138 O C O D 12 276 10 773

Divide x 11x 38x 40 x 2 x 9x 20 O A x 13x 12 1 64 X 2 x 9x 20 B x 13x 64 168 x 2

O A 5 and 3 9 21 10 I 5 OB 9 i 141 10 9 21 10

2 Calculate the sum of the series O A 221 OB O C O D 1873 1904 1926 1 4 7 103 106 P

The Petersons have an apple pressing machine that they use to make apple juice The first pressing gets about 13 of the total juice in the apple 4 Each succeeding pressing extracts about of the remaining juice in the apples What is the least number of pressings it will take to get at leas 4 3 of the apples juice X pressings 6 What is the least number of pressings it will take to get at least of the juice

Factor out the GCF w w 9 w 9 0

Researchers recorded that a certain bacteria population declined from 320 000 to 100 in 30 hours At this rate of decay how many bacteria will there be in 22 hours Round to the nearest whole number Provide your answer below bacteria

Three pets are competing in a best pet contest Sixty children vote and the pet with the most votes will win What is the smallest number of votes that a pet could receive and still win the contest votes

Find the Maclaurin series for the function Use the table of power series for elementary functions f x ex 3 f x co n 0 3 X 3 n n

R N R N S 2 Can someone show me the steps

5 Show that the subgroup V 1 12 34 13 24 14 23 is a normal subgroup o A 5 pts

The number of bacteria in a culture is n t after t hours n t 500e0 15t How many bacteria are present after 12 hours Round to the nearest whole number Provide your answer below

Solve the triangle if a 37 ft b 58 ft and c 34 ft a 36 X B 108 Y 32 X Assume Za is opposite side a Z3 is opposite side b and Zy is opposite side c Enter your answer as a number answer should be accurate to 2 decimal places

SA 12 m Calculate Surface Area Give the exact answer or round to 2 decimal places m 8m

6 8 9 Find the value of y 12 8 O 15 X 6 Y

The figure shows the graph of a function f Suppose that Newton s method is used to approximate the roots of the equation f x 0 with initial approximation x 6 y4 1 0 1 T a Draw the tangent lines that are used to find x and x3 and estimate the numerical values of x and X3 Round your answers to one decimal place x2 x3 b Would x 8 be a better first approximation Explain We know that x 8 Select be a better first approximation because the tangent line at x 8 intersects the x axis Select s than does the first approximation X 6

Solve the logarithmic equation 1 64 x log 41 The solution set is

Solve for a in this equation 6 13 7 Enter an exact answer or round your answer to the nearest tenth Provide your answer below X

You are considering a moving company to help you move They charge 68 per hour plus a base fee of 340 If C represents the total cost of the move and H represents the number of hours of time what is the relationship between C and H Select the correct answer below O H 68C 340 O H 340C 68 OC 340H 68 OC68H 340 FEEDBACK

Puerto Rico saw a population decrease of 11 8 since 2010 If the population of Puerto Rico in 2010 was approximately 3 72 million people write an exponential equation to model Puerto Rico s population in millions after t years Provide your answer below A

A huge Ferris wheel with a diameter of 130 meters completes one rotation every 30 minutes Riders board from a platform 1 meter above the ground Express a rider s height above ground as a function of time in minutes O 65cos t 66 O 66cos t 65 O 65cos t 66

When solving the following equation by factoring 3x2 19x 140 Which of the following is a factor x 7 x 2 3x 7 3x 2 None of these

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5 7 9 2n 1 896 n A 25 B 27 C 29 D 30 E 3

10 7 6 5 4 thot 9 7 The domain of f is 6 The range of f is 2 6 7 4 9 fot a Consider the function y f x shown in the graph above f has an Select an answer of f is increasing on the interval s f is decreasing on the interval s 89 at 57

The sum of the digits of the positive integer n is 161 The sum of the digits of 2n is 196 The digits of n include one 2 five 4s six 8s p 3s q 5s and no other digits What is p2 q2 A 265 B 509 C 245 D 353 E 293

Find the mean 5 18 12 3 7 19 A 10 5 B 9 5 10 97