Sequences & Series Questions and Answers

The comprehensive graph of a polynomial function y f x is shown How many real zeros does the function f have The function f has real zero s 8 JA Q S

5 4 J 2 1 Y intercept End Behavior 24 22 20 18 16 14 12 10 0 10 Degree 6 4 2 0 C 2 Zeros and multiplicity 6 Leading coefficient As x g x As x g x 2 g x Equation of g x in intercept form Challenge Equation of g x in standard form

Which of the below is the completely factored form of the polynomial show 4a 96 2a 3b 2a 3b 2a 3b 2a 36 4a 9b a b

The comprehensive graph of a polynomial function y f x is shown How many real zeros does the function f have The function f has real zero s 125 125 T8 O Q

Decide whether the following statement is true or false If false tell why For f x x 5 x 8 5 is a zero of multiplicity 3 Choose the correct answer below A The statement is true OB The statement is false because 5 is not a zero of f x OC The statement is false because 5 is a zero of multiplicity

State the excluded values for each n 4 4n 8 9 11 63 2x x x 2x 35 10 12 10 12 m 17m 72 8m 72m p 12p 27 p 16p 63

Find the value of the property given the following Annual Rent 612Vacancy and collection los 5 Operating expenses 35 of gross income Capitalization rate 9

Consider a retirement savings account where the monthly contribution is 110 for the first 20 years is increased to 215 for the next 25 years and then is increased once again to 425 for the last 10 years The APR is always 6 5 compounded monthly What is the value of the account at the end of 55 years The value of the account at the end of 55 years is Round the final answer to the nearest cent as needed Round all intermediate values to two decimal places as needed

Solve the following system of equations If there is a unique solution enter it as an ordered pair in the form x y If there is no solution enter Inconsistent If there are infinitely many solutions enter your answer as a line in the form y mx b 2x 4y 24 5x 7y 54

els that are the same 6x 2 2 6x 1 a Show that when x 3 Arun s answer is incorrect Explain why his method is incorrect f Discuss your answers to parts a to e with other learners in How will you convince them about your findings if your ans Simplify these expressions Make sure you factorise the numerator before you cancel with the denominator 6x 3 b 5x 10 3 5 Show that 6x 4 20x 25 simplifies to 7x 3 C 6x 9 3 d 8x 20 4

13 How does the graph of y y m x x compare with the graph of y y m x x Include examples in your explanation

12 Which equation matches each graph Describe each graph in terms of its slope and y intercept b y 3 x 2 d y 3 x 2 a y 3 2 x 1 c y 3 2 x 1 Graph A Graph B y 4 2 b Graph C 0 2 4 14 Match each graph with its equation Justify your choice a 2 2 0 0 2 0 y f x 6 ly 2 13 How does the graph of y y m x x compare with the graph of y y m x x Include examples in your explanation 0 2 Graph D 2 X 0 2 y 1 2 x 2 y 2 2 x 1 y2 2 x 1 y 1 2 x 2 X y g x y 1 x 2 1 y 2 x 1 y 1 3 x 2 2 c a y 4 b y h x 2 0 7 10 b y 3 c y 1 4 d y y 2 3 2 35 2 x 8 15 Use a graphing calculator or a computer with graphing software Graph each equation Sketch or print the graph Write instructions that another student could follow to get the same display x 5 x y 1 x 2 3 y 1 y 1 Volume of Liquid mL 10 20 2 y 2 x x 11 x 2 x 2 0 375 x 4 0 5 x 6 3 16 Chlo conducted a science experiment where she poured liquid into a graduated cylinder then measured the mass of the cylinder and liquid Here are Chlo s data Mass of Cylinder and Liquid g 38 9 51 5 a When these data are graphed what is the slope of the line and what does it represent b Choose variables to represent the volume of the liquid and the mass of the cylinder and liquid Write an equation that relates these variables c Use your equation to determine the mass of the cylinder and liquid when the volume of liquid is 30 mL d Chlo forgot to record the mass of the empty graduated cylinder Determine this mass Explain your strategy

8 Solve each equation below 4 pts each a 0 05 1 15 5 c log 2x 4 2 b log x log x d 4ln 6x 5 15 2

quation 2 pts each log 1 243 x 7 Graph f x log4 x 2 5 pts a What is the y intercept s b What is the x intercept s c What is the domain of f x d What is the range of f x log 49 1 log 0 log 2 0 x

a 3 3 3 3 11 5 7 1 27 13 15 x 8 15 17 19 1 n 11 21 12 b 2 5 x 10 7 x 15 3 k 5 V 5 2 3 2 3 2 x 2 14 9 4 8 10 12 6 2 21 1 14 16 m 12 5 18 x 2 2 3 11 v 4 n 5 6 3 m 14 4 b 8 8 1 P 6 n 3 3 2 2 1 7

USE SALT A report set a goal of 0 541 for the proportion of babies still being breastfed one year after birth The organization also used the survey data to estimate the proportion who were still being breastfed one year after birth to be 0 351 for babies born in a particular year Suppose that the survey used a random sample of 1 000 parents and that you want to use the survey data to decide if there is evidence that the goal is not being met Let p denote the population proportion of all babies born in that particular year who were still breastfeeding at 12 months Hint See Example 10 10 Hp The shape of the sampling distribution is approximately normal The sampling distribution is centered at 0 0224 x a Describe the shape center and variability of the sampling distribution of p for random samples of size 1 000 if the null hypothesis Ho p 0 541 is true Round your standard deviation to four decimal places 0 541 MY NOTES PRACTICE ANOTHER b Would you be surprised to observe a sample proportion as small as p 0 532 for a sample of size 1 000 if the null hypothesis Ho P 0 541 were true Explain why or why not Round your answer to four decimal places Consider the event surprising if the probability the event occurs when Ho P 0 541 is true is less than 0 05 Since the probability of a sample proportion this small or smaller is 0 met The standard deviation of the sampling distribution is We would not B be surprised to observe a sample proportion of p 0 532 for a sample of size 1 000 if the null hypothesis Ho P 0 541 is true The probability of a sample proportion this small or smaller is 0 0132 X which is greater than 0 05 c Would you be surprised to observe a sample proportion as small as p 0 507 for a sample of size 1 000 if the null hypothesis Ho p 0 541 were true Explain why or why not Round your answer to four decimal places Consider the event surprising if the probability the event occurs when Ho P 0 541 is true is less than 0 05 0 05 there is 0 We would B be surprised to observe a sample proportion of p 0 507 for a sample of size 1 000 if the null hypothesis Ho p 0 541 is true The probability of a sample proportion this small or smaller is 0 05 which is less than d The actual sample proportion observed in the study was p 0 351 Based on this sample proportion is there convincing evidence that the goal is not being met or is the observed sample proportion consistent with what you would expect to see when the null hypothesis is true Round your answer to four decimal places Consider the evidence that the goal is not being met convincing if the probability the event occurs when Ho P 0 541 is true is less than 0 05 which is less than O convincing evidence that the goal is not being

a Assuming that L 3 in the figure below sketch the function to which the Fourier e series converges for 0 x 3 g x 3 if 0 x 1 0 if 1 x 2 1 if 2 x 3

3N a101 b 22 c 34 Submit Answer 3 57 Points DETAILS STITZTRIG3 2 3 006 ASK YOUR TEACHER Use the Law of Cosines to find the angles if possible Round your answers to two decimal places If an answer does not exist enter ONE MY NOTES PRACTICE ANOTHER

You may need to use the appropriate appendix table or technology to answer this question The average U S daily internet use at home is two hours and twenty minutes A sample of 81 homes in a certain city showed an average usage of one hour and 40 minutes with a standard deviation of 90 minutes We are interested in determining whether or not the average usage in that city is significantly different from the U S average a State the null and alternative hypotheses in minutes to be tested Enter for as needed 1 00 Your answer cannot be understood or graded More Information Ho H 1 00 X X b Compute the test statistic 0 65 X Your answer cannot be understood or graded More Information c The null hypothesis is to be tested using a 0 05 Determine the critical value s for this test Round your answer s to two decimal places If the test is one tailed enter NONE for the unused tail test statistic 2 58 test statistic 2 2 58 X X d What do you conclude O Reject Ho We can conclude that the average usage in that city is significantly different from the U S average O Do not reject Ho We can conclude that the average usage in that city is significantly different from the U S average O Do not reject Ho We cannot conclude that the average usage in that city is significantly different from the U S average Reject Ho We cannot conclude that the average usage in that city is significantly different from the U S average X

5 Solve the following exponential equation 1 25 55 6

Find the unknown angles in triangle ABC for the following triangle if it exists A 29 1 b 44 1 ft a 26 9 ft Select the correct choice below and if necessary fill in the answer boxes to complete your choice Round to the nearest tenth as needed A There is only one possible set of remaining angles The measurements for the remaining angles are B and C B There are two possible sets of remaining angles The measurements for when B is smaller are B 52 9 and C 98 The measurements for when B is larger are C 23 8 C No such triangle exists

3 Solve the following exponential equation 64 1024

1 Solve the following exponential equation 1 625 54 3

6 Rewrite the given expression using natural logarithms only Ing 17

If in air at 30 C will cool from 100 C to 70 C in 1 minute find its temperature at the end of 2 minutes

4 Find the exact value of the following logarithmic expression logi 81

Use the parent function f n log and transformation techniques to graph A z log x 7 Als indicate which transformation s is are applied Determine the domain range and vertical asymptote of Select all transformations that apply DReflect the graph of f about the n axis Horizontally stretch the graph off by a factor of 7 O Horizontally compress the graph of f by a factor of 7 Dvertically compress the graph of f by a factor of 7 Shift the graph of f 7 units down Oshift the graph of f 7 units to the left Vertically stretch the graph of f by a factor of 7 Reflect the graph of about the y axis shift the graph of f 7 units up shift the graph of f 7 units to the right

Julio deposits 1500 in a savings account that pays 2 4 interest per year compounded monthly The amount in the account after n months is given by An 1500 1 0 024 0 024 12 a Find the first six terms of the sequence Round your answers to the nearest cent A A A3 A4 A5 A6 S b Find the amount in the account after 5 years Round your answers to the nearest cent Aso

that exists B 147 7 c 8 124 b 14 121 Select the correct choice below and if necessary fill in the answer boxes with in the choice A There is only one possible solution for the triangle The measurements for the remaining angles A and C and side a are as follows A 14 4 C 18 a 6 6 Round to the nearest tenth as needed A B There are two possible solutions for the triangle The measurements for the solution with the longer side a are as follows O C 0 A O Round to the nearest tenth as needed Round to the nearest tenth as needed The measurements for the solution with the shorter O O Round to the nearest tenth as needed C Round to the nearest tenth as needed Round to the nearest tenth as needed C There are no possible solutions for the triangle Round to the nearest thousandth as needed a Round to the nearest thousandth as needed side a are as follows a Round to the nearest thousandth as needed

KSJ between 12 00 noon and 1 00 pm are the minute and hour hands of a

3 Diyagram bir enine taraf ndan kesilen iki paralel izgiyi g stermektedir 23 7x 12 l s ise 26 n n l s ka t r A 3x 12 B 7x 12 C 7x 12 D 192 7x 12 34 LO 5 0 6 78

from a survey of 1 015 hiring managers and human resource professionals The article noted that many employers are using social networks to screen job applicants Of the 1 015 people who participated in the survey 699 indicated that they use social networking sites to research job applicants For the purposes of this exercise assume that the sample can be regarded as a random sample of hiring managers and human resource professionals a Suppose you are interested in learning about the value of p the proportion of all hiring managers and human resource managers who use social networking sites to research job applicants Thi proportion can be estimated using the sample proportion p What is the value of p for this sample Round your answer to four decimal places p b Based on what you know about the sampling distribution of p is it reasonable to think that this estimate is within 0 02 of the actual value of the population proportion Explain why or why not Round your answer to four decimal places and the standard deviation of this distribution can be estimated as In addition the We know the sampling distribution of p will be centered at the Select sampling distribution is not mound shaped and symmetric X So we cannot O The Empirical Rule implies about 95 of our sampling distribution s values will fall within two standard deviations of the center but two standard deviations is greater than 0 02 say our value of p is likely to be within 0 02 of the actual value because of the following fact O The Empirical Rule implies about 95 of our sampling distribution s values will be at most one standard deviation away from the center and our standard deviation is less than 0 02 O The Empirical Rule implies about 95 of our sampling distribution s values will be at most one standard deviation away from the center but our standard deviation is greater than 0 02 We cannot make use of the Empirical Rule since our sampling distribution isn t mound shaped and symmetric The Empirical Rule implies about 95 of our sampling distribution s values will fall within two standard deviations of the center and two standard deviations is less than 0 02 Submit Answer 3 4 Points DETAILS PREVIOUS ANSWERS MY NOTES 0 200 PECKSTAT3 8 3 503 XP MI MY NOTE An article included data from a survey of 2 183 hiring managers and human resource professionals The article noted that many employers are using social networks to screen job applicants and tha this practice is becomin Of the 2 192 people who participated in the sunoy 1 211 indicated that they use social networking sites such as Facebook MySpace and LinkedIn to

When a website asks you to agree to a privacy policy do you actually read the policy before agreeing Researchers asked people in a representative sample of 4 272 adults in the United States if they read privacy policies and found that 940 said that they always or often read them The paper also says that of the 2 600 people who said they at least look at privacy policies before agreeing to them 32 said that they understood very little or none of the privacy policies they read LUSE SALT a Use the given information to estimate the proportion of people who at look at privacy policies before agreeing to them who understand very little or none of the policies Use a 95 confidence interval You can assume that the sample of 2 600 people is representative of the population of interest Enter your answer using interval notation Round your numerical values to three decimal places MY NOTES Give an interpretation of the interval in context There is a 95 chance that the actual proportion of people who at least look at privacy policies before agreeing to them who understand very little or none of the policies falls within this interval O There is a 99 chance that the true proportion of people who at least look at privacy policies before agreeing to them who understand very little or none of the policies falls directly in the middle of this interval We are 95 confident that the actual proportion of people who at least look at privacy policies before agreeing to them who understand very little or none of the policies is within this interval We are 95 confident that the actual proportion of people who at least look at privacy policies before agreeing to them who understand very little or none of the policies falls directly in the middle of this interval We are 95 confident that the mean number of people who at least look at privacy policies before agreeing to them who understand very little or none of the policies falls within this interval b Would a 90 confidence interval be wider or narrower than the 95 confidence interval from part a A 90 confidence interval would be narrower than the 95 confidence interval from part a because the z critical value is smaller 8

When a website asks you to agree to a privacy policy do you actually read the policy before agreeing Researchers asked people in a representative sample of 4 271 adults in the United States if they read privacy policies and found that 920 said they always or often read them LUSE SALT Use the five step process for estimation problems EMC3 to construct a 99 confidence interval for the proportion of adults in the United States who always or often read privacy policies Enter your answer using interval notation Round your numerical values to three decimal places Interpret the interval There is a 99 chance that the true proportion of adults in the U S who always or often read privacy policies falls directly in the middle of this interval We are 99 confident that the mean number of adults in the U S who always or often read privacy policies falls within this interval We are 99 confident that the true proportion of adults in the U S who always or often read privacy policies falls directly in the middle of this interval We are 99 confident that the true proportion of adults in the U S who always or often read privacy policies falls within this interval O There is a 99 chance that the true proportion of adults in the U S who always or often read privacy policies falls within this interval Submit Answer DETAILS MY NOTES PREVIOUS ANSWERS PECKSTAT3 9 3 051 S MY NOTES

Write the Roman numeral as a Hindu Arabic numeral MMDCLXVI OA 2 656 OB 2 666 OC 2 565

Consider the equation z 1 i Find the value of z which satisfies this equation and which has the second smallest positive argument 0 0 0 2 Express your answer as z reie where r and 0

Find the solution to the following lhcc recurrence an 34an 1 an 289an 2 for n 3 with initial conditions a 204 a2 3468

A a da a b ve a b i lemlerinin modellemeleri verilmi tir a b a b k Buna g re pozitif tam say lar k mesinde X m a la b ve PLO 6 m b y X ifadelerini sa layan m nin alabilece i ka farkl de er va DIA

Two forces act at a point in the plane The angle between the two forces is given Find the magnitude of the resultant force forces of 310 and 249 newtons forming an angle of 67 The magnitude of the resultant force is Round to the nearest newton as needed newtons

26 x x x 5 x A 5 B 10 5 2 C 15 5 3 D 20 5 4 E 30

The graph of a circle with equation x 3 y 2 9 is shown y 764 3 2 OP 234 5 56 7 234567 If this circle is dilated by a factor of 2 what will the equation of the new circle b O A x 3 y 2 18 O B x 3 y 2 36 OC x 6 y 4 18 x OD x 6 y 4 36

Rationalize the denominator Assume that the variable is positive 15 n

Rationalize the denominator 7 10 77

K Determine whether the following statements are true and give an explanation or counterexample Assume x 0 and y 0 a In xy In x Iny b In 0 1 d c In x y In x Iny d e e dx e ex x x 1 dx f d dx x 3 e x for any integer n21 1 g The area between the curve y and the x axis on the interval 1 e is 1 X GREEEED A The statement is false The Product Rule of Logarithms states that In xy In x In y B The statement is true The Quotient Rule of Logarithms states that In xy In x Iny CC The statement is true The Product Rule of Logarithms states that In xy Inx Iny D The statement is false The Sum Rule of Logarithms states that Inx In y In x y b Choose the correct answer below OA The statement is false because In 0 0 OB The statement is true because e 1 OC The statement is false The natural logarithmic function In x is not defined at x 0

Determine whether the following statements are true and give an explanation or counterexample Assume x 0 and y 0 a In xy In x Iny b In 0 1 c In x y In x Iny d e 2 ex x x 1 1 g The area between the curve y X a Choose the correct answer below d dx x 3 e3x for any integer n 2 1 and the x axis on the interval 1 e is 1 OA The statement is false The Product Rule of Logarithms states that In xy In x In y B The statement is true The Quotient Rule of Logarithms states that In xy In x Iny OC The statement is true The Product Rule of Logarithms states that In xy In x Iny OD The statement is false The Sum Rule of Logarithms states that In x In y In x y

422 459 420 406 457 401 436 360 406 372 336 331 324 269 474 333 458 396 242 402 279 418 531 415 493 564 436 242 211 456 What is the total of these number added

Find the perimeter and area of the shown figure 12 108

Find the perimeter and area of the shown figure 20 180 The exact perimeter of the rectangle is Simplify your answer Type an exact answer using radicals as needed The exact area of the rectangle is

1 Is the table below an example of inverse variation Justify your choice 2 pts X 3 9 12 Justification y 24 86

S 1 2 and T Fun S R be the linear transformation defined by Find bases for Ker T and Im 7 Basis of Ker 7 Basis of Im 7 Enter functions using characteristic funtions writing 4 for y etc T f 2 21 2 4f 1 3f 2 6f 1