Sequences & Series Questions and Answers

Find all solutions in positive integers x y of the equation x 2 15 Hint Consider that for every integer x x 0 1 6 mod7

Find the first three nonzero terms of the Maclaurin series for the function and the values of x for which the series converges absolutely f x 2 cos x In 1 x What are the first three nonzero terms of the Maclaurin series for f x Type an exact answer What are the values of x for which the series converges absolutely Simplify your onewer Tune your answer in interval notation

The values of a period 2x function f t in one full period are given Sketch several periods of its graph and find its Fourier series 9x 9t x t 0 0 0 1 f t Sketch several periods of its graph Choose the correct graph below OA 9A 1 9x Find its Fourier series f t Q E OB 9 1 9x Q CCLLS

The following table shows the distribution of household incomes in 2010 for a sample of 1 000 households in a country with incomes up to 100 000 Income Bracket Households 0 19 999 240 20 000 39 999 290 40 000 60 000 80 000 59 999 79 999 99 999 1800 170 120 Use this information to estimate to the nearest 1 000 the average household income for such households HINT See Example 6

x 2 if x 2 if x 2 Graph g x 2x 1 5 pts

The model below represents a division problem H 0 1

The elevations in feet of three cities are marked on the number line shown below City P 10 5 City Q 0 5 10 15 City R 20 25 30 The point O on the number line represents sea level Which statement must be true A City P and City Q are above sea level B City Q and City R are below sea level C City P is above sea level and City Q is below sea level D City P is above sea level and City R is below sea level

5 Lindsey is on the second floor of a building 9 2 meters up and the angle of depression from Lindsey to Pete is 79 Find the distance from Pete to the base of the building to the nearest tenth of a meter

Sam borrowed 5 118 at an annual rate of 5 4 If he will repay this debt weekly for 41 weeks how much will each payment be Round your answer to the nearest dollar

The sum of two numbers is 46 Their difference is 8 Find the numbers The smaller number is The larger number is

Compute the future value of an annuity in which quarterly payments 4 each year of 149 are made for 10 years at an annual rate of 4 2 Round your answer to the nearest dollar

Question 11 Complete the table to determine whether each function represents exponential growth or exponential decay Select Growth or Decay for each function Function x 4x 1 x 16 f 1 5x 7 f x 2 12 3x f x 6 0 5 x x 4 f x 1 53 4 8 2x f x x 4 1 Growth O O O O O O

4 al 1 If y is the solution of the initial value problem 2 ryy dx 20 dy 0 v e 2e then g e s 1 20 e C2 OP 20 none of these

What is the area of the circle 15 m sq meters 23 55 O C L

1 Let B 2 x x 1 2x x 2 x C 1 x x be bases for P a Find P the transition matrix fromB to C b Use matrix inversion to find P 1 the transition matrix from C to B

a Expand x 5 and simplify your answer Use the expansion to estimate 3 02 correct to four decimal places 5 Marks

MP Justify Conclusions Rodrigo is buying a 5 foot long fishing rod for his father for his birthday He wants to put it in a box so that his dad will not be able to guess what is in the box The box he wants to use is 4 feet long and 4 feet wide Will the pole fit in the box Justify your reasoning

10 The red tailed fox is becoming extinct There are only 450 known to exist in the world and their number is decreasing at 27 per year In how many years will there be less than 25 foxes left

onential Functions Question 12 4 1 65 Part 2 of 5 HW Score 48 84 21 of 43 O Points 0 of 5 Use a calculator with a key or a key to solve the following The exponential function f x 565 1 026 models the population of a country f x in millions x years after 1968 Complete parts a e a Substitute 0 for x and without using a calculator find the country s population in 1968 The country s population in 1968 was 565 million b Substitute 27 for x and use your calculator to find the country s population to the nearest million in the year 1995 as modeled by this function The country s population in 1995 was million

nential Part 1 of 5 Use transformations of the graph of f x e to graph the given function Be sure to give the equation of the asymptote Use the graph to determine the function s domain and range h x e x 4 Which transformations are needed to graph the function h x 2x 4 Choose the correct answer below OA The graph of f x ex should be stretched horizontally by a factor of 2 and shifted downward by 4 units OB The graph of f x ex should be shrunk horizontally by a factor of 2 and shifted upward by 4 units OC The graph of f x ex should be shrunk horizontally by a factor of 2 and shifted downward by 4 units D The graph of f x ex should be stretched horizontally by a factor of 2 and shifted upward by 4 units CILE

Part 1 of 5 Next question a Substitute 0 for x and without using a calculator find the country s population in 1968 The country s population in 1968 was million O Points 0 of 5 Use a calculator with a key or a A key to solve the following The exponential function f x 565 1 026 models the population of a country f x in millions x years after 1968 Complete parts a e

Part 1 of 5 Begin by graphing f x 2x Then use transformations of this graph to graph the given function Be sure to graph and give the equation of the asymptote Use the graph to determine the function s domain and range If applicable use a graphing utility to confirm your hand drawn graphs g x 2 1 Which transformation is needed to graph the function g x 2 1 Choose the correct answer below A The graph of f x 2 should be shifted 1 unit to the right B The graph of f x 2 should be shifted 1 unit upward OC The graph of f x 2 should be shifted 1 unit downward OD The graph of f x 2 should be shifted 1 unit to the left

Question 10 10 points A partial set of values for the function of g x is given 1 3 2 n x 4 75 1 0 4 5 4 776 2 1 Determine the average rate of change from x 1 to x 2 0 2 2 O O H

Question 4 points Identify the end behavior of the polynomial function g x x 3 Hint It may help to graph the polynomial function with your calculator first O As the graph of the polynomial continues to the left the graph moves upward As the graph of the polynomial continues to the right the graph moves upward As the graph of the polynomial continues to the left the graph moves upward As the graph of the polynomial continues to the right the graph moves downward As the graph of the polyn mial continues to the left the graph moves downward As the graph of the polynomial continues to the right the graph moves upward As the graph of the polynomial continues to the left the graph moves downward As the graph of the polynomial continues to the right the graph moves downward

Question 3 10 points The function g x 4 2 is graphed at the right Asx o determine g x i e As x approaches negative infinity what does g x approach g x co g x co g x 4 g x 4 2 9 3 Asymptote y 2

Aisha surveyed 300 of the students in her school about their favorite color 285 students said their favorite color was red What percentage of the surveyed students said their favorite color was red

Question 2 20 points Which shows the equation 3x 2y 8 solved for y y y 3x 4 Or Y x 4 y 3x 4 Question 3 20 points Consider the following system

Ana Paula currently sells stoves for Lester s Stove Store at a salary of 16 000 plus a 25 commission for each stove she sells Wayra s Stove Store offers her a position with a salary of 11 000 plus a commission of 45 for each stove she sells How many stoves would she need to sell for the options to be equal

Nathaniel has been offered positions by two car dealers The first company pays a salary of 18 000 plus a commission of 300 for each car sold The second pays a salary of 10 200 plus a commission of 600 for each car sold How many cars would need to be sold to make the total pay the same

Solve the system of equations If there is exactly one solution write as an ordered pair If not choose one of the other options 2x y 9 4y 34 8x No solution O Infinite number of solutions

Annual Percentage Rate APR Mr Winking is purchasing a car and needs to finance a 24 000 from the bank with an annual percentage rate APR of 4 8 He is financing it over 5 years and making monthly payments What is the monthly payment Monthly Payment 104 54 378 21 P T 28 x2 22 1

Jessie purchased a used car from a small business They offered to let him finance or borrow 3200 for a term of 2 years at 11 a year using Simple Interest How much interest will Jessie have to pay the used car dealer 176 352 387 20 704 Question 2 18 points

Quizzes Phoenix 2023 Algebra X ett k12 ga us d2l Ims quizzing user attempt quiz start frame a Quiz Stephanie Vega Martinez Attempt 2 Question 4 14 3 points V Saveu

A bakery sold 76 mocha cupcakes in a day which was 95 of the total number of cupcakes sold that day How many total cupcakes did the bakery sell that day

Anumeticseres Determine S26 for the arithmetic series shown below 7 10 5 14 17 5 21 94 5 1319 5 88 98 1365 Question 3 14 3 points Arithmetic Series Find the sum of the finite arithmetic series

21 12 3 14 15 S 37 Time Left 1 28 59 Neftall Moreno Miranda Attempt 1 Cannot be determined because the sample size is too small Question 27 3 3 points A manufacturer found that the crack pressure of their football helmets is normally distributed with a mean of 150 lbs and a standard deviation of 11 lbs If 28 helmets were randomly selected to be tested find the probability that the crack pressures have a mean that is less than 145 lbs 0 0051 0 0081 0 0451 0 5247 Sign out

Data Value Question 20 3 3 points Given the heights of U S men aged 18 to 24 years are approximately normally distributed with a mean of about 69 inches and a standard deviation of 3 inches What percent of men are shorter than 6 feet 72 inches H N 1418 3435 120N

A science teacher recorded the pulse rates for each of the students in her classes after the students had climbed a set of stairs She displayed the results by class using the box plots shown Pulse Rates nda Attempt 1 Class I Class 1 Class 2 Class 3 Class 2 Class 3 Class 4 60 65 70 75 80 85 90 95 100 Which class generally had the highest pulse rates after climbing the stairs

J 9 15 Question 10 3 4 points Justin and TJ are servers at a local restaurant The table below shows the tips they earned Tips Torsday Thursday Rodin 632 100 333 542 42 Which student has a higher median tip for the week and by how much LL 334 40 40 SHI Justin s median tip is 4 more than TJ s median tip TJ s median tip is 4 more than Justin s median tip Justin s median tip is 3 more than TJ s median tip T s median tip is 3 more than Justin s median tip

Question 17 3 3 points In the following data set what word would best describe the data entry 10 10 18 18 19 19 20 21 21 23 23 24 27 Bias Outlier Range Mean Question 3 3 points Consider the following histogram

4 x 24 x 2 4 f x 5 x 6 f x x 1 X 0 0 10 Zeros VA Domain HA Range Zeros VA Domain HA Range Zeros VA Domain HA Range

What interest rate would be necessary for 3 350 investment to grow to 6 000 in an acco compounded weekly for 19 years Number

16 Springs A formula used in the study of springs is T 2n k Where T is the period of a spring the time for the spring to stretch and return to its restin point m is the mass on the spring in kilograms and k is the spring s constant in newtons meter A mass of 1400 kilograms rests on a spring Determine the period of the spring if the spring s constant is 65 000 newtons meter

Solve the equation 5x 2 7 28 0 108 Ox x 2 X 6 201 X 21

Condense the logarithm and simplify if possible Slog x 3log y log x O log 15 log 14xy log x log x y xy

Find the inverse of the following y log x 15 O O Y 6 15 y 6 15 y 6 15 y 6 15

What is the domain of the following function which is also shown in the graph y log z 3 All Real Numbers R X O 0x 3 Ox 0 432

Suppose that Diana felt comfortable with a monthly payment of 200 for a used car she doesn t want to pay more than four years and her credit rating gets her a 1 99 APR financing What formula should Diana use if she wants to know how large of a loan she can get Group of answer choices

Starting at noon Gabriel observed the amount of snow on his lawn during a blizzard He wrote an equation to represent s how many inches of snow were on the lawn s 0 021x 6 5 where a represents the number of minutes past noon What is the meaning of the s value when x 1 The amount of snow on the lawn at 1 p m The amount of snow on the lawn at noon The amount of snow on the lawn at 12 01 p m How much more snow is added to the lawn every minute

The graph below is the function f x 5 4 3 2 5 32 1 Find f 1 N 2 03 4 5 Find lim f x x 1 Find lim f x 1 Find lim f x 1 3 4 5 d