Sequences & Series Questions and Answers

1 Find the radius of convergence and interval of convergence of the following series x 3 n 5 3

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1 Sketch each of the following equations on the graph grid below Label each with its equation y 4sin x 2 y 2 cos x 4 y sin x 4 2 3 2 T 7 2 T 3 2T XA

Find a polynomial function f for the graph with vertex 5 4 and x intercept 1 0 www 10 X 110 Q The equation of the parabola is y x Simplify your answers Type an integer or a fraction

Find the function y ax bx c whose graph contains the points 1 8 2 13 and 2 7 What is the function y Simplify your answer

3 10 points Find the Taylor series of the function e2x 5 around x 3

Determine if the values of the variables listed are solutions of the system of equations 3x z 4z 26 2y x 5y x 2 y 3 z 5 2 3 5 11 6z 43 Is 2 3 5 a solution of the system of equations OA No the solution does not satisfy either 2y z 11or x 5y 6z 43 OB No the solution does not satisfy 3x 4z 26 OC Yes this is a solution to the system of equations OD No the solution does not satisfy either 3x 4z 26 or 2y z 11 OE No the solution does not satisfy either 3x 4z 26 or x 5y 6z 43 OF No the solution does not satisfy x 5y 6z 43 OG No the solutions does not satisfy any of the equations OH No the solution does not satisfy 2y z 11

If two indistinguishable dice are rolled what is the probability of the event 6 6 1 6 5 0 0833 X What is the corresponding event for a pair of distinguishable dice 6 6 1 6 5 6 6 6 1 6 5 6 6 5 6 1 O 6 6 1 1 5 5 6 5 6 1 O 1 6 5 6 6 5 6 1 O 1 6 5 6

A dodecahedral die has 12 faces numbered 1 12 If the die is weighted in such a way that 2 is twice as likely to land facing up as 1 3 is three times as likely to land facing up as 1 and so on what is the probability distribution for the face landing up Outcome 2 5 6 7 8 9 Probability 1 3 4 10 11 12

TB MC Qu 04 61 Static Anchor Company sold merch Anchor Company sold merchandise with a cost of 560 to a customer the failure to make the necessary entries have on the company s finan

Question 52 of 60 Sam invests 1 600 in a bank The amount of money in his account increases at a constant rate each year The table below shows the amount in Sam s account after each year Which linear function best models the given data O fix 1 800x 200 Of x 200x 1 600 O fix 200x 1 600 Of x 1 800x 200 O f x 1 600x 200 Next Reset Year 1 2 3 4 5 6 Amount 1 800 2 000 2 200 2 400 2 600 2 800

07 27 ok 2 nt D Inces A substantial portion of Inventory owned by Prenties Sporting Goods was recently destroyed when the roof collapsed during a rainstorm Prentics also lost some of its accounting records Prentiss must estimate the loss from the storm for Insurance reporting and financial statement purposes Prentiss uses the periodic Inventory system The following accounting Information was recovered from the damaged records Beginning inventory Purchases to date of storm Sales to date of storm The value of undamaged Inventory counted was 80 355 Historically Prentiss gross margin percentage has been approximately 17 percent of sales Required Estimate the following a Gross margin in dollars b Cost of goods sold in dollars c Ending Inventory d Amount of lost Inventory 203 100 398 000 601 500 a Gross margin b Cost of goods sold C Estimated ending inventory d Inventory lost

Question 42 of 60 The following pie chart shows the percentage of students that participated in the given sports If the total number of sports participants is 500 what is the ratio of the number of students who participated in football to the number of students who participated in soccer 4 21 O 5 4 O 20 7 O 1 4 O 4 1 Student Sport Participation Soccer 10 Rugby 10 Tennis 25 Footba 40 Baseball Other 5 10

Three relationships are described below I The amount of fuel used on a trip increases as the size of the car increases and as the distance traveled increase II As the number of people helping mow a lawn increases the time it takes to mow the lawn decreases III The cost of having a house painted increases as the size of the house increases What type of variation describes each relationship I is joint II is inverse and III is direct O I is direct II is inverse and III is joint O I is joint II is direct and III is inverse I is direct II is joint and III is inverse

can be worth more or less including zero depending on your answer A new crew of painters takes two times as long to paint a small apartment as an experienced crew Together both crews can paint the apartment in hours How many hours does it take the experienced crew to paint the apartment It takes hours for the experienced crew to paint the apartment

40 ACT PREP MATH PART ACT Math Test 1 Edition 3 Question 40 of 60 Gary is driving a car along a straight road at a uniform speed The following table shows the number of miles he travels every hour How many miles does Gary travel in one hour O 240 miles O 360 miles O 120 miles O 60 miles O 480 miles Ned Reset Hours Number of Miles Traveled 120 2 4 240 6 8 360 480

Question 38 of 60 Sabrina s family held a garage sale last weekend They recorded the cost for each item as shown below What is the median cost of the data O 3 00 O 4 00 O 2 50 O 2 00 O 3 50 Item 1 2 3 4 5 Cost 2 3 6 4 3 1

Question 39 of 60 Samantha uses of a tablespoon of sugar for of a batch of pudding How many tablespoons will she use for the entire batch of pudding O 8 tablespoons O 6 tablespoons O 16 tablespoons O4 tablespoons O2 tablespoons

Add State the sum in simplest form 3x 2 x 4 X I x x 12 4x 1 x 2x 8 4x 1 x x 12 3x x 7 x x 12 be uneven because questions can be worth more or 3x 6x 7 x x 12

Start R Suppose they run at a constant speed of 2 meters second An expression giving their distance from the starting line is expression in terms of t An expression giving their distance to the finish line is in terms of t Submit Question Finish a Enter an Enter an expression

Question 50 of 60 A researcher surveyed 200 people from various age groups asking if they like action movies The results of the survey are shown in the table below That percentage of the people in the 31 40 age range responded yes 44 O 60 67 40 11 Ages Ages Ages 10 20 21 30 31 40 Yes Responses 31 No Responses 16 23 17 21 14 Ages Ages 41 50 51 24 20 12 22

An earthquake in California measured 4 9 on the Richter scale Use the formula R log A to determine approximately how many times stronger the wave amplitude A of the earthquake was than Ao O A 79 433 Ao O A 389 221Ao O A 134 340

Suppose f x 2x 15 f x 4 f 4x For full credit you must upload or show all of your work below Edit Y Insert Y Formats Y E 6 BIUX X AA

x y satisfy the equation SFJ 55 2 a solution to the equation y 2

The amount y in grams of the radioactive isotope beryllium 7 remaining after t days is y a 0 5 t 53 where a is the initial amount in grams What percent of the beryllium 7 decays each day Round your answer to the nearest tenth of a percent

Given that lim f x 2 and lim g x 6 find the indicated limit X 4 X 4 lim g x f x X 4 Which of the following shows the correct expression after the limit properties have been applied O A OB O C O D lim g x X 4 g x f x lim f x X 4 lim f x lim g x X 4 X 4 lim g x lim f x X 4 X 4 lim g x f x Y 4

3 Exercise 4 20A Algo Effect of Inventory transactions on the Income statement and balance sheet Perlodic system Appendix LO 4 9 Bill Rose owns Rose Sporting Goods At the beginning of the year Rose Sporting Goods had 2 900 In Inventory During the year Rose Sporting Goods purchased Inventory that cost 13 500 At the end of the year Inventory on hand amounted to 4 100 Required 45 56 a Calculate the cost of goods available for sale during the year b Calculate the cost of goods sold for the year c Calculate the amount of Inventory Rose Sporting Goods would report on the year end balance sheet a b Cost of goods sold c Inventory reported on year end balance sheet Cost of goods available for sale

01 40 27 The following Information for Year 2 is taken from the accounts of Tuttle Company The company uses the periodic Inventory system Inventory December 31 Year 1 Purchases Purchase returns and allowances Purchase discounts Freight on goods purchased under terms FOB shipping point Freight on goods sold under terms FOB destination Cost of goods sold Based on this information what is the Inventory as of December 31 Year 22 Multiple Choice 28 320 20 920 19 240 8 800 40 800 680 480 1 680 880 29 200

A zero coupon bond with a face value of 3000 and a 2 5 interest rate compounded semiannually will mature in 9 years What is a fair price to pay for the zero coupon bond today A fair price to buy the band at would be Do not round until the final answer Then round to the nearest cent as needed

A plane flies 1 2 hours at 110 mph on a bearing of 30 It then turns and flies 2 1 hours at the same speed on a bearing of 120 How far is the plane from its starting point 30 120 1

23 CT PREP MATH PART ACT Math Test 1 Edition 3 Question 23 of 60 Betty attempted to prove that the diagonals of a parallelogram bisect each other using the image shown In which step did Betty make her first error Step 4 Step 6 Statements 1 Diagonals PR and QS intersect at point Given T 2 PQ and RS are parallel PS and QR Given are parallel 3 PQRS 4 ZQPR SRP PQS RSQ 5 APQT ARST 6 PT RT QT ST Reasons Opposite sides of a parallelogram are congruent Alternate interior angles theorem SAS congruence criterion Corresponding parts of congruent triangles are congruent 7 PR and QS bisect Definition of each other segment bisector

1 Select one Exponential Functions and Equations Question 9 The number of people at a concert can be modeled by the following equation where p is the number of people and t is the time passed in minutes P 30 1 10 20 61 Based on the model which of the following statements is true 8 1 O There were 20 people attending at the start of the concert There were 30 people attending at the start of the concert O There were 50 people attending at the start of the concert O There were 110 people attending at the start of the concert

Select one De Exponential Functions and Equations How will the graph of f x 2 3 2 be different from g x 2 3 De O O O O g x is shifted down 2 units g x is shifted up 2 units g x is shifted left 2 units g x is shifted right 2 units

ET PREP Question 27 of 60 Which expression represents the area of the square inscribed in the circle 04x 4 x 1 2x 4 D2r Ned Reset

Exponential Functions and Equations Question 4 If log10 2 what is the value of x Select one 8 O O O X X O 100 I 1 100 100 100

ACT PREP MATH PART ACT Math Test 1 Edition 3 Question 20 of 60 Consider the following table of values for the function fx x 3 1 If the function f undergoes the vertical and horizontal shifts shown below which table accurately shows the values of the function g O X O O g x X 200 2 g x 14 8 X 2 g x 5 2 g x 5 x 2 g x 20 3 3 3 9 132 10 3 2 3 10 4 0 4 6 AT 4 15 4 1 4 4 5 1 5 5 5 10 5 2 5 2 6 0 6 6 6 5 6 5 6 4 x 0 10 1 5 2 NN 2 g z f z 2 4 3 1 4 2

The augmented matrix that corresponds to a system of linear equations in 2 and T is T 3 15 2 11 1 Ex 42 I2 Ex 42

ACT PREP MATH PART ACT Math Test 1 Edition 3 Consider the function and its graph below Which statement describes the function O The function has one y intercept at 1 O The value of f x approaches 1 as x approaches infinity The function has one x intercept at 1 O The value of f x approaches 1 as x approaches negative infinity O The value of f x approaches infinity as x approaches infinity A 1 0 6 f z log z 1 f x ME 2 0 6 2 8 X

Find the given trigonometric ratios Write each ratio as a fraction and as a decimal rounded to the nearest hundredth 9 sin R cos R 10 cos D cos E 3 sin R 30 15x 16 cos R x 12 Given that sin 15 13 Given that cos 62 30 12 35 X O 16 R Find the value of x to the nearest tenth 14 15 D 65 97 61 0 259 write the cosine of a complementary angle 0 469 write the sine of a complementary angle 72 28 11 sin M sin N 12 16 N W 15 40 M

Question 18 of 60 Sam opened a savings account with an initial deposit of 2 000 Since then he has never made any other deposits or withdrawals His savings account earns 0 4 interest monthly and an annual bonus of 1 5 interest Which equation gives the approximate amount A x he has in his savings account as a function of x the number of years since his initial deposit O A x 2 000 1 019 O A x 2 000 1 059 x O A x 2 000 1 019 x O A x 2 000 1 065 A x 2 000 1 059 x

ACT PREP MATH PART ACT Math Test 1 Edition 3 Question 14 of 60 Judith throws a ball in the air The height of the ball is represented by the following function where h f represents the height of the ball in feet when the ball has been in the air for t seconds h t 16t 32t 4 What will be the height of the ball at 2 seconds 32 feet O 8 feet O4 feet 6 feet 20 feet Nexx Reset 2023 Edmentum All rights reserved NASDAQ 1 08 Search O

For problems 4 and 5 solve each equation for x Round to the nearest thousandth Show each step 4 9 5

adult s ticket and a child s ti 7 Jamil always throws loose c

In Exercises 15 22 describe the transformation from the graph off to the graph of g See Example 3 15 16 17 19 20 21 X f x g x f x k X f x g x a f x X g x f x k 2 f x g x X 2 1 0 f x 8 3 g x 26 11 f AYA A 6 2 9 11 2 X 2 1 85 2 89 6 1 2 2 g 1 0 2 1 4 3 18 0 0 0 1 2 2 2 0 1 5 4 9 8 1 g x f xh WAYA 1 2 0 13 2 37 0 2 2 16 16 N 24 f 2 X X

X cises 27 30 th determine whether the function is even odd or neither See Example 3 2 g x 2x5 6x 2 25 3x h x x 4x 1 26 AY X j x 2x 5x

1 O O Fill in the blank with an appro Cubic centimeters cm cm Cubic centimeters cm are a

3 Draw a Finite State Machine whose first two outputs are 11 then outputs 001 001 001 without the spaces for any infinite input string The input alphabet is 0 1 E g For any infinite string the output would be 11 001 001 001 without the spaces

Evaluate the sum of the following finite geometric series 128 4 8 16 32 Sn Type a whole number

Forty percent of consumers prefer to purchase electronics online You randomly select 8 consumers Find the probability that the number of consumers who prefer to purchase electronics online is a exactly five b more than five and c at most five a Find the probability that the number that prefer to purchase electronics online is exactly five P 5 1 645 Round to three decimal places as needed b Find the probability that the number that prefer to purchase electronics online is more than five P x 5 Round to three decimal places as needed c Find the probability that the number that prefer to purchase electronics online is at most five P x 5 Round to three decimal places as needed

a It is shifted 4 unit s left b It is shifted 4 unit s right What are the solutions of the equ 9 x 4x 21 10 5z 2z 3 0 11 15 8x 14x 12 z z 12 0 13 c 5c 0