Questions

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3 Find the vertex of the parabola which is the graph of the function f x x 12x 11

2 Find all the seroes of the polynomial function a 32 18x 27 State their multiplicities

3 Find the vertex of the parabola which is the graph of the function f x x 12x 11

Which is not involved in adaptive immunity Tear flow Antibody production T cells B cells Tear flow AND B cells

Select the TRUE statement regarding viruses Viruses have completely random shapes Viruses may be unicellular or multicellular Virus are considered living because they contain nucleic acid Most viruses are smaller than bacteria but bigger than ribosomes Viruses always cause death of the host cells they infect

5 You are given a dataset of 450 observations which was collected over two years from a service oriented system The observations represent service processing time in minutes You have constructed several histograms using the provided dataset one of them is shown below Discuss what you would do to model the input distribution for the service processing time 10 points Histogram Plot Decrease incbase merval width by 5 Histogram 054 0 51 0 08 0 06 0 03

Given the equation f x 4 2 2 answer the following A Growth or Decay B h C k D Horizontal Asymptote E Find f 1 Write as a coordinate pair

hich graph represents f x 3 4 2

4 For each of the following functions determine the domain Then choose the answer choice that matches each function to its domain correctly f x 3x 1 9 x 2 x 2 h x 2x 5 OA f x D 0 g x D 0 2 U 2 h x D 0 00 OB f x D 0 g x D 2 U 2 h x D OC f x D 0 g x D 2 h x D x u OD f x D Ju g x D 00 h x D OE f x D u g x D 2 0 h x D

Your local Chipotle receives an average of 20 customers per hour and can complete their order in 2 minutes Assume exponential interarrival time deterministic service time one server in the system and that customers leave as soon as they receive their order 15 points a If you plan to go to Chipotle how much time in minutes do you expect to wait in queue b What is the probability in four decimal places that there are no customers there when you arrive to Chipotle c How many customers on average will be in Chipotle

3 You have just submitted your final report for a semester long project for your Modeling and Simulation course Despite reviewing your work several times you understand that there may still exist some minor grammar or spelling errors Assuming your number of errors per page 0 1 and your report is 20 pages long answer the following questions round your answers to 5 decimal places 15 points a What is the chance that a single page contains more than 1 error is b If the first page contains 2 errors what is the chance that the next page also contains exactly 2 errors c What is the chance that your entire report contains no errors

6 Quantity y varies directly with the square root of x y has a value of 8 when x has a value of 16 Find the value of y when x 20 Round your answer to two decimal places A 17 89 OB 40 OC 8 94 OD 20 E 24 64

Given the following graph of the function y f x and n 6 answer the following questions about the area under the curve from 20 to z 6 x 1 Use the Trapezoidal Rule to estimate the area Answer T6 2 Use Simpson s Rule to estimate the area 1 0

The left right Trapezoidal and Midpoint Rule approximations were used to estimate 2 f z dz where f is the function whose graph is shown below The estimates were 0 78 0 8675 0 8632 and 0 9540 and the same number of subintervals were used in each case a Which rule produced which estimate 0 7811 1 Trapezoidal Rule estimate 2 Right hand estimate 0 7811 3 Left hand estimate 0 8675 0 8632 4 Midpoint Rule estimate 0 9540 Derween which two approximations does the true value of 2 f x dx lie A 0 8632 f x dx 0 8675 B 0 8675 f x dx 0 9540 c 0 7811 f x dx 0 8632 D No conclusions can be drawn YA 1 y f x

The graph of a function f is given below Estimate f x da using four subintervals with a right endpoints b left endpoints and c midpoints a f f x dx b f f x dz f c So f x dx 0 1 f X

a house purchased for 140 000 is expected to in value in 15 years find its appreciation equation let x be the number of years since the purchase and let y be the value of the house in dollars

The Cupcake Caf makes 4 times as much 2 revenue on doughnuts as muffins If total sales were 44 000 for May what dollar amount of each was sold

A parabola has the equation f x x 3 2 4 Complete The first one is done for you 1 What is the horizontal translation 2 What is the vertical translation 3 What is the vertex 3 to the right The following graphs are translations of y x2 Use them for 4 9 The first one is done for you 0 4 What is the horizontal translation 8 0 7 What is the horizontal translation 5 What is the vertical translation 8 What is the vertical translation 6 What is the quadratic equation 9 What is the quadratic equation Graph the following equations for parabolas 10 y x 1 2 2 11 y x 3 2 4 2

Evaluate the integral x2

A parabola has the equation f x 2 x 3 2 4 Complete 1 The vertex is 3 The function has a minimum value of 2 The graph opens The following graph is a translation of y x Use it for 4 7 4 What is the horizontal translation 5 What is the vertical translation 6 What is the sign of a 7 What is the quadratic equation for the graph Graph the following parabolas 8 y 2 x 2 5 12 9 y x 3 2 A ball follows a parabolic path represented by f x 2 x 4 8 Use this equation for 10 12 10 What is the vertex 11 Graph the parabola 12 Why does the graph stop at x 2 and x 6 12

Use the derivative f x x x 4 x 2 to determine the local maxima and minima of f and the intervals of increase and decrease Sketch a possible graph of f f is not unique The local maximum maxima is are at x Use a comma to separate answers as needed The local minimum minima is are at x Use a comma to separate answers as needed The interval s of increase is are Type your answer in interval notation Use a comma to separate answers as needed The interval s of decrease is are Type your answer in interval notation Use a comma to separate answers as needed Which is a possible graph of f O A O B C Q Q 80 80 G 10 G G O D Q G

csc e cot e sec e

Evaluate the integral 18e e2x 5

a Sketch r 6 6 sin 0 and y on the same diagram b Find the area of the region inside r 6 6 sin 0 and above the line y 2

Use the reduction formula to evaluate the integral Note Use an upper case C for the constant of integration In x dx x ln x n In x 1 In x dr

3 Sketch the graph and show all local extrema asymptotes and inflection points Show your work 15 points y xln 8 x 4 2 1 3 2 1 2 3 5 X 2 3

The form of the partial fraction decomposition of a rational function is given below A 1 B 4 C 0 Now evaluate the indefinite integral 5x 12x 4 x 3 x 4 dx ln x 3 2ln x 4 C 5x 12x 4 x 3 x 4 A Bx C x 3 x 4

Use the graph of the function to evaluate the given expressions f 4 and f 1 f 4 0 f 1 54 3

To date Jay Ward has cumulative earnings of 131 600 This week he is paid 3 000 The total amount of Social Security tax for this week is assume a rate of 6 2 on 132 900 income limit for Social Security and 1 45 for Medicare 186 00 80 60 57 66 180 00

The future value of 6 000 for four years at 8 compounded semi annually will grow to do not include cents or round your calculation 8 991 8 950 8 211 9 990

Maximize z 4x 5y x 5y 40 7x Y VI VI INI 42 Subject to x 0 Y 0 Maximum is x y

MAT 201 1 Find the extreme values of the function and where they occur Show yo work 10 points In x 1 y x 1

Bill Burne s earnings are subject to deductions for Social Security Medicare and FIT This week Bill earns 1 200 Bill who is married is paid weekly and claims three exemptions Assume the Social Security rate is 6 2 and 1 45 for Medicare His net pay for the week is Use Table 9 1 and Table 9 2 in your textbook 528 43 1 026 89 1 690 93 1 609 93

FICA tax base Never changes Changes yearly Changes once every two years Is never more than 60 000 None of these

2 Sketch the graph and show all local extrema and inflection points Show your work 15 points y x 2 6 10 500 250 250 10 500

Al Miler the owner of Al s Garage estimates that he will need 29 000 for new equipment in 15 years Al decides that he will put aside the money now so that in 15 years the 29 000 will be available His bank offers him 10 interest compounded semiannually Al must invest today 6 710 60 6 942 60 6 701 60 125 335 10 None of these

Gracie Shay wants to buy a new Hummer in five years Gracie estimates the cost of the Hummer will be 28 000 If she invests 12 000 now at a rate of 6 compounded semiannually she Will have enough money Will have exactly 16 000 Will have 18 000 Will have 16 126 80 None of these

On May 17 Jane took out a loan for 33 000 at 6 to open her law practice office The loan will mature the following year on January 16 Using the ordinary interest method 360 days what is the maturity value due on January 16 34 342 34 320 34 323 62 34 254

Jim Smith is a salesman who receives a 1 100 draw per week against his commission He receives a 12 commission as an incentive on all sales Sales for Jim were 205 000 for the month Assuming a four week month Jim s commission is 24 600 20 200 23 500 26 400 None of these

Lisa Richter made a one time deposit of 5 000 at 4 compounded semiannually for 5 years What would her balance be at the end of five years assuming she is still earning 4 compounded semiannually 5131 8131 8 800 6 095

1 Find the derivative for each function below at x 1 Leave your answer in radical a f x 2x 1 x3 b y 3 3x 1

Matty Kaminsky owns a new Volvo His June monthly interest is 400 The rate is 8 Matty s principal balance at the beginning of June is use 360 days 65 740 58 64 470 58 65 704 58 56 470 58

Differential pay schedule is based on FICA Different levels of performance FUTA Gross pay None of these

Jim Murphy borrowed 30 000 on a 120 day 14 note Jim paid 5 000 toward the note on day 95 On day 105 he paid an additional 6 000 The payment was applied first to the interest owed with the remaining payment applied to the principal balance Jim s adjusted balance after the first payment is 25 000 28 891 67 1 108 33 26 108 33 None of these

A 40 000 loan at 4 dated June 10 is due to be paid on October 11 The amount of interest is assume ordinary interest 503 00 2 500 00 546 67 105 33 None of these

If you are paid twice a month you are being paid Weekly Biweekly Semimonthly Monthly None of these

Banks and other financial institutions sometimes calculate simple interest based on Exact interest method Using 30 days for each month Using 366 days in the year Bankers rule ordinary interest None of these

Find the values of the six trigonometric functions using calculator if 0 26 Round answer to the nearest thousandth

Evaluate the integral Remember to use absolute values where ap 49 x4 dx X