Sequences & Series Questions and Answers

Player His Average Points Other s Average Points Other s Standard Deviation Fredo 125 145 Karl Table 2 57 137 O Fredo O Karl a Which player had the higher average points when compared to the other players on his team 153 Enter the exact answers 10 Fredo s team Number Karl s team Number 20 b Use Table 2 57 to find the value that is three standard deviations above the mean for each team c Use Table 2 57 to find the value that is three standard deviations below the mean for each team

Solve the linear programming problem Maximize and minimize P 7x 8y subject to x y s3 x 3y 4 4x 5y 220 x y 20 What is the maximum value of P Select the correct choice below and fill in any answer boxes present in your c OA P Type an integer or a fraction OB There is no maximum value of P

Match the graph given to the right to its function Choose the correct answer below O Constant function Cube function Square function O Reciprocal function ACCEND O D Identity function Square root function Absolute value function Cube root function O

150 50 572 16 6pts Make the following conversions a 2016 82 2x3 2x6 0x68 0x6 b 57 71 oight 17 3pts Place a digit in for each letter where all identical letters must have the same digit and different letters must be represented by different digits RST R

Let A 13 9 1 Find the eigenvalues of A 9 2 Find bases for the eigenspaces of A 9 3 Is A diagonalisable Give reasons 9 4 Find a matrix P and a diagonal matrix D such that P AP D 2 9 5 Find 421 You may write 221 for example as it is without calculating its value 4 9 6 Use the above to solve the following system of differential equations 6 1 2x 2x 1 2 3x 3

43 the 2 24 3 Write an equation for the shifted absolute value function graphed abo

24 Find all solutions of the equation in the interval 0 2 5 in x sin x 1 de formula using

Run a regression analysis on the following data set where y is the final grade in a math class and z is the average number of hours the student spent working on math each week hours week Grade State the rea 6 6 7 8 11 12 14 17 20 20 y 61 4 55 4 64 8 72 2 66 4 75 8 79 6 89 8 100 100

Use a Maclaurin series in this table to obtain the Maclaurin series for the given function 5e 7x n 0 1 1 x ex f x e 00 n 0 n on 7x x 1 x x x 1 0 tan x 1 15 x2n cos x 1 2n n 0 1 sin x 2 1 2n 1 x n 1 n 0 n 1 In 1 x 1 x n 1 2n 1 2 3 n 1 1 x k x 1 A 0 n X X X 2 x 1 kx 3 3 2 4 5 5 3 k k 1 2 7 xo 6 x 4 k k 1 k 3 2 x R 1 R 0 R 00 R 00 R 1 R 1 R 1

Vehicles approaching a T intersection from a minor road in a single lane have the option of turning left or right Traffic flow data in vehicles per hour is given in Figure 1 The critical gap and follow up gap are 3 secs and 2 secs for the left turn and 6 secs and 4 secs for the right turn The total approach capacity of this T junction for the minor road is designed to be 720 vehicles per hours veh h during the peak hour 400 GIVE WAY 600 200 veh h Figure 1 a Determine the number of the left turning vehicles in the peak hour 3 marks Ent puke Jongth including head of queue delay 2 marks

For the following function find the value of a f 2 and b f 4 if possible y x 5 if x 0 x 1 if x 0 a Select the correct choice below and if necessary fill in the answer box to complete your answer O A f 2 Simplify your answer There is no solution

Which of the following best explains why tan 6 tan 57 The angles do not have the same reference angle O Tangent is positive in the second quadrant and negative in the fourth quadrant O Tangent is negative in the second quadrant and positive in the fourth quadrant O The angles do not have the same reference angle or the same sign

Based on Pythagorean identities which equation is true O sin e1 cos e sec e tan e 1 O cos 1 sin e COS O cot e csc e 1 SC

Find the Taylor series at x 0 1 tan 3x4

What is the measure of angle B in the figure below A C O 30 O 45 O 60 O 90 3 B 3 2

Which equation gives the length of an arc s intersected by a central angle of 3 radians in a circle with a radius of 4 i O s 23 0 Os 1 3 O s 4 3 O s 4 3

Which expression converts 45 to radians O 45 180 180 O 45 O 45 O 45 X 180

What is the approximate degree measure of angle B in the triangle below B A 16 3 43 8 46 2 O 73 7 25 24 C

Determine intervals on which the function is increasing decreasing and constant CZER

Q 22 Determine the function of the slope shown in graph below Function of the slope ie y mx c

1 Employ the regresion function y excel solver Plot the Solutions X y 2 1 0 0 ao 1 eax to fit the following data via 2 4 45 5

Find an equation for the graph sketched below 15 4 3 2 f x 0 8 7 5 ANWAV 0 2 3 J T 766 00 11 8 IN in ky VIT

What is the magnitude of V 10 17 V Round to the nearest hundredth 1 Enter

transformation to applying a vertical compression by a dilation factor of Justify your response thoroughly to communicate your understanding of the concepts For f x log x describe the given transformation and determine an equivalent transformation to it g x f

AB passes through the points A 3 2 and B 6 8 A B is the image of AB after a dilation with a scale factor of centered at 0 2 Which of these statements is true A B has slope and y intercept 0 2 A B has slope and y intercept 0 0 A B has slope and y intercept 0 2 3 A B has slope and y intercept 0 0 3 A B has slope and y intercept 0 2 A B has slope and y intercept 0 2

Given the inscribed circle with center K which statement can you NOT conclude A B C D XK YK ZNZK ZOZK NK LYZ MK OK 0

The graph of y f x is shown in black and the graph of its transformation g x af bx c d is shown in red Determine a b c and d b d a C f x g x 13 124 114 10 94 8 54 6 7 8 9 10

10 Point A is the incenter of AFGH Find AS A B C D 3245 F R 3 5 H

A 2 4 5 6 8 B 1 5 6 and C 2 4 5 a A B C b A B c B C d Is B C Why e Find 5 different subsets of C

3 4 Let ABCD be a rectangle Let F on CD such that and E BD n AF If CD 36m and CB 14m determine the area of triangle EDA Justify your work B 14m C F 34m 14m FD AB D B E 4 E 3

and ing ing 5 Scientist studied the decay of a radioactive element The mass of the element reduces by a factor of 1 2 after each half life as show in the table below a Write the exponential equation that represents the relationship shown in the table b Use the equation to find how much of the element remains after 15 years Number of half lives t 0 Remaining Mass m 100

aluate using your calculator a e 2 b e

Question 6 Write an equation for the function graphed below The y intercept is at 0 0 5 7 6 5 4 3 2 1 1 2 3 4 5 y 4 3 2 Submit Question 1 2 3 4 5 6 7 Q Question Help Video Message instructor

Find the exact lengths x y and The figure is not drawn to scale Write your answer as a simplified fraction if possible Rationalize the denominators in necessary Part 0 3 30 260 ft 60

Which radical of 13 17 2 14 and 32 is not a real number Choose the correct answer below O 14 O 32 O 17 O 13

The data in the table below represents the percentage of patients who have survived after diagnosis of advanced stage breast cancer at 6 month intervals of time Time after Diagnosis years 0 5 1 1 5 2 2 5 3 3 5 Percentage Surviving 94 2 83 6 75 0 58 5 46 8 41 7 32 6 a Using a graphing utility build an exponential model from the data y Type integers or decimals rounded to four decimal places as needed

Given the periodic function g x x 1 1 2 g x g x 7 i Determine whether g x is even odd or neither ii Obtain the Fourier Series expansion for g x

Consider the transformations T R R T x Evaluate A B 3 D 3 4 5 3 2 7 3 4 C 7 R 7 x X1 X2 2x1 x2 2 3 5

Simplify the following radical expression 8 6 a b 8 6 ab 11 Simplify your answer

ot the ordered pair State in which quadrant or on which axis the point lies

be the line with parametric equations B 3t 5 3t 6 2t the vector equation for a line that passes through the point P 3 3 8 and intersects I at a point that is distance 3 from the point Q 3 5 6 Note that there are two possible correct answers L are root symbol where needed to give an exact value for your answer 0 8 8 10

A population of beetles are growing according to a linear growth model The initial population week 0 is Po 6 and the population after 8 weeks is Pg 70 Find an explicit formula for the beetle population after n weeks P After how many weeks will the beetle population reach 166

A car accessory is sold for 38 78 The store s markup based on cost is 53 a What is the cost of the car accessory b What is the rate of markup based on selling price a The cost of the car accessory is Round the final answer to the nearest cent as needed Round all intermediate values to six decimal places as needed b The rate of markup based on selling price is Round the final on two decimal pla Round all intormedioto volueo to oix dogimol plogo

Used P MY NOTES The profit function for a certain commodity is P x 160x x 1000 Find the level of production that yields maximum profit and find the maximum p X units ASK YOUR

Find the residual values and use the graphing calculator tool to make a residual plot 1 2 3 4 5 Given 2 7 0 9 1 1 3 2 5 4 Predicted 2 84 0 81 1 22 3 25 5 28 Residual Does the residual plot show that the line of best fit is appropriate for the data O No the points are in a curved pattern O No the points are evenly distributed about the x axis OYes the points are in a linear pattern O Yes the points have no pattern

Which statement below best characterizes the frequency distribution below 40 v n 35 30 25 20 15 10 5 3 5 7 9 13 15 OA The mean median and mode of this frequency distribution are the same B The mean of this frequency distribution is less than the median and the mode O c The mean of this frequency distribution is greater than the median and the mode D None of the statements above accurately reflect the frequency distribution above

Julia saved 1 cent 0 01 on the first day of the month 2 cents 0 02 on the second day 4 cents 0 04 on the third day and double the previous day s amount on each successive day Julia s savings for the first five days are shown in the table below Julia s Savings Day 1 2 3 4 5 On what day will Julia first save an amount greater than 1 00 Select one O day 8 day 50 day 7 Amount Saved 0 01 0 02 0 04 0 08 0 16 day 20

Write an expression for the nth term of the sequence Your formula should work for n 1 2 2 3 4 5 3 4 5 6 an n 1 n 2 Determine whether the sequence you have chosen converges or diverges converges

A major league baseball diamond is actually a square 90 feet on a side see the figure What is the distance directly from home plate to second base the diagonal of the square The distance directly from home plate to second base is approximately Type an integer or decimal rounded to two decimal places as needed feet 3rd base 90 ft 90 ft 2nd base Pitching rubber 1st base Home plate

Given the three different functions below which of the statements is NOT true f x g x X y 0 1 2 3 1 1 16 4 h x 2x 3 1 5 4 16 64 4 Oh x has the greatest y intercept Og x is a quadratic function Of x has the smallest value at f 2