Sequences & Series Questions and Answers

The D O T collected data for a particular stretch of 1 85 and found that the average speed was 70 mph with a standard deviation of 15 mph and the distribution is approximately normally distributed The actual Speed Limit for the stretch of road is a maximum of 70 mph and minimum of 40 mph What percentage of drivers actually drive between 40mph and 70 mph A 34 1 34 1 13 6 15 9 47 7 84 1 97 7

The scores of the top ten finishers in a recent race are listed below 65 66 66 67 67 67 68 70 70 71 Find the mean score 66 67 67 7

Complete the following parts given the line 6x 19y 25 Enter all answers in exact reduced form No decimals are allowed a If y decreases by 19 units what is the corresponding change in x b If x increases by 2 units what is the corresponding change in y c If x decreases by 3 units what is the corresponding change in y d If y increases by 6 units what is the corresponding change in x

What effect does k have on the parent function y 1 x when k 0

11 Show that there exists a root of the g x 3r 2 in between 3 4

The balance on a credit card that charges a 20 APR interest rate over a 1 month period is given in the following table Days 1 3 200 initial balance Days 4 20 300 100 purchase Days 21 30 150 150 payment What is the finance charge on the average daily balance for this card over this 1 month period finance charge Round to the nearest hundredth

1 For each of the following sets G and operations state with justification whether or not a is a closed binary operation b is associative c there is an identity element d all elements have an inverse e G under is a group R 0 and f g x f x g x i G is the set of functions f R o 20 Here Ro is the set of non negative real numbers ii G is the set of functions f RR and f g x f x g x

Solve the system of equations if possible If there are infinitely many solutions express X X X3 and x4 in terms of the parameter t If there is no solution enter NO SOLUTION X 3x 6x3 2x4 11 5x2 16 X1 X 2x 1 X2 14 2x1 X1 X2 X3 X4 10x3 3x4 4x3 2x3 3x4 X

Verify vector space axioms for the following sets 2 12 3 i V ii V y 0 x y e R and x 0 y X y x y ze R and xyz 0 2

Answer the following questions a Determine whether the sequence is arithmetic geometric or neither If the sequence is geometric find the common ratio 0 125 0 25 0 5 1 2 b Determine whether the sequence is arithmetic geometric or neither If the sequence is geometric find the common ratio 6 8 11 15 20 c Determine whether the sequence is arithmetic geometric or neither If the sequence is Geometric find the common ratio 2 1 1 1

9 Write the arithmetic sum using sigma notation 9 4 1 26

12 Find the infinite sum if it exists for this geometric series 2 0 5 0 125

13 Find the infinite sum if it exists 964 1

Answer the following questions a Find a formula for the general term an of the sequence assuming the pattern of the first few terms continues 0 8 4 20 100 b Find ag

1 Write the first five terms of the sequence an k 1

How many cubes are in the top layer of the model O 8 OO 10 6 7

Graph the function Find any relative maxima or minima write the ordered pair for each 4 f x x3 3x2 9x 4 5 600 32x 9x 5

For the piecewise function find the specified function value 8 f x x 5 for x 2 6 x for x 2 f 0 f 4 3x 4 for x 0 for 0 x 7 for x 7 9 f x 5 7x X f 8 f 1

Using the graph determine any relative maxima and relative minima of the function 3 f x x3 3x2 1 H 4 3 2 5 4 3 2 11 F1 2 3 4 2 3 4 5 x

The formula d rt is used to calculate the distance an object travels over a period of time t at a constant rate r Based on this formula what is the rate r in terms of d and t A r C d B r dt t t d D r d t

Question 23 Consider LU factorization of the nx n matrices A 0

8 The parent function f x x is shifted right 4 units reflected over the x axis and then shifted up s units Which is the equation for the transformed function g x A g x x 4 5 B g x x 4 5 C g x x 4 5 D g x x 4 5 9 Which is the explicit equation for the nth term of the arithmetic sequence 7 1 5 11 17 23 A an 7 n B a 7 10 What type of sequence is 1 3 9 27 81 243 C a 13 6n D a 7n 6

1 Which is the complete simplification of V A 72 2 Which is equivalent to A NE 3 Which is equivalent to 5x9 Algebra 2 Moors Semeter 1 Final 2022 33 No Graphing Callculator Part 1 Form y10 2828 4 2 2 B 2x 2 b el 07 625x y10 C 7 VT 625x20 y 24 D 625x yle 16

6 T 7 y 2 2 3 4 6 10 12 F14 16 18 2 2 4

1 5 y 8 4 6 4 18 20 16 14 H12 10 Ay 2 6 X

Find all solutions of the following system of linear equations x 2y z 1 2x 5y 3z 2

Si O mng 2013 Kuta Software LLC All rights reserved fy Note Some radicals cannot be simplified C 1 8 2 8284 3 384 5 80 7 128 210

At a certain online bookstore the price of each book is the same The total price of a customer order is the sum of the prices of the books in the order plus a shipping fee that is constant regardless of the number of books purchased Last year the average arithmetic mean number of books per customer order was 1 5 and the average of the total prices of the orders was 10 50 Which of the following amounts could be the book price and the shipping fee last year Indicate all such amounts 4 00 per book and 4 50 shipping fee 4 50 per book and 3 50 shipping fee 5 00 per book and 3 00 shipping fee r book and 2 25 shipping fee 50 per

y x 2 x y Ordered Pair 2 1 0 1 2 8y 16x 32 x y Ordered Pair 2 1 O 1

c Here are two straight lines ABCDE and PQ In the diagrams all the lengths are in cm AE 2PQ Find an expression in erms of x for the length of DE Give your answer in its simplest form

Who correctly converted from point point equation of a line to slopeintercept equation of a line Carmen y 5 3 x 3 y 5 3 x 3 y 3x 9 5 y 3x 4 chase y 5 3 x 3 y 5 3 x 3 y 3x 9 5 y 3x 14

1 Evaluate the following limits or prove that the limit does not exist If the limit does exis use the e 6 definition to prove the value of the limit 2 lim x y 0 0 a lim x y 2 3 y 3 b c lim 2 HI d lim e lim 1 sin y x z y 3 2 Y 1 x y z y 0 0 x y zy 1 z y 1 1 2 1

What type of distribution type would best describe the data displayed in the histogram O bimodal uniform multiple outlier skewed right Frequency 2 321 1 2 3 4 5 6 7 8 9 10 Data Value Question 7 14 3 points Is the data normally distributed If so estimate the mean 6 8 10 12 14 16 18 20 22

Consider the following Basic Box Whisker Plot T 5 10 What is the Lower Quartile Q of the data set shown in the graph 1 3 08 8 Question 2 14 3 points Given that a data set has a Median of 5 and an Inner Quartile Range of 3 what is the possible range of values that could be the Lower Quartile Q for the data set It may help to create or think about a box and whisker plot 0250 58 0050 52 zspiss

Which data set graphed below would most likely consider the MODE as the best measure of central tendency measure just based on the data points O 6 1 5 20 18 5 40 10 10 Question 4 14 2 points In the following data set what would be considered the outlier 60 18 18 18 19 19 20 21 21 23 23 24 32

Consider the following data set 20 22 31 37 39 40 How would the range be affected if the data point 28 was added to the data set The range would decrease by 0 5 The range would decrease by 3 The range would increase by 8 There would be no effect on the range Question 2 20 points Two different gas stations below list the price per gallon of gasoline over 5 days Day Gas Plus Go Station Monday 2 50 2 48 Tuesday 2 51 2 56 Wednesday 2 52 2 46 Thursday 2 57 2 59 Friday 2 55 52 44 Which gas station has more variation based on their range Gas Plus has more variation Go Station has more variation The two gas stations have the same variation

Solve by the quadratic formula b x b 4ac 2a 4x 12x 9 0 If you need a sign type pm or use the black keyboard icon If the square root gives you a whole number calculate the two values and enter then as number number Type a response

Dimensions Let V be a finite vector space and U and W subspaces of V Prove dim U dim W dim V then dim UnW 0

Box Met tior ef fact be Numbers dupplev 10 0 4 Trinomia G x 14x 72 loring Activity the color Color the picture according to your answers Directions Factor each trinomial Identify the binomial factors from below and record the number with Trinomial A x 14x 48 Trinomial B x 3x 40 Trinomia Ex 11x 18 Trinomidx 10x 21 Trinomial K x 9x 70 x 4 x 4 Trinomial Cx 13x 30 x 9 x 14 Red x 5 Light Green x 2 Dark Blue x 8 Pink x 3 2 5 8 OMIALS x 15 x 7 x 1 x 8 Name Date Orange x 10 Dark Green x 5 Light Purple x 10 Gray Trinomial D x 16x 63 Trinomial F 6x 40 Trinomial Hx 5x 6 Trinomial x 15x 36 Trinomia L x 11x 10 3 6 9 12 x 12 x 6 x 1 x 9 Yellow x 7 Light Blue x 2 Dan Per D3 Ass

1 point Consider the function given in the following graph the domain is its range Write your answers in inter Enter the componding to 1 MO I 2 3 1 4 2 I

Let f x 3x 1 and g x x 4 Find f o g 4 Then fog 4 Simplify your answer

3 Graph the following quadratic function f x x 4x 5

Write the sum using sigma notation 3 6 12 48 i 1

Write the sum using sigma notation 3 4 11 46 i 1 Question Help Vidar 1 Preview

Write the sum using sigma notation 6 5 4 1 i 1 Preview

Use the References to ac Which of the following statements are correct Select all that apply a a b b 2 2 2 None of the Above

The partial sum 1 10 19 307 equals C

Find the partial sum S6 for the geometric sequence with a 3 r 4 S6

An auditorium has 45 rows of seats The first row contains 100 seats As you move to the rear of the auditorium each row has 3 more seats than the previous row How many seats are in the row 16 How many seats are in the auditorium

A man gets a job with a salary of 37 800 a year He is promised a 2 450 raise each subsequent year During a 5 year period his total earnings are