Sequences & Series Questions and Answers

Evaluate the formula n n Z O 2 when z 1 992 E 11 and o 208 COO Round up to the nearest whole number as needed

A student s savings account has a balance of 4500 on September 1 Each month the balance decline by 350 Let B be the balance in dollars at t months since September 1 Complete parts a through e a Find the slope of the linear model that describes this situation What does it mean in this situation The slope is The balance declines by per month

2 Find two possible trigonometric functions that would yield the following graph One must include a phase shift 4 T 3M Function 1 Function 2 min max amplitude midline period B sin or cos hor shift

Use the Pythagorean Theorem to find the length of the missing side Then find the indicated trigonometric function of the given angle Give an exact answer with a rational denominator Find cot 9 5 B 5 29 29 O 10 2 2 29 29 Z n 2

X Evaluate the formula p for n 1059 and x 556 n p Round to three decimal places as needed

p p Evaluate the formula z pq Z when p 117 n 580 p 0 25 and q 1 p 580 Round to two decimal places as needed

Claim The mean weight of beauty pageant winners is 119 pounds A study of 15 randomly selected beauty pageants resulted in a mean winner weight of 124 pounds Express the original claim in symbolic form

Age frequency mean median mode 6 13 14 12 13 47 13 42 13 14 25 9 13 15 14 11

10 Mabel Cousino has 35 000 to invest in a certificate of deposit for 4 years The certificate of deposit earns interest at 4 75 compounded daily What is the annual percentage yield to the nearest thousandth a percent

12 May Wattson has 50 000 to invest in a 4 year certificate of deposit that earns interest at a rate of 3 75 compounded monthly or 3 50 compounded daily Based on annual yield which is the better investment

K a 29 ile ands Vo 14 Ben Garison invested 15 000 at 5 compounded daily in a credit union account that matures in 1 year He also invested 20 000 at 5 25 compounded monthly in a Silver Screen account that matures in 4 years a What is the interest earned at maturity for both accounts b What is the annual percentage yield for each account Terras invests 10 000 at 4 compounded

would have a margin of error of 2 b Suppose the finance director would like to reduce the cost of the survey by using a random sample of 100 What would be the margin of error for this sample size Substitute 100 for n in the margin of error formula margin of error 100 100 or 10 V100 A random sample of 100 would have a margin of error of 10 Question 3 Select Margin of error formula n 100 Some reasons that a research center might decide that a survey with a margin of error of 3 would be more desirable than one with a margin of error of 2 include the cost would be Select the survey would take Select v V 1 pts and it would require 1

Prove An odd times an odd equals an odd 2m 1 2n 1 mn m n 2 mn m 1 odd

6 in 10 in Find the area 6 in 18 in Area of O in Area of A Area of Figure Remember Ao r Use 3 14 in in

Find the sum of the first 8 terms of the following sequence Round to the nearest hundredth if necessary 24 48 48 96

Answer the following questions about the equation below x 34x 12 0 CCXL a List all rational roots that are possible according to the Rational Zero Theorem Choose the correct answer below A 1 12 13 14 16 12 OB 12 OC 1 2 3 4 6 12 OD 1 b Use synthetic division to test several possible rational roots in order to identify one actual root One rational root of the given equation is 6 Simplify your answer c Use the root from part b to solve the equation The solution set is Simplify your answer Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression Use a c

Answer the following questions about the equation below 12x 53x 34x 5 0 a List all rational roots that are possible according to the Rational Zero Theorem Choose the correct answer below 1 5 1 5 A 1 5 3 OB 1 12 13 14 6 12 OC 1 15 5 1 5 1 5 12 12 Part 3 of 3 2 3 4 6 12 OD 1 12 13 14 16 12 555555 b Use synthetic division to test several possible rational roots in order to identify one actual root One rational root of the given equation is 3 Simplify your answer c Use the root from part b to solve the equation ts The solution set is Simplify your answer Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression U

Part 2 of 2 What are the possible numbers of positive real zeros 0 Use a comma to separate answers as needed What are the possible numbers of negative real zeros Use a comma to separate answers as needed HW Score Points C Use Descartes Rule of Signs to determine the possible numbers of positive and negative real zeros of f x x 8x 2x 5

e lowest point of a positive parabola is the ect one a maxima b axis of symmetry c endpoint d minima

The axis of symmetry of a parabola Select one O a determines the lowest point of the parabola O b determines the highest point of the parabola O c divides the parabola into symmetrical halves O d always lies on the X or Y axis

26 DETAILS LARMPMT1 7 4 034 The receipt shows your total food cost of a 40th Street DATE JUNE09 1 TABLE 29 SERVER APRIL Food Total Tax Subtotal

23 DETAILS LARMPMT1 6 3 028 Evaluate each complex fraction Write yo a WIA WIN

A student decided to start saving money On the first day he saved 1 cent on the second day an additional 2 cents on day 3 he saved 4 cents Each day he doubled the amount he saved the previous day How much would he be saving on day 20 Hint The first term of the geometric sequence is 0 01 and the common ratio is 2 What is the 20th term 3 80 5242 88 10 485 75 10 485 76

Arithmetic Series Determine S17 for the arithmetic series shown below 15 7 1 9 17 113 121 833 901 Question 6 3 points Arithmetic Series at holow has a different answer than the res

Arithmetic Sequence Jonah Sesquare started creating the following pattern in steps a represents 1 square tile a az 57 61 a3 represents 5 square tiles a a3 If Jonah continues this pattern how many square tiles will be needed for the 15th step 268 435 456 as 36

Question 5 12 5 points Given the following graphs of the two function which statement must be true f x 5 4 3 2 1 5 4 3 2 11 2 3 g x f x O g x f 9 x O g x 9 f x 8 x f x 1 2 3 4 5 5

O up 4 The graph would be translated left 1 and down 4 Question 2 12 5 points Consider the parent function x 5 How would the original graph be transformed if it were to be changed to Ax 5 x 2 The graph would be translated left 2 O The graph would be translated right 2 O The graph would be translated down 2 O The graph would be translated up 2 Question 3 12 5 points Given h x is a transformation of the graph f x 2x determine which of the below correctly describe h x

4 Show algebraically that the inverse of f x 6x 3 is f x x 12

Question 1 10 points A wedding planner is preparing a wedding reception dinner and has determined that the overall cost will require 25 for each guest that attends and a maximum of 200 guests This situation can be represented by c x 25x where x is the independent variable and represents the number of guest and c x is the dependent variable and represents the cost of the reception Which best describes the appropriate DOMAIN of this situational function O O The set of Integers i e 2 1 0 1 2 The set of Whole Numbers i e 0 1 2 3 O The set of All Real Numbers R where x 0 O The set of All Real Numbers R where x 0 Question 2 10 points

Question 3 20 points Using the graph below solve the equation x 4x 5 x 2x 1 5 g x x 4x 5 4 O 3 2 1 Ox 1 O x 2 52 2 2 3 xs 0 41 or x 2 41 x 11 or x 51 2 f x x 2x 1 3 4

Nertall Moreno MI nda Attempt 1 Graph the solutions of the linear inequality y x 1 O O O 5 4 3 2 1 43 3 5 4 3 2 1 2 1 21 3 4 5 31 2 2 3 5 3 2 1 2 3 4 5 1 2 3 4 5

Question 2 20 points Which graph below shows the system 5 4 3 2 1 5 5 4 3 2 1 th 3 2 1 1 2 3 Y A 3 2 1 11 2 N 2 3 4 97 5 4 5 x 4y 4 x 2y 8

Question 2 18 points Compound Interest Kelly invested 5 000 in a CD at Charter Bank The annual rate is 4 9 compounded monthly How much is her investment at the end of 8 years O 2 393 78 O 5 000 49 O 7 393 78 O 8 2114 22 Certificate of Deposit ye Question 3 18 points Determine the value of the account if the initial investment is 800 compounded wookly at a rato

Question 6 10 points Annual Percentage Rate APR Ms Morrison is purchasing a house and needs to finance a 150 000 mortgage from the bank with an annual percentage rate APR of 3 8 She is financing it over 30 years and making monthly payments What is the monthly payment Monthly Payment 416 67 O 698 94 P 1 xt 1 1 1 Fo SOLD

50 How many numbers from 2 through 100 can expressed as p where p is a prime number

Simplify each expression sin cos cot 8 csc 8 O sec 8 O cos 8 O csc e Question 14

Question 4 18 points The equation for compound interest is A P er t where P is the initial amount invested r is the interest rate as a decimal and t is the number of years Determine the value of the account if the initial investment is 8 000 compounded continuously at a rate of 6 after 10 years O 16 097 57 14 576 95 O 14 326 78 O 8480 00 Question 5 18 points If the rate of an investment is 5 the time is 12 years and the principle is 500 which investment would be worth the most Simple Interest

Question 7 14 2 points Infinite Geometric Series Find the sum of the infinite geometric series if possible 1 2 4 8 1 5 1 5 135 45 03 0 O 02 20 O O N W O co the series is divergent 9

1 Draw Bohr d a CHA H b CCl4 C NCI 3 n 7 Ci 17 d H O H 1 0 8 e NH3 N 7 4 1

Name the following compounds 6 Marks a P Os b CCl4 C NH d CO e PCls

1044 O 1098 Question 2 14 3 points Arithmetic Sequence What is the common difference of the sequence shown below 32 27 22 17 12 05 O 44 5 44 Question 3 14 3 points Arithmetic Series Find the sum of the finite arithmetic series

Question 3 14 3 points Arithmetic Series Find the sum of the finite arithmetic series n 2 1 O7832 3872 3916 O 7744 Question 4 14 3 points Geometric Sequence

Question 4 14 3 points Geometric Sequence What is the common ratio of the sequence 2 6 18 54 162 33 3 6 O IN Question 5 14 3 points Geometric Series Find the sum of the finite geometric series

Find the values of x for which the series converges Enter your answer using interval notation x 3 n 0 47 Find the sum of the series for those values of x

Question 1 16 7 points Arithmetic Sequence The first term in this sequence is 1 1 2 5 1 7 n an 1 O 3 3 Which function represents a recursive definition of the sequence ax ax 1 1 an ax 1 2 ax 2 1 1 ax 2ax 1 3 4 5 Question 2 16 7 points Arithmetic Sequence Consider the first six terms of this sequence 3 8 13 18 23 28 If the sequence defines a function what is the domain

O an O Question 2 16 7 points Arithmetic Sequence Consider the first six terms of this sequence 3 8 13 18 23 28 If the sequence defines a function what is the domain O 2 1 3 1 2 3 4 5 6 O ALL REALS R 3 8 13 18 23 28 ALL INTEGERS Question 3 16 6 points Arithmetic Sequence Jessica was trying to prepare for a marathon S

Arithmetic Sequence Jessica was trying to prepare for a marathon She had already started preparing and beginning on week 1 of training she ran 3 5 miles every other day On week 2 she increased to running 5 miles every other day On week 3 she increased to running 6 5 miles every other day So each week she continued to increase the amount she ran by 1 5 miles Week Miles O 016 14 1 3 5 18 O 19 2 5 0 A marathon is 26 miles long In which week will she be actually practicing by running 26 miles during her practice runs 3 6 5 Question 4 167 points

Question 4 16 7 points Geometric Sequence Consider the first six terms of this sequence 5 7 11 19 35 67 Which equation below explicitly defines the sequence an 2n 3 Oax ax 3 2 a 3 2ax 1 an 3m 2

hat is the complete solution to 5 10 2x 35

Evaluate the following a 7 9 1 7 b 9 0