Sequences & Series Questions and Answers

10 The expression 3n 11n k can be factored into two linear polynomials with integer coefficients Determine the possible values of k

Describe the difference between simple and compound interest Choose the correct answer below OA Simple interest involves interest calculated only on the principal Compound interest is interest computed only on the accumulated interest B Simple interest involves interest calculated only on the principal Compound interest is interest computed on the original principal as well as on any accumulated interest C Simple interest is interest computed on the original principal as well as on any accumulated interest Compound interest involves interest calculated only on the principal D There is no difference between simple and compound interest

A bank offers a CD that pays a simple interest rate of 4 5 How much must you put in this CD now in order to have 4000 for a graduation trip in 3 years You must put in this CD now in order to have 4000 for a graduation trip in 3years Round up to the nearest cent

Exit Ticket 9 20 1 If the ratio of boys to girls in a school is 4 5 and there are 175 girls how many boys are there a 19 b 35 c 119 b 61 cups 2 2 To make a pie the ratio of sugar to flour is 3 2 If Amanda uses 4 1 cups of flour how much sugar does she need 2 a 3 cups c 6 d 140 3 cups 4 e 615 d 13 1 cups 2

Write the decimal as a percent 0 0744 0 0744

Click here to Express 0 158 as a percent Use integers or decimals for any numbers in the expression

Express the percent as a decimal 65 65 Type a whole number or a decimal

The polynomial function f x has the given zero Find the other zeros 3 f x x 4x 2x 8 4 The other zeros are Type exact answers using radicals as needed Use a comma to separate answers as needed

Fill in the blank so the resulting statement is true The line that best fits a set of points is called a an The line that best fits a set of points is called a an scatter line distribution line regression line

Correct The volume of a gas in a container varies inversely as the pressure on the gas If a gas has a volume of 340 cubic inches under a pressure of 10 pounds per square inch what will be its volume if the pressure is decreased to 5 pounds per square inch Round your answer to the nearest integer if necessary Answer Keypad Keyboard Shortcuts

To help with the startup costs of his new comic book store Jose is taking out a 56 000 amortized loan for 10 years at 8 5 annual interest His month payment for this loan is 694 32 Fill in all the blanks in the amortization schedule for the loan Assume that each month is 1 12 of a year Round your answers to the nearest cent Payment number 1 2 60 61 Interest payment 242 91 Principal payment 0 0 451 41 New loan balance 55 402 59 33 841 96 0 X S

Correct Answer 2 The mass varies directly as the kinetic energy K and inversely as the square of the velocity V If the kinetic energy is 40 joules and the velocity is 2 meters per second then the mass is 20 kilograms Express the mass as a function of kinetic energy and velocity Keypad Keyboard Shortcuts

Determine whether the graph is connected or disconnected O Connected

rite the expression as a complex number in standard form 6 9 3 9 3

16 36

A small country is comprised of five states A B C D and E The population of each state is given in the following table Congress will have 60 seats divided among the five states according to their respective populations Use Jefferson s method with d 32 920 to apportion 60 seats State Population C 395 817 State Number of Apportioned Seats A A 134 915 B 228 632 CITE D 547 168 E 726 514

complete each statement and name the property of real numbers you have used a ab Select b Associative Property of Addition Associative Property of Multiplication Commutative Property of Addition Commutative Property of Multiplication Distributive Property a b c Select Associative Property of Addition Associative Property of Multiplication Commutative Property of Addition Commutative Property of Multiplication Distributive Property a b c Select Associative Property of Addition Associative Property of Multiplication Commutative Property of Addition Commutative Property of Multiplication Distributive Property

The concept slavery rather than the term is covered O 0 O 1 O 2 3 04 O 5 times in the original U S Constitution

Jared creates a number sequence that has a first term of 2 and a second term of 5 Each term after the second is created by subtracting the term before the previous term from twice the previous term He uses s t to denote te number t in his sequence For example s 1 2 and s 2 5 Which of the following can be used to find the value of s n for some positive integer n greater than 2 AS n S n 2 2S n 1 S n 2S n 2 S n 1 S n S n 1 2S n 2 S n 2s n 1 S n 2

10 10 f x 8x 13 12 12 x x 13x 56x 81 11 11 x x 3x x 1 M 13 13 f x x 4x 3x 12 13 Select Select Select falls rises to t to t to ti to th

A carnival purchases 2300 stuffed animals to give away as prizes If the total cost to buy the stuffed animals is 7452 find the cost per stuffed animal The cost per stuffed animal is Simplify your answer

Find the missing number in the proportion 5 25 x 20

56x 81 ware LLC All right 13 K 13 f x x 4x 3x reserved 64 Made with Infinite Algebra 2

Consider the following function k x 2 Step 2 of 2 Find the length of the individual line segments of this function Then find the positive vertical separation between each line segment Simplify your answer Answer Enable Zoom Pan Keypa Keyboard Shortc

A high school art teacher conducts a survey on whether or not students would be interested in an after school art club The teacher knows that it would be too time consuming to survey all 632 students in the high school so she decides to ask the 32 students currently in her classroom One of the students states that this survey cannot be used to make an inference about the entire high school Which of the following statements best justifies the student s interpretation of the survey A The survey sample was too small B A cafeteria worker should have conducted the survey C The survey method was flawed since the sample was not random D An observational study should have been used

4 Suppose that the weights of 4800 registered female Labrador retrievers in the United States are distributed normally with a mean of 62 5 lb and a standard deviation of 2 5 lb What percent of the Labrador retrievers weigh less than 65 lb A 34 B 50 C 84 D 99 7

Convert the following number bases a AE91 to octal 624 to decimal b QUESTION B2 10 Marks A survey of machine shop reveals the following 44 employees can run on a lathe A B C D E a b c information about its emplo 49 employees can run the milling machine 56 employees can operate a punch press 27 employees run a lathe and milling machine 19 employees can run a milling machine and operate a punch 24 employees can run a lathe and operate a press punch 10 employees can operate all three machines 9 employees cannot operate any of these three machines Let L number of employees who can run on a lathe M number of employees who can run a milling machine P number of employees who can operate a punch press Draw a Venn Diagram to represent the situation above Determine the number of people employed at the machine shop Find LUM P 1 2n 1 2 1 2x 2x 4 1 4x 4x QUESTION B3 10 Marks Given the following functions f x 1 2x g x x 3

Use the rational zeros theorem to list all possible rational zeros of the following g x 7x 7x 5x 9x 8 Be sure that no value in your list appears more than once 0

About the sequence x kezt we have the following a x 1 EB x b for each 1 to b t b 1 x MKk k 1 te t b t b k20 c x keZ is uniformly Cauchy on t b t b verification of these properties is left for the reader We consider the uniform limit of the sequence x to 6 1 8 B xo b which is given by x t lim x 1 11 b t b b Thus x t lim x ff s x s ds 60 x 60 de lim ff s x s ds x lim f s x s ds Finally the validity of this integral equation has the following two implications 1 x f f s lim x s ds x ff s x s ds E 00 Thus the function 1x 1 satisfying the integral equation x 1 x f f s x s ds for all t t b t b 2 X t x f s x s ds x 0 x dt S dt 0 ff s x s ds f t X t This now proves that the curve X 1 8 4 89 thus obtained is a solution of the initial value problem

Fall 2023 Math 108 Section Due Wednesday September 27 at 6 00 PM Multiple Choice For each question there is one correct answer Indicate your choice by circling the letter If no letter is circled credit may not be given even if your work is correct Determine the value of sin 0 3 4 A sin 0 D sin 0 A N 16 cos 23 4 sin 23 4 16 B Determine a trigonometric expression for N D N B sin 0 1 E sin 0 4 16 A N 23 4 B N E N cos 23 4 16 16 sin 23 4 C sin 0 C N 16 cos 23 4

A lighthouse is located at the edge of a cliff near the ocean To measure the height of the light sightings are taken 2400 meters from the base of the cliff If the angle of elevation from the ground to the top of the cliff is 3 94 and the angle of elevation from the ground to the top of the lighthouse is 5 71 what is the height of the lighthouse Round your answer to two decimal places and include units 5 71 2400 meters h 3 94 2400 meters 2400 meters Show how you found the height of the lighthouse below Make sure you round your answer to 2 decimal places and include units

Given s t 2t 4t where s t is in feet and t is in seconds find each of the following a v t b a t c The velocity and acceleration when t 2 sec a v t b a t c When t 2 sec the velocity is Simplify your answer When t 2 sec the acceleration is

Lena invested 400 in a fund for 3 years and was paid simple interest The total interest that she received on the investment was 36 As a percentage what was the annual interest rate of her investment If necessary refer to the list of financial formulas n

To be able to take her dream vacation Kaitlin decides to save for 3 years She opens a savings account with 800 The account pays simple interest a annual rate of 4 She doesn t make any more deposits Answer the following questions If necessary refer to the list of financial formulas a How much total interest will Kaitlin earn b What will the total amount in the account be including interest X

For the equation 5w 23 w 12 0 determine the appropriate substitution and write the equation in the form au bu c 0 The appropriate substitution is u The equation with substitution is Tyne an equation in terms of u

2 Anton 10 B i Mostres a 10 10 x x 8x 13 KOCAELO swyckel CERNISERI KAGAME DRE NT PETER BARE MA SAAN MAINE BAGES SEMENTAREDIMIES HERBERA COMPRUERENT THESTATE 11 11 3x x 1

8 Describing end behavior Sketch the graph of each function 8 y x 4x 8 24 T

4 Plot the inequality on the number line Explain why you chose those endpoints and its locations Lesson 1 05 1 x 0 9 or x 1 1 0 2

est Jse divisions to convert the base ten numer given base 2 874 to base seven O 11 224seven O 11 244seven O 11 422 seven 11 442 seven

Find the least common multiple of the numbers 45 and 54 O 405 O 270 O 2430 O 486

Express the expanded form as a 5 10 0 10 0 10 1 1 O 5001 05 O 51 Hindu Arabic nume F01

2 The population of a town is 2500 and is decreasing at a rate of 3 5 per year Use an exponential function to find the population of the town after 5 years

4 The population of a school is 800 students and is increasing at a rate of 2 per year Use an exponential function to find the population of the school after 9 years

This is a 2 page document Directions Write the formula for each function below EXPONENTIAL GROWTH FUNCTION y a 1 r EXPONENTIAL DECAY FUNCTION a 1 x Directions Read each problem carefully choose the correct model then solve 1 Annual sales for a fast food restaurant are 650 000 and are increasing at a rate of 4 per year Use an exponential function to find the annual sales after 7 years 11

18 x dx 182 x dx i 18 x dx We will use these notations in this article Example 1 Obtain approximate solutions upto of the following initial value problem dx 2x 3y x 0 1 dt dy dt Solution t y y 0 2 We have x 1 1 2 x 1 1 f 2 x s 3y s ds 1 8ds 8t 1 3 1 2 s y s ds 81 1 2 f s 2 ds 2 2t Thus 3 0 21 2 21 1 2 2 Next x 0 1 1200 35 03 d 1 1 8 2x2x 3x d 2x s 3y s ds s y s ds 2 2 35 2 ds y 1 2 s y s ds 2 31 3 2 6 3 21 2 24

3 Interpret a slope of

di di Such an equation is said to be an ordinary differential equation Thus an ordinary differential equation is a differential equation in which the constituent function X X t is a function of a single real variable We often use the acronym ODE in place of the full term ordinary differential equation II On the other hand there are differential equations in a function u xu x of a real multivariable x x x x which ranges in an open subset of R Such a function u u x gives rise to mixed partial derivatives du x 1 i n Du x x jl i j n Grer er D u for various multi indices 0 0 o with o EZ i 0 1 2 the mixed partial derivative D u having the order 0 9 a Now a differential equation in such a function u ux of a multi variable x x x ranging in an open subset of R is an equation of the type du Fx u 11 d u D u ox m 0 2 its order being m Equation 2 is said to be a partial differential equation in u x because it involves the mixed partial derivatives of u We use the acronym PDE for this type of differential equations There is more about the setting of a differential equation In a mathematical problem a differential equation is accompanied by auxiliary data A solution of a differential equation is required to satisfy this auxiliary data To be more specific we are given a subset of the domain of a prospective solution and some of its derivatives of the solution at the points of this subset

we regard the equation 3 as standard form of an UDE OI course the ODE has order k Note that the function X tX t is a vector valued function of the real variable t and as such it is a curve in R Each X has n components X t X 1 X 1 X t and therefore all the derivative of it has n components X 1 X 1 for 1 k Consequently the function f appearing on the right hand side of 3 has n components f f ff each f being a real valued function d X 1 dt MATHEMATICS Consequently the DE 3 is actually the following system of ODE in the functions t X t t X t t X t d X dX 1 X d di d X dr 1 1 X d X di ft X t X t dX d X dt dit 1 dX dt dx dt 1 3 At this stage we become more specific about the features of the ODE 3 or equivalently about the system 4 Let I be an open internal and let denote an open subset of R We consider the open sets Ixnx R xXR there being k 1 copies of R in the above Cartesian product This set is being designated to accommodate the variable quantities 4 dit 1 Clearly the function f appearing on the right hand side of 3 must have this set as its domain of definition dX dk X Choosing 1 1 x En and www in R we form the initial Now the initial value problem for the ODE condition fo W WW 3 is the following pair d X f

Solve triangle ABC If an answer does not exist enter DNE Round your answers to one decimal place Below enter your answers so that A is smaller than A b 127 c 163 LB 49 ZA 55 4 2C 75 6 a 138 5 X X O O LA 26 6 4C 104 4 a2 75 4 XXX 0 0 O

1 Evaluate the function for the given value of x 3 ifx 0 2 if x 0 g x f x https goformative com formatives 6329af67d481e6e0db19dbcc 1 2 5 g 7 9 h 4 2 f 4 6 g 0 10 h 2 x 5 if x 3 2x 1 if x 3 3 f 0 7 g 1 11 h 1 h x zoom in 2x if x 2 4 8 g 3 12 h 6 N A