Sequences & Series Questions and Answers

a Use numerical evidence a table of values to find the limit of lim x sin x

z varies jointly with x and y If x 8 y 3 and z 6 write the variation equation and find x when z 12 and y 16 Find x and write the value in the blank

X Solve for x 8 9 4 5 50 Hint It may be easiest to start by using the Pythagorean Theorem to solve for the leg of the largest right triangle that is not labeled before setting up a proportion and cross multiplying 19 6 45 POSSIBLE PC

To anolilin ou ready for more to noits percentage of the initial amount of c rs less than 25 exactly 25 or mo

10 Exam Jan Feb 2023 If we rewrite the expression 2 log z 4 4 log z 3 log z 2 as a single logarithm We obt Choose the correct answer

For the function f x 4 f x h f x 11

Let f x x 2x and g x 9x fg 4 fg 4 Simplify your ar

2 bonus Let G G Ge be groups t22 and G 22 for each i and suppose that G is infinite Prove that G X G xx G is never cyclic

Suppose that the functions fand g are defined as follows f x 4x 5 g x 5x 2 nd 1 Then give their domains using interval notation Find g and 8 x Domain off 8 0 H 90 1 1 Domain of ba U

A person invested 7500 for 1 year part at 8 part at 10 and the remainder at 13 The total annual income from these investments was 84 The amount of money invested at 13 was 700 more than the amounts invested at 8 and 10 combined Find the amount invested at each rate The person invested at 8 S at 10 and S at 13

2 Find the inverse of the function Show your work Is the inverse a function Give a reason for your answer a y 3x 1 b y 1 2x 5

Let the domain o The domain is

Use the graph shown to find the following a The domain and range of the function b The intercepts if any c Horizontal asymptotes if any d Vertical asymptotes if any e Oblique asymptotes if any b Find the intercepts if there are any Select the correct choice below and if necessary fill OA The intercept s is are Type an ordered pair Use a comma to separate answers as needed the answer box complete your choice OB There are no intercepts c Find the horizontal asymptotes if there are any Select the correct choice below and if necessary fill in the answer box es to complete your choic

Complete the sentence below 2 The x coordinate of the vertex of f x ax bx c a 0 is The x coordinate of the vertex of f x ax ax bx c a 0 is b 4ac b 2a

Steven had to rent a truck for moving The first time he rented the truck he drove 30 miles and it cost him 56 50 The second time he rented a truck from the same company he drove 65 miles and it cost him 75 75 Let y be the total cost to rent the truck and x be the number of miles the truck is driven In other words consider the information as ordered pairs 30 56 50 and 65 75 75 Part 1 Instructions Using the information given write a linear equation that models the total cost y to rent a truck in terms of miles x Using your equation determine the cost to rent a truck and drive it for 150 miles Be sure to answer the question and to clearly indicate how you arrived at that answer Show your work Even if using a calculator show how and why you took the steps you did not just what buttons you pushed Equation Cost to rent truck and drive 150 miles

Express the lengths a and b shown in the figure in terms of U a b 19 a

Save The point at which a company s profits equal zero is called the company s break even point Let R represent a company s revenue let C represent the company s costs and let x represent the number of units produced and sold each day R x 20x C x 12 5x 37 500 a Find the firm s break even point that is find x so that R C b Find the values of x such that R x C x This represents the number of units that the company must sell to earn a profit

3 24 2 13 Chus the cane OA OF GOB OB OD OB

2 Find the following limits a b lim n 1 n 1 lim n n 1 n 2 rn 1 X 1 x5 1 3n dx

Jews and Muslims both refrain from consuming Chicken O Beef Alcohol Pork

The founders of the Ottoman Empire were O Turks O Persians O Kurds O Arabs

Let A b d e and B c e f How many distinct elements are in AxB n BxA

Write a function that describes the cost of hiring the painter in terms of the number of rooms painted Let the function f x represent the painter s charges and the variable x represent the number of rooms f x 40x 47 Part 1 4 Part 2 of 4 Use your equation to find the cost of painting a five room house

Part 2 3 Part 3 of 3 c Use your answers to the other parts parts a and b to find what the illumination will be at 80 ft Round to the nearest tenth if neces When the distance from the car s headlight is 80 ft the illumination will be rounded to the nearest tenth candles fc foot X

Some bodybuilders claim that within safe limits the number of repetitions that a person can complete on a given weight lifting exercise varies inversely as the amount of weight lifted Roxanne can bench press 45 lb for 25 repetitions Note Round down the answer to the nearest whole number if necessary Part 0 3 Part 1 of 3 a How many repetitions can Roxanne bench with 55 lb of weight Roxanne can bench complete repetitions X

Part 0 3 Part 1 of 3 a Write an equation of variation that describes the relationship between illumination I and distance from the headlight d Use k for the constant of variation The equation of variation is 0 0 0 0 4

the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y axis y y 0 x 1 x 3 X

BlueBolt Bottlers has a bottle filling process with a mean value of 58 ounces and a standard deviation of 6 0 ounces a Suppose that the upper and lower tolerance limits are 66 and 50 ounces respectively The process capability ratio is 0 444 Enter your response rounded to three decimal places In order for the BlueBolt bottling process to meet the tolerance limits 99 7 of the time the standard deviation would need to be 2 7 ounces Enter your response rounded to one decima place b Now suppose BlueBolt Bottlers makes some process improvements thereby lowering the standard deviation of the process to 3 5 ounces rather than 6 0 ounces The process capability ratio is Enter your response rounded to three decimal places

A dietitian at a hospital wants a patient to have a meal that has 106 grams of protein 116 grams of carbohydrates and 107 milligrams of vitamin A The hospital food service tells the dietitian that the dinner for today is salmon steak baked eggs and acom squash Each serving of salmon steak has 20 grams of protein 20 grams of carbohydrates and 1 milligram of vitamin A Each serving of baked eggs contains 20 grams of protein 3 grams of carbohydrates and 20 milligrams of vitamin A Each serving of acorn squash contains 3 grams of protein 25 grams of carbohydrates and 32 milligrams of vitamin A How many servings of each food should the dietitian provide for the patient How many servings of each food should the dietitian provide Select the correct choice below and fill in any answer boxes within your choice A The dietitian should provide salmon steak x baked eggs y and acorn squash 2 Simplify your answers OB There are an infinite number of combinations of servings of salmon steak x baked eggs y and acorn squash 2 that the dietitian can provide Using ordered triplets the solution can be written as x y z x z is any real number y Simplify your answers Type expressions using z as the variable as needed OC There are no combinations of servings of each food that the dietitian can provide

7 1 48 points Skipped eBook 0 Files Print 5 References Exercise 2 31A Static Identifying transaction type and effect on the fl Required Identify whether each of the following transactions is an asset source AS asset use AU CE Also show the effects of the events on the financial statements using the horizontal st Increases 1 or decreases D each element of the financial statements If an event Increas account equally within the same element record I D For events that do not effect the finar Cash Flows column designate the cash flows as operating activities OA Investing activiti that do not affect the cash flow leave the cell blank The first two transactions have been require entry a Provided services and collected cash b Purchased supplies on account to be used in the future c Pald cash in advance for one year s rent d Pald cash to purchase land e Pald a cash dividend to the stockholders f Received cash from the issue of common stock g Pald cash on accounts payable h Collected cash from accounts receivable 1 Received cash advance for services to be provided in the future J Incurred other operating expenses on account k Performed services on account 1 Adjusted books to reflect the amount of prepaid rent expired during the period m Pald cash for operating expenses n Adjusted the books to record the supplies used during the period n Recorded accrued salarles

The y intercept is 0 2800 Part 1 2 Part 2 of 2 b Explain what the y intercept means in this context At 2800 seconds 2800 seconds the time the skydiver lands the time the chute opens the altitude is feet X

Sandi weighs 150 lb but she has started a new diet plan that promises she will lose 2 lb per month every month until she reaches her goal weight Write a linear function that describes how much Sandi weighs f x each month and then use your function to find out how many months it will take her to get to 130 lb Use x to denote the number of months since Sandi started her new diet Part 0 2 Part 1 of 2 The linear function that describes how much Sandi weighs each month is f x 0 X 3

Using the Law of Sines to find all triangles if ZA 46 0 31 6 34 Round all answers to the hundredths place Assume A is opposite side a ZB is opposite side b and C is opposite side e For the acute angle we have of no answer extits enter ONE for all answers ZBI degrees 20 degrees For the obtuse angle we have If no answer exists enter DNE for all answers 2B W degrees 20 is degrees du

a Q Structure 2 O How many blocks the smallest squares would be needed for Structure 83 5 How many blocks the smallest squares would be needed for Structure 96 Structure 1 Answer Answer Structure 3 How many blocks the smallest squares would be needed for Structure Give your answer as a

meone is using a pattern to build structures out of square blocks The first three structures are shown low A Structure 1 Structure 2 Structure 3 Q

roblem 2 Compute the local extrema of the following functions Use that information to grap e functions f x y cos x cos y q x y cos x y

What is c p x c x 4x 1 p x 4x 3 Write your answer as a polynomi

40 24 56 16 72 8 48 32 What is the missing numb

Let f x 9x 6 Find f o f 9 f of 9 Simplify your answer

In a study of children a total of 1 558 children were examined Of these 1 020 had rickets Of the 243 urban children in the study 92 had rickets a How many children living in nonurban areas had rickets children b How many children living in nonurban areas did not have rickets children

random sample of 40 college professors is selec es 61 41 43 46 33 59 48 41 48 28 57 65 52 42 58 23 39 61 42 43 33 35 64 36 39 41 20 31 40 35 37 54

Aubrey opened a savings account with 1400 that pays no interest She deposits an additional 70 each week thereafter Write a recursive formula to show how much money Aubrey has in the account n weeks after opening the account

x varies inversely as p If x is 32 when p is 40 find x when p is 128 x X

Given the graph of f x shown sketch the graph of the function described y f x 6 Which of the following is the graph of y f x 6 OA O B Q IS O C O D Q Q

Question 5 Describe the right hand and the left hand be m x 3x 10x 10

Question 3 ind all real zeros of the polynomial f x x utiplicity of each

Fill in the missing number to complete the linear equation that gives the rule for this table X 4 LO 5 7 y y x 81 6 83 84 82

The percentage of the adult population that smokes can be modeled by the function P x whose graph is shown below The input x is years after 1955 60 50 40 30 20 10 10 P r 20 30 40 50 60 Use the percentage of adults that smoke in 1955 and 2015 to find a linear formula for the function P x

how that the set is linearty dependent by finding a nontrivial linear combination of vectors in the set whose sum is the zero vector Use 3 5 and sy respectively for the vectors in 5 2 2 6 1 1 2 0 0 0 xpress the vectors in the set as a linear combination of the vectors sy and s

d the average rate of change of f x 3x 2 from 2 to 3 from 4 to 1