Sequences & Series Questions and Answers

The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points For this question DO NOT apply the standard deviation rule a What proportion of the students scored at least 27 points on this test rounded to five decimal places 0 00621 I A b What is the 80 percentile of the distribution of test scores rounded to three decimal places

The given graph is a graph of a one to one function f Sketch the graph of the inverse 1 function f OA Q O B G O C 10 3 6 10 1 16 Q 5 O D G bns

VAV IT The xy plane above shows a portion of the graph of which of the following functions O y 3 cos 2x Oy 3 cos 2x Oy 3 cos x Oy 3 cos x

6 Given the formula M r solve for r O T Or O r 8T 5M BM 5T 8M O r 5 7 Given the formular x txp i solve for the variable p Hint click the button next to the answer box to make sure your answer is formatted correctly Use parentheses if needed P x

A zoologist is studying the reproduction rates of two different breeds of chinchillas in country Y He discovered that the Eastern chinchillas in his study produced 30 percent more offspring than the Western chinchillas did Based on the zoologist s observation if the Eastern chinchillas in his study produced 143 offspring how many offspring did the Western chinchillas produce 100 103 110 186

The specific heat capacity of substance K in calories per gram cal g is approximately 30 less than that of methyl alcohol The specific heat capacity of methyl alcohol is 0 60 cal g Which of the following is closest to the specific heat capacity in cal g of substance K

A certain high school has 250 students in the sophomore class Each sophomore selects an elective class 40 students take art 100 take music 60 take gym and the rest take computers Which class is chosen by 40 of the students Music Gym Computers

Three friends go to dinner At the end of the meal they decide to leave a 15 tip for their waitress If the bill is 21 00 the total cost of the meal will be which of the following 3 00 15 00 24 15 3 15

D 1 2 5 x y23 B M 6 3 D 4 6 61542 7x 3y2 24

are LL C ualities mach system of inequalities 2 A B zoom in

1 Try It Unit 1 Lesson 2 Directions Fill in the table The first one is done for you as an example Example 2 3 yi 10 10 20 30 y X 4 3 2 1 4 Answer based on the continuous function that is given in this table f y 1 0 1 2 Value of the zero s 3 0 2 Value of the y intercept s 0 Identify the interval s where the function is negative 3 x 0 2 x 00 Identify the interva where the function positive x 0 x

6 4 5x 16 8 1 5a 2 29

Zhan has a credit card charge of 250 on a card that charges 19 annual interest compounded daily If he makes no other charges or payments on the account what would be the balance of his account in 1 year Round to the nearest whole dollar Use A p 1 957 323 832 302

can automatically know if the graph of an absolute value inequality is an And or Or just by looking at the inequality symb O Faise

In 2014 the population of Kenya was estimated to be 45 121 040 with a growth rate of 3 each year Which of the following models the estimated population in t years OP t 45121040 1 03 OP t 45121040 0 97 P t 45121040 0 03 OP t 45121040 1 3

Kuta Software Infi Date Parallel Lines and Transversals Identify each pair of angles as corresponding alternate interior alternate exterior or consecutive interior 2 1 F 7 3 5 4 6 Period 8

V is the midpoint of UW Complete the proof that AUVX AWVY X Y U 1 2 3 4 5 Statement V is the midpoint of UW WY UX VX VY V UV VW AUVX AWVY W Reason Given Given Given Definition of midpoint CPCTC Definition of congruence SAS

SUM Find all solutions a y E Z to the following Diophantine equations a x 4y 4y 3 b x2 3x9y 6y 1

If x x 4 g x x 6 anc h x x find the following a f g h x b f g h 4

7 x 3 x Let f x a Enter the domain of f g x in interval notation and g x 15 x 1 b Enter the domain of g f x in interval notation

2 Let f x x g x 3x and h x X x 4 Express the following functions as compositions of f x g x and or h x Note Type your answers in the form u v x instead of u v x 2 a S x 9x S x b T x 3x 4 T x

Let f x x 4 and g x the following compositions a ff x b fog x c gof x 1 x 3 Finc

4 The table shows the volume of water in cubic meters V in a tank after tank after water has been pumped out for a certain number of minutes Which equation could represent the volume of water in cubic meters after t minutes of water being pumped out vers bas doss 02 0 A V 30 2 5t B V 30 0 5t C V 30 0 5t D V 30 0 1t volume of water time after pumping begins cubic meters 02 2 krokigs brin earned 30 0 eslags bus ananed 27 5 10 of bos ensued qui 15 20 7 5

Write an inequality for each graph 17 3 2 1 Solve each inequality and graph its solution 19 b 2 2 0 bz9 2 3 2 3 4 5 6 7 21 14 11 A 152 153 154 155 156 157 158 159 160 161 162 154 18 122 12 7 6 20 2 n 8 10 8 n 10 22 30 15a A 2 1 0 1 2 7 012 3 4 5 azz 6 7 9 10 67

2 cos 0 1 sec Write the expression in terms of sine and cosine and then simplify so that no quotients appear in the final expression 0 Choose the correct answer below OA sin 0 OC cot20 OE sin 0 Question 12 5 1 59 CIP OB sec 0 O D OF 1 2 cos 0 1 COS 0 HW Sco O Poin

Choose the correct answer below Write the expression in terms of sine and cosine and then simplify so that no quotients appear in the final expression sin xcsc x O A 1 OB OOO OO 1 C cos x D tan x E cot x O F Question 11 5 1 57 sec x HV COF

Which equation reveals the minimum or maximum value of f 2 without changing the form of the equation f x x 3 x 4 B f x r 8r 15 f x x 2 1 f 1 2x 1

QUIZ 11 4 11 6 11 7 Question 8 of 14 The probability of selecting a P or a Z is Type an integer or a simplified fraction The game of Scrabble has 100 tiles The diagram shows the number of tiles for each letter and the letter s point value One tile is drawn from Scrabble s 100 tiles Find the probability of selecting a P or a Z This question 1 point s possible www Submit quiz A F2 K B 2 G 3 L C 2 H 2 D 4 1 19 N 6 S X1 4 E 12 J 1 O 8 T6Y2 P 2 U Z1 Q V 2 M 2 R 6 W2 M 2 Nanb of till 2 A 9 Paint vales

Use the spinner shown to answer the question Assume that it is equally probable that the pointer will land on any one of the colored regions If the pointer lands on a borderline spin again If the spinner is spun once find the probability that the pointer lands in a red region The probability that the pointer lands in a red region is Type an integer or a simplified fraction This question 1 point s possible green red red green yellow red

In bungee jumping a bungee jump is the amount the cord will stretch at the bottom of the fall The stiffness of the 2W S L where W is the weight of the jumper cord is related to the amount of stretch by the equation K s in pounds K is the cord s stiffness in pounds per foot L is the free length of the cord in feet and S is the stretch in feet Use this equation to answer parts a and b a A 140 pound person plans to jump ott a ledge attached to a cord of length 33 feet It the stiffness of the cord is no less than 26 pounds per foot how much will the cord stretch O A less than 25 feet O B exactly 25 feet O C less than 26 feet O D more than 25 feet O E between 25 and 26 feet

The mathematics faculty at a college consists of 10 full professors 10 associate professors 7 assistant professors and 10 teaching assistants TAS If one faculty member is randomly selected find the probability of choosing a full professor or a TA The probability is Type an integer or a fraction Simplify your answer

Today the population of the town of Wallingford Pennsylvania is 11 300 people In 1980 ere were 10 000 people while in 1990 there were 10 500 people By what percent did the opulation grow from 1990 to today

7 Two competing bakeries are both selling birthday cakes Store A decreased the cost of its cake from 18 to 15 50 Store B decreased the cost of its cake from 21 to 18 Which store decreased the price of its cake by the larger percent

6 At the end of a season Chris records a 100 meter sprint time of 12 5 seconds At the begin ning of the season his time was 14 2 seconds What was the percent decrease in his time over the course of the season

5 20 of the books in a book shelf are mysteries 30 are science fiction and the rest are historical fiction If there are 10 mysteries on the shelf how many historical fiction books are there

4 The average American family of 4 uses 400 gallons of water each day To try to save water the Smith family plans to only use 250 gallons of water a day By what percentage are they de creasing their water consumption

3 At a supermarket the hourly pay was 14 before increasing by 1 50 to 15 50 What is the percent increase in the amount of money that an employee at the supermarket would earn

Multiply 192 90 0 192 90 0

Click here to watch the video Subtract the fractions 7 88 78 Enter your answer as a fraction 85 45 4 5 Simplify your answer

Write the fraction in simplest form 180 210 180 210 Type a whole number or a simplified fraction

Analyze the graph of the function 4 2 X x 8 R x 2 x 49 200 16 1 16 OB There is no horizontal or oblique asymptote d Which graph shown below is the correct graph for R x O A O B Q j 16 400 16 Q O C 16 I I 200 1 16 Q O D 160 x 7 16

Analyze the graph of the function R x OC 24x 35x 49 2 3x 25x 42 xXx 0 X 7 x 7 and x 6 0 OD All real numbers A b What is the equation of the vertical asymptote s of R x Select the correct answer boxes within your choice X Use a comma to separate answers as needed Type an integer or a frac OB There is no vertical asymptote

Analyze the graph of the function 2 x X 90 2 x x 72 R x OC xlx 0 x 10 x 9 and x 8 OD All real numbers b What is the equation of the vertical asymptote s of R x Select the correct choice below a answer boxes within your choice A x Use a comma to separate answers as needed Type an integer or a fraction

Simplify the complex rational expression using either Method I or Method II s 81 2 S s 9 2 s 81 2 S S 81 S S 9 1 s 9

Zemember A B 8123 C 0 6201 Football Team Points 337 44 7 8 7 4 7 8 Which data set below is represented by the stem and leaf plot Key 113 13 points 8 6 12 13 14 17 20 23 24 27 28 30 37 38 8 The Key for this stem and leaf plot tells you each stem represents the tens value and the leaves represent the ones value for each data value represented by the plot 6 12 13 14 17 20 23 24 24 27 28 28 28 30 37 38 0 1 2 3 6 2 3 4 7 0 3 4 4 7 8 8 8 0 7 8

ind the domain of each of the following functio 3 x x 6 4 x 9 1 f x 2 h x 3 g x 4 p x 3x x x 4 5x x 2 x 4 x 3 r 2

Verify the identity algebraically Use a graphing utility to check your result graphically 7 csc x csc x sin x 7 sin x 7 cos x 7 cot x 7 csc x sin x Expand the expression and then use the Reciprocal Identities to simplify Simplify your answers completely 7 csc x sin x sin x 7 csc x 7 7 7 csc x csc x sin x 7 sin x 7 cos x sin x 7 cot x 7 cot x 7 7 7 cot x

h x x 3 Which transformations are needed to graph the function h x x 3 Choose the correct answer below A The graph of y x should be shifted to the left by 3 units and reflected across the y axis B The graph of y x should be shifted to the right by 3 units and reflected across the x axis OC The graph of y x should be shifted to the left by 3 units and reflected across the x axis OD The graph of y x should be shifted to the right by 3 units and reflected across the y axis

Use any method to determine if the series converges or diverges Give reasons for your answer 2 0 1 21 Select the correct choice below and fill in the answer box to complete your choice OA The series converges because the limit used in the nth Term Test is OB The series diverges because the limit used in the nth Term Test is OC The series converges because the limit found using the Ratio Test is OD The series diverges because the limit found using the Rafin TI 1

Determine whether the alternating series 00 1 1 n 1 5 n 3 INC converges or diverges Choose the correct answer below and if necessary fill in the answer box to complete your choice OA The series does not satisfy the conditions of the Alternating Series Test but converges because it is a geometric series with r B The series does not satisfy the conditions of the Alternating Series Test but diverges by the Root Test because the limit used does not ex OC The series does not satisfy the conditions of the Alternating Series Test but diverges because it is a p series with p OD The series converges by the Alternating Series Test OE The series does not satisfy the conditions of the Alternating Series Test but converges because it is a p series This question 8 p with