Sequences & Series Questions and Answers

Find the a mean and b standard deviation for the data set Round to two decimal places International Travel Destinations of U S Citizens in 2000 U S Citizens in thousands Country ABCDEFGH 982 582 202 182 142 87 85 84 72 62 a 242 b 9 000 Ba 242 b 300 55 Ca 248 b 300 55 OD a 248 b 9000

5 Find the variance of the data set below 55 63 68 70 70 74 76 OA 7 09 OB 50 27 OC 43 14 OD 6 57

1 Describe how relative frequencies of past events are used to predict future events For example if a student passed seven out of ten assignments in a course what do you think is the probability that this student will pass the next assignment in the course How did you calculate this probability

The second term in a geometric sequence is 30 and the fourth term is 120 What is the equation an for the nth term of this sequence that contains both positive and negative terms Find the value of ag

A new Ford F 150 costs 26 050 Its value depreciates at a rate of 5 5 per year How much would a Ford F 150 cost after 6 years Round your answer to the nearest dollar amount

2 1 1 2 Determine the period 2 A 4 9 8 10 12 14 Ente

Function f is a rational function given by the equation f x mea Complete the table 100 50 2 2 4 10 50 b Describe the end behavior of f x As x f x c Write an equation for the horizontal asymptote of f x 5 David is on the school soccer team At practice he practices shooting penalty kicks He makes 14 out of 16 penalty kicks attempted a Write an expression representing the proportion of penalty kicks that David made MACERA b David attempts more penalty kicks He misses all of them Write an expression representing the proportion of penalty kicks that David made after k more kicks c Based on the expression you created in part b what value of k gives David a proportion of penalty kicks made equal to 0 70

Find the measure of angle Round to the nearest tenth x 18 98 9 Show Transcribed Text

cide if the function below is linear or exponential and find a formula t 0 f t 400 1 2 3 4 600 900 1350 2025

The number of bacteria P in a certain population increases according to the following function where timer is measured in hours P t 2700 0 25t Find the number of bacteria in the population after 4 hours and after 8 hours Round your answers to the nearest whole number as necessary Number after 4 hours Number after 8 hours bacteria bacteria

A department store has some colorful teacups on clearance An employee noted the numbers and kinds of teacups that are left Small Medium Green 5 5 Yellow 3 5 Blue 4 1 What is the probability that a randomly selected cup is given that the cup is small Simplify any fractions 55 01 C 12re

An ice cream shop offers ten different flavors and eight different toppings If you can only pick one flavor and two different toppings how many different combinations can you have

1 16 2 3 2 2 2 Select one O a 1 5 O b 1 9 O c 9 O d 1 4

Sive the magnitude and direction of the final vector in 9 Select one O a 6 4 38 7 O b 7 8 50 3 O c 38 6 4 O d 7 3 15 9

1 Calculate each missing item in the chart Principal a 250 b 925 c 1387 500 SIMPLE INTEREST CALCULATIONS I Prt 250 0506 2 d e f 1000 Rate 6 8 5 10 Linne 2 years 67525 3 months 8 weeks 5 years Interest 8 months 30 18 25 10 40 320 249 50 8 22 23 84

Given the hyperbola x 25 y 16 1 a 6 points Graph the hyperbola and label the coordinates of the center the vertices and the foci on the figure

e a system of two equations in two variables a and d to write a formula for the general term the nth term of the arithmetic sequence whose sixth term ag is 3 and whose ninth term ag is 27

1 If y varies directly as x2 and y 20 when x 2 find y when x 7

1 Find three consecutive even integers such that three times the first plus two times the second minus the third equals 16

V Answer 2 Points 2 X 2 f x 2 f 8 X 2 Step 1 of 3 Evaluate this function at x 8 Write the exact answer Do not round If the answer is undefined write Und as your answer if x 3 if 3 x 3 if x 3 Keypad Keyboard Shortcuts M

A manufacturer of ski clothing makes ski pants and ski jackets The profit on a pair of ski pants is 2 00 an the profit on a jacket is 1 50 Both pants and jackets require the work of sewing operators and cutters There are 60 minutes of sewing operator time and 48 minutes of cutter time available It takes 8 minutes to sew one pair of ski pants and 4 minutes to sew one jacket Cutters take 4 minutes on pants and 8 minutes on a jacket Find the number of pants and jackets the manufacturer should make in order to maximize the profit pairs of pants jackets

I had a CD certificate of deposit with ABC Bank through 2010 that paid 4 69 interest compounded daily What was the APY for this rate

2 A set of test scores is normally distributed with a mean of 100 and a standard deviation of zu Use the 68 95 99 7 rule to find the percentage of scores in each of the following categones a Draw the model for these test scores Clearly label it showing what the 68 95 99 7 Rute predicts b What is the percentage of scores greater than 100 c What is the percentage of scores greater than 120 d What is the percentage of scores less than 80 e What is the percentage of scores less than 140

Eric earned some money doing odd jobs last summer and put it in a savings account that earns 3 interest compounded continuously Afte 1 year there is 200 00 in the account How much did Eric earn doing odd jobs Round your answer to the nearest cent

9 x y 30x 16y 288 0 2 N 30x16y 28850 26x 22 124 0 10 x y 22x 16y 149 0 12 x y 12x 8y 16 0

18 cm A B 147 C 45 cm 47 cm D centimeters 9 cm T S U 91 89 These figures are congruent What is BC 47 cm 33 R

An exponential function f x passes through 4 2 and 5 10 and has a horizontal asymptote at y 8 What is an equation of f x 10 10 0 5 10 1 4 2 10 4 8

7 A function f x Is shown y 5 4 3 2 5 4 3 2 21 1 2 40 4433 2 3 4 1 2 3 4 5 What is an equation of f x x 1 e

4 Which statements are correct about the function 1 2 Select all the correct statements A The graph of g x has an x intercept As x g x 8 g x 10 B 8 c The y intercept of g x is 0 18 D The domain of g x is all real numbers E The range of g x is all real numbers F The function g x models exponential decay

An investment of 8 500 has an annual interest rate of 6 6 The interest is compounded quarterly Which equation models the value A of the investme years AA 8500 1 0165 6 A 8500 1 066 6 A 8500 1 066 A 8500 1 0165

Which of the following vectors is perpendicular to the plane 2x 3y 5z 7 0 Question 1 options 6 1 3 1 3 5 3 2 5 2 3 5

Bonus The four sections in this square all have the same area What s the length markes x The dashed lines show the midlines of the square 9 9 X 9

4 Verify that Stokes Theorem is true for F x y z 2yz y 3x and S is the part of the paraboloid z 5 x y that lies above the plane z 1 oriented upward

Find the sum of the finite geometric series 2 2 1

A city doubles its size every 82 years If the population is currently 139 000 what will the population be in 246 years people

O Finite Type Infinite discrete O Continuous Flip a coin three times Y Finite Type Infinite discrete O Continuous galaxy A the number of planets that can support life O Finite Type Infinite discrete the number of heads that come up Take 5 shots at the goal during a soccer match W Roll a pair of dice until you get a double 1 Z the number of times you roll the dice Finite Type Infinite discrete Continuous Check Check Check the number of times you score Check

A playground in the kinder garden has a shape of triangle PRQ with the sides p 324ft q 421 ft and r 298 ft Find the angles P Q and R

14 Solve the system of equations Be sure to show all work and to check your solution 3 3x 2y z 4 5x 2y 2z 9 2x y 3z 20 St 2 9 45 24 22 9 32 20 Cozumi

Use properties of logarithms to solve the equation for a log 5z 3 18 A B C3 E x 3 T 21 5 018 3 5 e183 5 9 4

Jolene invested her savings in two bank accounts one paying 6 percent and the other paying 9 percent simple interest per year She puts twice as much in the lower yielding account because it is less risky Her annual interest was 4683 Construct a system of equations and solve it to find out how much did she invested at eac She invested She invested at 6 at 9

5 What is the reference angle for the angle shown 400 degrees x

1 true Classify the values of 0 In radians that will make sin 0 7 20 DRAG DROP THE ANSWER K 7T 6 3 2 11T 6 19T 6 13T 6 Values in Ra

9 Debbie cut a cord into sixths She used five of the pieces to make necklaces She used equal lengths of the remaining cord for each of four bracelets What fraction of the original cord did Debbie use for each bracelet 1 O 12 16 1 24 draw a picture to help slay

In a binomial experiment with 22 trials and a probability of success 0 566 compute the probability of exactly 13 successes If we were going to compute this using the binomial probability formula which of the following is correct 22 0 566 3 1 0 566 22 13 22 22 13 22 13 13 22 22 13 0 566 3 1 0 566 22 13 0 56622 1 0 566 13 22 22 13 22 13 0 56613 What is the probability rounded to four decimal places

Question 23 2 points Geometric Sequence What is the common ratio of the sequence 27 9 3 1 01 O O 3 6 Question 24 2 points

A high school student spends an average of 6 hours 6 on their phone a day with a standard deviation of 2 5 hours a 2 5 If samples of size 16 n 16 were taken from the population what would be the mean of the sample means 4 1 5 02 5 04 6

Question 48 2 points Use the central limit theorem if possible For a sample of n 100 find the probability of a sample mean being greater than 24 given 22 and 0 9 The population is not normally distributed 13 6 34 1 34 1 0 0131 0 4121 0 9869 Cannot be determined because the sample size is too small 13 6

An algebra class has 12 students and 12 desks For the sake of variety students change the seating arrangement each day How many days must pass before the class must repeat a seating arrangement days must pass before a seating arrangement is repeated Suppose the desks are arranged in rows of 4 How many seating arrangements are there that put Larry Moe Curly and Shemp in the front seats seating arrangements that put them in the front seats What is the probability that Larry Moe Curly and Shemp are sitting in the front seats The probability is There are

2 If L 2 M 3 3 N 16 P 9 which expression results in a rational number 1 L M M N 2 3 N P 4 P L

Build as few sine and or cosine functions as possible to satisfy each constraint at least ond A C E Trigonometric Functions Menu Task G Has a period of less than 27 Goes through the point 27 0 Has a maximum at 0 2 Has a horizontal translation of B D F H Goes through the point 0 3 Never enters quadrant III Has a period length of 47 Has a midline of 0 Be sure to identify which functions satisfy which constraints Check your functions using desmos com graphing to make sure that they do what you think they do