Sequences & Series Questions and Answers

COSO sino 3 i tanh 6 i sech 6 tanh 3 i F

Find all values of x satisfying the given conditions x 6 3 9 x x 8 7 f x OA 4 OB 4 5 O C 4 5 OD 18 and f x g x

OA 4 200 OB 4 000 OC 3 800 D 3 400

K The logistic growth function f t nearest whole number OA 437 butterflies OB 9 880 butterflies OC 237 butterflies OD 337 butterflies 520 1 6 4e 0 13t describes the population of a species of butterflies t months after they are introduced to a non threatening habitat How many butterflies are expected in the habitat COLL

Your oldest daughter is about to start kindergarten in a private school Tuition is 30 000 per year payable at the beginning of the school year You expect to keep your daughter in private school through high school You expect tuition to increase at a rate of 5 per year over the 13 years of her schooling What is the present value of your tuition payments if the interest rate is 5 per year How much would you need to have in the bank now to fund all 13 years of tuition PV C r a 1 9 9 r

39 If 9x 8 18 x O x 9 O O x O x 100 9 100 9 x 10 EN English United States 81 F CO

Write down the first four terms of the given sequence an 1 1 3m

If o 3 are acute angles such that sin a and cos 3 calculate cos a 3 If your answer is a fraction type it using the symbol For example if the answer is write 3pi 2

In the diagram shown below two ships are at points P and Q The ships are in the same vertical plane as an airplane at point R When the height of the plane is h 3650 feet the angle of depression from point R to point P is 58 degrees and the angle of depression to Q is 41 degrees Determine the distance between the two ships Enter an exact expression or round to the nearest whole number To present an angle in degrees type deg or use the MathPad degree symbol For example sin 30deg P distance from P to Q ft Q

5 Islamic calligraphy is the art of A writing in a beautiful and elegant manner OB weaving textiles with floral and geometric designs C painting rapidly in watercolor on wet plaster OD sculpting a pot and decorating it with geometric shapes

42 The temperature from midnight to noon on March 15 can be modeled using the function T h 4 2 h 42 where T temperature and h hours relative to noon note h 0 represents noon Find the domain of the function O 12 h 0 O 0 h 12 O 6 h 0 O 12 h 12 43 75 of 400 is O 10 O 30 O 100 O 300 44 Linear relations are not functions when they appear graphically as O horizontal lines Overtical lines

10 the ratio of their areas is what Mark all correct answers more than one answer may be correct 02 1 4 to 1 2 to 1 04 1 y k 2 1 04 1 6 Solve the equation below and find the variation constant k Find y when x 86 if y varies inversely as x and y 101 when x 13 Round your answer to the nearest thousandth if necessary x 7 Solve for x x 1x 1 Write your answer as a fraction

K Graphing utilities can be used to shade regions in the rectangular coordinate system thereby graphing an inequality in two variables Read the section of the user s manual for your graphing utility that describes how to shade a use your graphing utility to graph the following inequalities y 3x 2 Choose the correct graph below O A O C ON OU All graphs are 12 12 2 x 12 12 2 OB O D

Graph the union of the two inequalities y 5 2x 5 y 4 Use the graphing tool to graph the union Click to enlarge graph L

difference between the squares of two numbers is 8 Four times the square of the first number increased by the square of the second number is 37 e numbers are pe ordered pairs Use a comma to separate answers CXXB

Algebra 2 Homework 1 3 To perform compositions of linear functions Find the composite function 1 g x 3x 1 Find gog x 3 g a 4a f a 2a 4 Find gof a 5 g a a 3 f a a 4 Find gof a 7 g x 4x 2 Find gog x Name haiya Nelson f x 2x 4 g x 4x 3 Find fog x 4 h t 3t 2 g t 4t 3 Find hog t 6 g n 4n 1 f n n 3 Find gof n Period 8 g n n 1 f n 4n 4 Find gof n g f n 41 4 1 4n 4 1 10

different running classes 2 2 4 6 8 Class B mi 1 Compare the shapes of the dot plots 6 Class A mi 4 2 Compare the centers of the dot plots 3 Compare the spreads of the dot plots 10 4 Calculate the medians of the dot plots 5 Calculate the ranges of the dot plots 10 12 12 run per week for two 14 14 Definitions Measures of Center Mean Used for symmetric distributions Median Used for skewed distributions Mode Used for data with multiple peak usually separated with a gap Measures of Spread Variability IQR Used for skewed distributions Range Mostly used in symmetric distributions with no outliers 6 What do the medians and ranges of two dot plots tell you about the data

Problem 2 Find the missing sides and angles of the triangle below given that A 10 C 11 a and assuming that y is an acute angle A B B B Y C a

40 Solve the equation below and find the variation constant k Find a when y 20 if y varies inversely as and y 9 when 56 Round your answer to the nearest thousandth if necessary 41 Convert to standard form y x 4

23 Which of the following sets is a finite set of rational numbers Ott O O O O C 3 2 3 14 1 2 0 1 1 4 1 1 3 5 7 9

sidering the mequality is described by O shaded below a dashed line O shaded below a solid line O shaded above a dashed line O shaded above a solid line graph 46 Replace the with the correct symbol or which will make a true statement from the following expression

Tony owned a 1 year 15 000 certificate of deposit CD that was worth 15 885 60 at maturity What was the annual percentage yield APR for this investment 3 points

3 Robert invested 4 200 in a 1 year certificate of deposit CD which pays 2 5 compounded daily How much will Robert have in his account after 1 year Use the table on the next page to help you 3 points

11 Harry deposits 10 000 in First Saving s 4 year CD which pays 4 5 compounded monthly How much will he have in the account at the end of 4 years You may use the table on p 2 to help you 4 points

0 A stockbroker charges you a 34 50 commission for a stock that sells for 96 57 a share How much would 75 shares cost you 3 points

2 Donald Westhoven is single After meeting his annual deductible he had the following non network plan costs co payments 7 physician visits and 2 specialist visits He also had the following pharmacy charges 3 local generic charges 2 local brand name drugs 10 mail order generic drugs and 1 mail order brand name drug There is also a hospital charge of 2 575 What amount did he pay 4 points

DIRECTIONS Complete each problem and show as much of your thinking as possible 1 Brandon Alverez is single and pays into an HMO The total cost is 9 370 annually and the employer pays 90 of the total cost He also pays 50 of the optional annual dental premium of 782 and 50 of the optional annual vision premium of 275 How much is deducted each week from his paycheck 4 points

Ernesto is 71 years old His IRA has a fair market value of 352 850 76 His life expectancy factor is 26 5 What is Ernesto s required minimum distribution 3 points

Many elevators have a capacity of 1500 pounds a If a child averages 30 pounds and an adult 100 pounds write an inequality that describes when x children and y adults will cause the elevator to be overloaded b Graph the inequality Because x and y must be positive limit the graph to quadrant I only a What is the inequality CIDE 50 40 30 20 10 Ay oi 0 20 40 60 80

Find the 7th term of the geometric sequence 4 20 100

27 Given the formula V r h solve for r O O O 31 AV V h

22 How many ounces of water must be added to 135 oz of 85 sodium nitrate solution to produce a 75 solution Round your answer to the nearest hundredth OZ 23 Tell whether the given lengths can be the sides of a right triangle a 3 b 4 c 2 O yes C no

3 Luke is driving home from work Let D t denote Luke s remaining distance to drive D 160 measured in miles after t minutes of driving x app ou opowo at app on What does the statement D 0 10 mean a The drive between Luke s home and his workplace takes 10 minutes b The drive between Luke s home and his workplace is 10 miles les long s c Luke s remaining distance is 0 miles after 10 minutes

A line is a line that approximates the relationship between variables on a scatter plot These lines can be different for each person The line that gives the most accurate model of the relationship between two variables on a scatter plot is called the of best fit This line can be found using linear regression on a calculator The r indicates the strength of the correlation The closer r is to 1 or 1 the more closely the data resembles a line and the more accurate your model

Find the distance between the points on a number line 4 0 The

LUC E Choose the correct interval OA c c t OB C C t OC c t t OD C C t 1 c t

Complete a and b You can verify your conclusions by graphing the functions with a graphing calculator lim a Use analytic methods to evaluate the limit If the limit is infinite enter or as appropriate If the limit does not otherwise exist enter DNE b What does the result from part a tell you about horizontal asymptotes O The result does not yield any information regarding horizontal asymptotes O The result indicates that there is a horizontal asymptote O The result indicates that there are no horizontal asymptotes

Name the whole numbers from the list below 11 7 5 0 90 3 93 7 4 1 17 1 2727727772 2 The whole numbers are Use commas to separate answers as needed

rove that S z C z 1 CX is isomorphic to 9 cos 8 sin sin 0 0 0 0 2 GL2 R cos 6

Add file Question 15 In a lottery game a player picks 8 numbers from 1 to 52 If 7 of the 8 numbers match those drawn the player wins second prize What is the probability of winning this prize Be sure to leave your answer as a fraction in order to earn credit

A computer password is required to be 5 characters long How many passwords are possible if the password requires 2 letter s followed by 3 digits numbers 0 9 where no repetition of any letter or digit is allowed possible passwords There are

Give the System of equations 1 atbc 8 2 btac 8 3 ctab

Compute R6 L6 and M3 to estimate the distance traveled over 0 3 if the velocity at half second intervals is as follows t s Incorrect R6 53 L6 0 Incorrect 0 43 5 v m s 14 Give an exact answer Use symbolic notation and fractions where needed M3 52 0 5 lim 13 1 18 Use Power Sums to evaluate 1 5 N35 4s 2 M3 2 25 19 Show Transcribed Text 2 5 3 19 C

Let A 0 1 2 1 2 3 B y EQ y 1 2 E Z and C 1 5 CR In answering the following questions you must give reasoning This means that you can t just write down an answer you should explain how you determined the answer i Find An B ii Express C B as a union of intervals iii Find A U Cn B

Calculate the following summation expression A 0 t 1 300 1 0 05

c 2 T x y dx 2 x x y Ha y dy 0 is

b Find the inverse Laplace transform of 2 38 28 4 a S 25 10 s 1 s 25 s 1 s 4 s 1 s 25 c Lise Laplace transform to solve the following differential equation 10 m

one I m still learning it I can compute the interest on a certificate of deposit CD 3 Clifford and Hazel Ida can purchase a 4 year CD for 10 000 at 4 5 compounded daily or compounded monthly a What is the amount of the CD at each rate at maturity What is the difference in the interest earned You can use the table on page 15 to help you 1 point I got it

4 Find the breadth first and depth first spanning trees for the graph below starting with the vertex E A B C E D F H K L

For the linear function f x mx b f 2 19 and f 4 23 Find m and b 11