Sequences & Series Questions and Answers

Use the ALEKS graphing calculator to solve the equation sinx 0 2x 0 3 Round to the nearest hundredth if necessary

A company is developing a new additive for gasoline The additive is a mixture of three liquid ingredients I II and III For proper performance the total amount of additive must be at least 5 oz 1 gal of gasoline However for safety reasons the amount of additive should not exceed 11 oz per gal of gasoline At least oz of ingredient I must be used for every ounce of ingredient II and a 4 east 1 oz of ingredient III must be used for every ounce of ingredient I The costs of I II and III are 0 30 0 24 and 0 36 per oz respectively a Find the mixture of the three ingredients that produces the minimum cost of the additive The minimum cost mixture has oz of ingredient I oz of ingredient II and Type an integer or a decimal Round to three decimal places as needed oz of ingredient III

There are 2 gumball machines at Beef O Brady s Each gumball machine is 12 inches in diameter A gumball has a volume of 1 cubic inch How many gumballs does Beef O Brady s need to purchase to fill both mach V lwh 4 V You may use one or both formulas to solve the problem

36 X 3 7 22 45 45 x 2 X 14 22 8 15 16 15 x 36 2 30 60 12 3 x 12 3 36 2x Special Right Triangles Directions Find each missing side Write all answers in simplest radical form Use your solutions to navigate through the maze Staple all work to this paper P 18 X 473d2 30 2 14 11 24 15 24 5 12 6 6 3 36 2 10 6 24 6 20 6 6 10 ZX X 15 2 6 5 15 2 2 A x 60 15 30 X 30 NIX 45 15 2 20 2 20 48 2 24 2 3 10 5 3 15 40 20 2 2 End 45 30 X 45 24 2 X X 2 X 4 30 2 15 X 2 15 2 28 3 45 7 3 7 2 2 15 4 15 2 30 24 X x 60 4 5 7 6 45 42 14 3 8 5 x 30 16 3 X 60 48 Gina Wilson All Things Algebra 2016

8 Solve the equation a 3 34 9 b 4

Sam s Pizza advertises that their delivery times are best in town If their delivery times are normally distributed with mean 30 minutes and standard deviation 5 minutes what is the probability that your pizza from Sam s will take more than 37 minutes to be delivered Justify your answer

K Choose the correct answer below Part 2 of 2 Determine whether the following series is arithmetic or geometric Then evaluate the finite series for the specified number of terms 81 27 9 3 n 200 The series is geometric The series is arithmetic The sum is 200 Type an integer or decimal rounded to two decimal places as needed Points 0 of 1 BELEID of a poin

The population of a certain country in 1998 was 282 million people In addition the population of the country was growing at a rate of 0 8 per year Assuming that this growth rate continues the model P t 282 1 008 1998 represents the population P in millions of people in year t According to this model when will the population of the country reach each of the following a 313 million people b 363 million people

survey to determine the remationsmp between gender and subject preference A total of 56 students were surveyed to determine if they like Math English Social Studies or Science as their favorite subject The results were then broken down based on whether the respondent was male or female Female Male Total Math 8 10 18 English 6 4 10 Social Studies Science 11 5 8 4 19 9 Total 30 26 56 a What is the joint relative frequency for female students who like English as their favorite subject Round to the nearest hundredth and interpret the meaning of this value b What is the marginal relative frequency for students who like math as their favorite subject Round to the nearest hundredth and interpret the meaning of this value

11 Solve the inequality Write the answer in i interval notation ii set builder notation x 3 1 x 2

8 The third term in an arithmetic sequence is 5 and the fifth term is 3 a What is the explicit rule for the n term of this sequence

One fifth equals the quotient of a number and 25 Find the number

Solve the trigonometric equation for all values 0 x 16 pi 2cos 1 8 x sqrt 3 0

The half life of hydrogen 3 is approximately 12 3 years Step 1 of 3 Determine a so that A t Aoa describes the amount of hydrogen 3 left after t years where Ao is the amount at time t 0 Round to six decimal places AnswerHow to enter your answer opens in new window 2 Points Keypad Keyboard Shortcuts

Unsaved An insect is stuck on the very tip of a second hand of a wall clock for a couple of minutes The tip of the second hand is 5 feet above the floor at its lowest point and 6 feet above the floor at it s highest The bug landed on the second hand at exactly 15 seconds after 10 10 pm Describe the bug s height as a function of time remember a second hand takes exactly 60 seconds to complete a full cycle 111212 13 9 8 FO 4 765 5 5 Which equation correctly describes the height of the fly as function of time correctly f t sin t 15 5 5 Of t 0 5sin 60 60 5 5 f t sin 1207 1 45 5 5

Other Regression Models A manager at a gas station realized that there appeared to be a quadratic relationship between the price he charged for a doughnut and the number he sold for the day What is the coefficient of determination 2 for the following data set using a quadratic model Price charged for a Doughnut at QT Number Sold that day FS 0 026 0 160 0 929 0 20 0 50 23 0 75 28 0 99 21 1 10 18 1 50

Basic Trigonometry Determine the approximate value of x N 8 56 2 78 9 X 72 F U

Consider the x and y values such that xo 2 x1 3 x2 5 x3 6 Yo 2 Y 6 y2 20 y3 30 If the Newton s divided difference second order polynomial for the given data is defined as follows P x 6 7 x a x b x c then find the values of a b and c A a 2 b 2 c 3 B a 2 b 2 c 5 OC a 3 b 3 c 5 OD a 2 b 3 c 5 E a 3 b 5 c 6

3 Find a positive angle less than 27 that is coterminal with support your answer 5 Draw a graph to

Use the Root Test to determine if the series converges or diverges 12 00 n 1 n n A Converges B Diverges Find the length of the curve 12 13 x 2 sin t 2t y 2cos t 0 st 13 B 2 A 8 C 12 D 4

While riding her bike to the ocean and back home 5 times Christine timed herself at 52 min 48 min 61 min 58 min and 60 min She had set a goal of averaging 56 minutes for her rides How many minutes will she need to spend on her sixth ride to attain her goal

cise 4 Hyperbola A hyperbola has its foci in F 1 2 and F 1 6 It also has a vertex in V 1 4 Find the standard equation the center the other vertex the equation of the asymptotes and the graph Center Standard Equation Vertex 2 10 5 10 0 6 5

se a power series to approximate the value of the integral with an error of less than 0 0001 Round your answer to five decimal places 1 4 3 4 5 1 4 x In x 1 dx x In x 1 dx X x 3 1 2 n 1 n 3 1 4 0

a City The estimated populations of several U S cities are shown Each population is rounded to the nearest thousand Write the range of whole numbers that each rounded population could represent b c d Baton Rouge LA The range is City Columbus OH The range is City Laredo TX The range is City Oklahoma City OK The range is 2010 Population 802 000 smaller value through 2010 Population 1 837 000 smaller value through 2010 Population 250 000 smaller value through 2010 Population 1 253 000 smaller value through larger value larger value larger value Save space by optimizing storage larger value Mana

The graph below shows the U S federal expenses for 2012 Dollars billions 3000 2000 1000 Interest All other departments and agencies Department of Defense Medicaid Medicare Other Social Security Discretionary spending Mandatory spending

What is AE if the bearing is 55 44 33 W 1000 00 O 823 57 O 826 52 O 567 22 O 562 91

Throw a pair of fair 4 sided dice and take X to be the sum of the numbers facing up Fill in the indicated values of the partial probability distribution table The other missing values appear when you correctly answer the question or press Do it X P X x 2 3 4 Check Clear Help Do it 5 6 7 8 Q How well does the line approximate the data A If we use the equation of the line to calculate the y coordinates we get slightly different values called predicted values for which we use the symbol 3 from the original observed values shown in the table

Decide whether each number is written in scientific notation If not write it in scientific notation If so restate the number in scientific notation a 0 74 x 1012 b d x 10 4 125 x 108 x 10 9 1 x 1003 x 10 1 04 x 1018 x 10

MY NOTES Continue the Sieve of Eratosthenes below through 155 Then list the prime numbers from 121 through 155 Enter your answers as a comma separated list 2 3 5 6 8 X 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

x x 5 x 2 0 Step 1 of 2 Write the polynomial inequality in the form p x 0 p x 0 p x 0 or p x 0 then find the real zeros of p x Answer Separate multiple answers with a comma X

P Cl QUESTION 3 A 388 T 8 Ra The superintendent wants to study the effects of phone distractions on math test scores In five math classes students were instructed to keep their phones face up on their desk while taking a math test In five other math classes stud dont compared the

10 The function g x contains the point 5 1 What will the point be if the function is transformed as follows 2f x 3

Peitra has 1 000 to deposit into a bank She puts the money into an account that earns simple interest of 1 25 each quarter Complete the following table that shows the amount in her account each quarter for the first year y balance x quarter 0 1 2 3 4 S 1 000 Think What about the table shows that this is simple interest Complete the following sentence After 5 years or 20 quarters Peitra will have 11

The price of gas went up by 0 5 last month Suppose gas currently costs 2 44 a gallon the price of gas continues to increase at this rate what will it cost one year from now after 12 months

Consider the following unorganized data set 12 15 8 29 30 27 19 12 What is the Interquartile Range IQR of the data set 12 16 17 28

7 Three brothers have ages that are consecutive even integers The product of the first and third boys ages is 20 more than twice the second boy s age Write an equation that represents the situation and 4 points find the age of each of the three boys

Tree Graphs Which graph below is a tree graph A O O

2 Make a sketch of a graph g x such that g x would have 3 real and 2 complex solutions

If tan 0 8 sec 0 with 0 in quadrant I what is sin cos 0 sin 0 cos 0 Tyne an integer or a simplified fraction

Chromatic Numbers Which graph below uses the correct number of minimum colors to determine the chromatic number of the graph FO C F D F B E D 2 colors B E 3 Colors B E 4 colors B 6 colors F E B

Which of the following is a digraph of Vertices A B C D Edges O D D D D B B C25 B B AB BC CD AD AC E BA

ghted averages blems Latrell works for a company that manufactures liquid dyes for clothing He currently wants to mix up some 38 concentrated pink dye He has 54 liters of 26 concentrated pink dye as well as plenty of 46 concentrated pink dye How many liters of the 46 concentrated pink dye will Latrell need to add to the 26 concentrated pink dye to make a batch with a concentration of 38 Write your answer as a whole number or as a decimal rounded to the nearest tenth liters

GRU Stage 0 Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 Stage 6 Stage 7 Stage 10 Stage 100 Stage n Number of sides 3 12 3 4 48 192 768 3076 Perimeter of Snowflake 1 Length of each side 1 3 Va 17 27 256 1024 3 Perimeter 44 16 64 256 1024 EXERCISE 5 Analyze the patterns which appear in each column in the chart above and fill in the last seven rows of the chart

Body Temperature normal distribution 96 2 96 9 97 6 98 3 99 0 99 7 101 4 Body Temperature degrees Fahrenheit Identify the standard deviation of the normal distribution Enter your answ by clicking the bubbles 2 3 5 6 2 4 5 6 7 2 3 5

if two legs of a right triangle are 9 and 11 the hypotenuse is

logarithmic and exponential equations Rewrite as a logarithmic equation 3 0 1

7 Solve each of the following equations if possible by showing your work 15 pts a csc 0 2 0 0 2n b tan 0 1 0 0 0 2n

Minimum Spanning Trees Which of the graphs below correctly use Kurskal s Algorithm to determine a minimum spanning tree A 3 B B 3 4 B 3 3 N 6 D D 2 F 3 D 5 2 E E O A 3 B C 3 7 D 5 F E

3 I Question 3 25 points Shortest Route Algorithm What is the cost of the shortest route from vertex A to vertex E use the shortest route algorithm 9 10 A B 7 1 D 11 C 9 1 13 E 2 2 F 12 3 H

Find the indicated sum Use the formula for the sum of the first n terms of a geometric sequen i 1 i 1 5 2 5 2 0