Sequences & Series Questions and Answers

Solve for a a 8 1 O a a 9 and a 9 b a 6 and a 6 O c a 4 and a 4 O d a 8 and a 8

value 6 Select the correct order of steps to match the work shown 10x 5 4x 47 14x 5 47 14x 42 x 3 Divide 42 by 14 Add 4x to the 10x Subtract 5 from the 47

2 An electrician charges a 40 fee to make a house call plus an hourly rate for labor If the total bill for a job that takes 2 hours comes to 99 what is the electrician s hourly labor rate 33 50 hour 29 50 hour 32 00 hour 28 00 hour

Use the law of cosines to solve the following problem The robot arm shown in the figure places packages on a conveyer belt What is the distance x Determine the expression that can be evaluated to find x A x 2 252 1 252 2 2 25 1 25 cos 100 0 B x 2 252 1 252 2 2 25 1 25 cos 100 0 Oc x 2 25 1 252 2 25 1 25 cos 100 0 D x 2 25 1 25 2 2 25 1 25 cos 100 0 What is the value of x X 2 25 m X 100 0 1 25 m Belt

Suppose u and v are orthogonal unit vectors to say that a vector is a unit vector means that it has a length of 1 Find the dot product 3u 8v 4u

Find a formula for an exponential model Of t 390 x 1 09t f t 682 5 x 0 55t Of t 292 5 x 0 82t Of t 585 x 1 54 Of t f t 195 x 1 36

Here is a bivariate data set in which you believe y to be the response variable X 45 7 2 Enter as an ordered pair 92 8 18 2 28 2 23 2 7 8 77 4 81 6 48 2 27 35 8 109 9 101 9 50 7 28 5 19 6 215 9 40 1 1 4 29 2 32 2 47 7 y 11 9 0 8 1 8 0 4 24 5 30 8 78 6 Make a scatter plot of this data Which point appears to be an outlier

1 Part 0 2 3 Part 1 of 2 4 5 6 7 8 9 10 11 Let s go to the movies A random sample of 41 Foreign Language movies made since the year 2000 had a mean length of 112 4 minutes with a standard deviation of 13 4 minutes 12 X 13 a Construct a 90 confidence interval for the true mean length of all Foreign Language movies made since 2000 Round the answers to one decimal place A 90 confidence interval for the true mean length of all Foreign Language movies made since 2000 is 0 S Espa ol 14 00 B 6 cla E

Brent William Charlie and Dave competed in the Olympics These four divers placed first second third and fourth in the competition 1 Brent ranked between Charlie and Dave 2 William did better than Charlie 3 Charlie did better than Dave Who finished in each of the four places William was first Brent was second Charlie was third and Dave was fourth

Let y 7 J U1 A 105 190 1 6 U2 2 8 1 28 Compute the distance d from y to the plane in R spanned by u and u 5

Major League Baseball s World Series is a maximum of seven games with the winner being the first team to win four games Assume that the Atlanta Braves and the Minnesota Twins are playing in the World Series and that the first two games are to be played in Atlanta the n games at the Twins ballpark and the last two games if necessary back in Atlanta Taking into account the projected starting pitchers for each game and the home field advantage suppose the probabilities of Atlanta winning each game are as follows Game 1 2 5 6 7 0 56 0 49 3 4 Probability of Win 0 59 0 54 0 49 0 44 0 47 Construct a simulation model in which whether Atlanta wins or loses each game is a random variable Use the model to answer the following questions Use at least 1 000 trials a What is the average number of games played regardless of winner Round your answer to one decimal place games b What is the probability that the Atlanta Braves win the World Series Round your answer to three decimal places

Find the radius of convergence R of the series x 5 n7 n 1 R Find the interval I of convergence of the series Enter

Table below contains the percentage of woman receiving prenatal care in 2009 for a random sample of countries Pregnant woman receiving 2013 Estimate the mean percentage of woman receiving prenatal car in all countries in 2009 using a 93 confidence interval percentage of woman receiving prenatal care in percent 93 68 87 76 78 6 86 3 78 6 96 23 94 51 91 8 94 3 92 2 78 6 93 4 95 78 6 93 8 88 4 80 34 80 6 98 2 99 95 8 97 9 91 5 97 95 78 6 81 9 99 87 7 92 1 90 7 92 47 93 63 100 92 41 92

K A group of 10 workers decides to send a delegation of 3 to their supervisor to discuss their grievances Complete parts a through c below a How many delegations are possible There are 120 delegations possible b If it is decided that a particular worker must be in the delegation how many different delegations are possible There are delegations possible

A group of 4 students is selected from a group of 13 students to take part in a class in cell biology Complete parts a and b below a In how many ways can this be done There are 715 possible ways b In how many ways will the group who will not take part be chosen There are possible ways ww

Decide whether the exercise involves permutations combinations or neither and then solve the problem In a club with 12 juniors and 13 seniors how many 7 member committees can be chosen that have a all juniors b 4 juniors and 3 seniors c at least 6 seniors Does the problem involve permutations or combinations O Combinations O Permutations ONeither permutations nor combinations

Ashley will rent a car for the weekend She can choose one of two plans The first plan has an initial fee of 57 and costs an additional 0 13 per mile driven The second plan has an initial fee of 44 and costs an additional 0 18 per mile driven What is the cost when the two plans cost the same

Write the sum of the first three terms of the binomial expansion expressing the result in simplified fom 10 The sum of the first three terms of the binomial expansion is Simplify your answer

12 Jose and Caroline are shopping for school supplies Caroline spent 15 50 on 5 notebooks and 3 folders Jose bought 4 notebooks and 4 folders and spent 14 This situation can be represented with the system 5x 3y 15 50 and 4x 4y 14 where x represents the cost of each notebook and y represents the cost of each folder What is the cost of one notebook and felder 2

Indicate whether each of the following systems of equations has no solution one solution or an infinite number of solutions y x 1 5y 3x 5 y 3 x y 2x y 2x 3 4y x 1 2x y 4 TITE No Solution O 0 One Solution O O O Infinite Solutions O O

Let the total cost function C x be defined as follows C x 1 200 3x 0 0009x2 0 x 6 000 Find the average cost function C C x Find the marginal average cost function C T x

2 3x 12y 18 6x 24y 36

10 Solve the system of equations by elimination y x 5 5y 9 x

Julio walked from one corner of a rectangular field to the opposite corner along a diagonal of the field This diagram represents the field and the path Julio walked 50 yards by 120 yards Based on the dimensions in the diagram what is the distance that Julio walked

Approximate the solution of 6e 4 11 to 3 decimal places You may use a graphing utility O 10 255 O 4 606 O 5 609 O 3 394 LOO

Solve 8 for x no solution 0 3 01 0 2 0 1

Approximate the solution to In 2x 3 2 Round to 3 decimal places O 0 470 O 792 447 4 953 12 266 3 003

Use a graphing utility to approximate the solution to log4x log 4 2x 1 3 Round to 3 decimal places 5 412 O 5 912

If f x x 7 5 and g x 14 determine where f x g x Express your answer using interval notation O 16 U 2 O 12 16 O 12 U 16 O 16 2

Jolene invests her savings in two bank accounts one paying 6 percent and the other paying 8 percent simple interest per year She puts twice as much in the lower yielding account because it is less risky Her annual interest is 2460 dollars How much did she invest at each rate Amount invested at 6 percent interest is 23800 Amount invested at 8 percent interest is 47600 X X

A concert to raise money for an economics prize is to consist of 8 works 4 overtures 3 sonatas and a piano concerto Complete parts a and b below K a In how many ways can the program be arranged It can be arranged in way s Type a whole number CO

Correct Find the zero s of the equation Round decimal values to two places If there is no solution indicate None 4 x 10 0 Answer Keypad Keyboard Shortcuts Enter your answer s starting with the leftmost box Do not leave any boxes empty in between answers You may not need all the boxes Selecting a button will replace the entered answer value s The value of the button is used instead of the value in the associated box es

Two forces of magnitude 30 newtons N and 20 N act on an object at angles of 210 and 45 with the postive x axis as shown below in the figure Find the magnitude and direction of the resultant force F F 210 deg F1 1 30 N 45 deg The direction is F211 20 N The magnitude is Round to the nearest tenth as needed newtons a

art 1 Growth Factor 1 The table below represents the growth of an investment account over 5 years Complete the table and answer the questions X of years O C 1 2 3 4 5 a What is the growth factor of this function y balance 283 50 312 56 344 60 b What is the annual rate of return in this account Hint By what percentage does this function increase each year What was the initial value in the investment account MO100

am must fly home to city A from a business meeting in city B One flight option flies directly to city A from B a distance of about 455 miles A second flight option flies first to city C and then connects to The bearing from B to C is N29 7 E and the bearing from B to A is N63 5 E The bearing from A to B is S63 5 W and the bearing from A to C is N78 1 W How many more frequent flyer miles will am receive if he takes the connecting flight rather than the direct flight more frequent flyer miles Question 12 9 2 45 am would receive ound to one decimal place as needed GUCCES

explain your reasoning Situation a You put 100 in a savings account that earns 1 interest every year b You put 10 in a savings account and deposit an additional 10 every month c You put 75 in a checking account with no annual interest d You invest 75 in a portfolio with an average of 6 annual returns e You have 1500 in savings Every year inflation causes your money to decrease by 2 in purchasing power exponential function and Linear or Exponential Reasoning

Clare surveyed some students at her school about their favorite professional sports Of the students surveyed 19 said baseball was their favorite sport while 38 of the students had other favorite sports What is the experimental probability that the next student Clare talks to will pick baseball Simplify your answer and write it as a fraction or whole number P baseball

Consider the following relation 1 8 0 9 9 7 7 8 5 8 2 7 Step 1 of 2 Determine the values in the domain and range of the relation Enter repeated values only once Enable Zoom Pan 10 1012 Correct 5 5

1 Find the equation for the line that passes through the point 2 0 and that is perpendicular to the line with the equation y 4 x 3 10 1072 Enable Zoom Pan

Apply appropriate identities to write as a single trig ratio 1 2 sin 22 a b c cosx cos4x sinx sin4x 2 tan 40 1 tan 40

1 The graph below represents the value of Lucas investments which average 8 annual returns account balance S 5000 4500 3 4000 3500 3000 2500 2000 4500 1000 500 0 500 10 20 a What was the initial balance in the account 25 30 35 years b Approximately how much did the value of Lucas investments increase in the first 10 years C Is the account growing by the same number of dollars each year Explain how you know

1 You ve won the world s strangest lottery and you have to choose how to receive your prize You have three options 1 to be paid 80 000 today 2 to be paid 3000 per day for the next month or 3 be paid 1 and have it doubled each day for the next month a Choose your top two options and create a visual representation of each option drawing graph etc justifyour response

Which type of study is most likely to involve a placebo A observational study B controlled experiment C survey

Which of the following is a survey given to those that volunteer A convenience sample C self selected sample B random sample D systematic sample

The graph off is shown a b c d e 15 6 J15 0 Evaluate each integral by interpreting it in terms of areas rx dx f x dx f x dx f x dx If x dx 10 7 1x dx 6 y f x 12 18 24

Use the Half angle Formula to find the exact value of the expression sin Which Half angle Formula should be used to find sin Select the correct choice below and fill in the answer box to complete your choice Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression OB Sin OA sin OC sin OE in G sin 1 cos 2 1 sin D 2 1 sin 2 1 cos 2 OD sin OF sin OH sin 5 1 cos 2 1 sin 1 sin 2 1 cos

Which of the following is the least biased type of sample A random sample B self selected sample C convenience sample

The half life of radium 225 is approximately 14 9 days Step 3 of 3 How much of a 15 gram sample of radium 225 would remain after 9 days Round to three decimal place

Twenty gallons of a salt solution consists of 40 salt It is the result of mixing a 55 solution with a 25 solution How many gallons of each of the solutions was used Let x the number of gallons of the 55 solution and y the number of gallons of the 25 solution The corresponding modeling system is y 20 0 55x 0 25y 0 4 20 Solve the system by using the method of substitution AnswerHow to enter your answer opens in new window 2 Points Enter the ordered pair below Keypad Keyboard Shortcuts

A piece of cardboard measuring 8 inches by 9 inches is formed into an open top box by cutting squares wit side length from each corner and folding up the sides Find a formula for the volume of the box in terms of a V x Find the value for a that will maximize the volume of the box