Permutations and Combinations Questions and Answers

A city doubles its size every 41 years If the population is currently 700 000 what will the population be in 123 years people

Now use the above frequency table to complete the estimated probability distribution of X X P X x 7 7 2 3 1

The function f x 2x 24x 72x 5 has one local minimum and one local maximum Use a graph of the function to estimate these local extrema This function has a local minimum at x 6 with output value 5 OF and a local maximum at x 2 with output value 145 K OF 0

10 freshmen 7 sophomores 7 juniors and 10 seniors are eligible to be on a committee In how many ways can a dance committee of 18 students be chosen In how many ways can a dance committee be chosen if it is to consist of 6 freshmen 5 sophomores 3 juniors and 4 seniors

Using the digits 2 through 10 find the number of different 4 digit numbers such that a Digits can be used more than once b Digits cannot be repeated but can come in any order ways ways c Digits cannot be repeated and must be written in increasing order d Which of the above counting questions is a combination and which is a permutation Explain why this makes sense Note You will not receive credit until your instructor reviews your answer ways

Using the digits 2 through 8 find the number of different 4 digit numbers such that a Digits can be used more than once This is an example n of Select an answer b Digits cannot be repeated but can come in any order This is an example of Select an answer ways c Digits cannot be repeated and must be written in increasing order This is an example Select an answer permutation neither ways ways

A bag contains 6 red marbles 5 green marbles 6 pink marbles 7 yellow marbles and 4 blue marbles How many sets of 8 marbles contain all of the blue ones

13 Simplify the logarithm 1 09 3l0g 1 2 Logs Alogs Logs N

Use the formula given below to find the area K of the triangle specified by A 10 B 20 and a 7 a sin B sin C 2 sin A K The area K is square units

Now fill in Start 0 82 0 18 0 90 0 10 0 08 0 92 Check Clear Help EX 0 738 0 082 0 0144 0 1656 Now we can use the tree above answer the original question If Hugo or any other player for that matter tests positive what is the probability that he uses ster

28 ERROR ANALYSIS Two students found the equation of the axis of symmetry for the graph of f x x 2x 1 Who is incorrect Explain the error A B X b 2a X 27 2 4 Axis of symmetry is x X b 2a 2 1 1 Axis of symmetry is x 1

Which is the only relationship below that could NOT be modeled by a linea function Hours Worked 3 Pay 36 Hours Worked Pay Hours Worked Pay Hours Worked Pay 5 50 4 48 1 20 6 60 0 450 450 30 5 60 72 3 450 HER 3 40 6 72 S 86 12 450 4 50 8 96 9 102 30 450 5 60 www

If the zeros of a quadratic function parabola are x 2 and x 4 what is the equation of the Axis of Symmetry Ox 0 Ox 1 Ox 2 Ox 3

Which is the graph of y x 1 2 2 O O 2 1 2 SP FA 51 2 y 7 2 3

What could be added to each expression to make it a perfect square 1 x 12x 2 x 6x 3 x 14x

given information to determine the number of elements in each the four disjoint subsets in the following venn diagram A 60 n B 45 n A nB 25 n U 150 ow many elements are in the subset A B A nB ow many elements are in the subset AnB ANB ow many elements are in the subset A nB A NB ow many elements are in the subset AnB C

2 How many degrees is radians 5 Submit

Florida has a population of about 2 X 107 The Earth has a population of about 8 X 109 About how many times more populated is the Earth than Florida Express your answer as a whole number

The globe ina classroom has a diameter of Cinches which Computation describes the volume

The value of the discriminant of 3x 2x 1 x 3x 2 is

For the pair of functions determine the domain off g f x 5x7 g x x29 x 7 8 x O 9 or 9 7 or 7 0 O 9 or 7 0 O 00 00 O 7 or 7 9 or 9

Find the indicated function valu f x 4x 5 g x 2x 1 Find f g 5 O 46 144 146 104

1 The probability that Jordan likes dolphins is 0 3 The probability that Stuart likes whales and that Jordan likes dolphins is 0 15 If these events are independent then what is the probability that Stuart likes whales A 0 25 B 0 625 0 375 D 0 5

A car averages 22 mpg with a standard deviation of 3 What is the standard error if 22 of theses cars were sampled for their mean average mpg 0 15 0 36 0 63 Onone of these Question 2 25 points

Simplify and write the expression as a complex number in standard form 7 21 3 For the toolbar press Al T F10 PC ALT EN 510 Mal

Prev Solve the following polynomial equation by factoring or using the quadratic formula Identify all solutions x4 15x 14 0 Answer 2 Points X Keypad Keyboard Shortcuts

For the polynomial function f x x x 2 x 4 answer parts a through e a Use the Leading Coefficient Test to determine the graph s end behavior A The graph of f x falls to the left and rises to the right OB The graph of f x falls to the left and falls to the right OC The graph of f x rises to the left and falls to the right D The graph of f x rises to the left and rises to the right b Find the x intercept s The x intercept s is are Type an integer or a decimal Use a comma to separate answers as needed At which zero s does the graph of the function cross the x axis Select the correct choice below and if necessary fill in the answer box to your choice OA The graph crosses the x axis at the zero s Type an integer or a decimal Use a comma to separate answers as needed OB There are no tor roph crocoon the x axic

Divide using synthetic division 6x 6x 5x 2 x 2 6x 6x 5x 2 x 2 Simplify your answer Do not factor

The set of natural numbers between Choose the correct answer below O A 19 151 OB 20 21 22 23 150 OC 19 20 21 22 151 19 20 21 22 151 20 150 OF 20 21 22 23 150 O D O E

Determine whether the set is finite or infinite The set of odd numbers greater than 55 Which of the following is the correct set description Finite

Select the correct choice that completes the sentence below Three dots placed in a set to show that the set continues in the same manner is called an ellipsis a dot triple a grouping an ellipse a universal set

The mean of a data set is 30 What is the deviation from the mean of a data point 27 that was part of the data set 1 5 O 1 5 3 3

3 You are dealt a hand of five cards from a standard deck of 52 playing cards Calculate the probability of the given type of hand None of them is a recognized poker hand a Double royal family wedding Two kings two queens of the same two suits and a last non royal card neither king queen jack or ace Answer Enter a formula Examples C 5 3 C 33 3 C 14 2 C 5 3 C 33 3 C 4 1 C 100 100 b Double royal interracial wedding Two kings of one color two queens of the other color and a last non royal card neither king queen jack or ace Answer Enter a formula Examples C 5 3 C 33 3 C 14 2 Check Clear C 5 3 C 33 316 4 Check Clear 11

Given the series 3 k k 2 k 1 does this series converge or diverge O diverges O converges If the series converges find the sum of the series 3 k k 2 k 1 If the series diverges just leave this second box blank Hint Try breaking up the summand using partial fraction

2 Evaluate the double integral where R is the triangle given below y 2 4 Jay xy dA 4 0 7 4 X

Ajar contains 4 red marbles 4 green marbles and 5 blue marbles If we choose a marble then another marble without putting the first one back in the jar what is the probability that the first marble will be blue and the second will be green

Kevin has an annual salary of 51 591 and he earned 20 52 interest from his savings account He also paid 1034 in student loan interest and contributed 3000 to an IRA retirement account Calculate Kevin s gross income Answer 2 Points Kons

Determine the cardinal number of the set X 2 3 4 6 7 9 13 16 18 20 21 22 AnswerHow to enter your answer opens in new

Find all solutions to the following polynomial equation x 51 2x 20x 34x Separate your answers with a comma Write the exact answer Do not round Answer 2 Points

Put the expressions in the appropriate order log 8 log3 8 log 8 O O The expressions are equivalent log 3 8 log 8 log 8 log 8 log 8 log3 8 3 log 8 log3 8 log 8 log3 8 log 8 log 8

7 7 2 2 CII y F 1 T 1 1 1 3 2 4 T A 3 TIIN

Two different gas stations below list the price per gallon of gasoline over 5 days Day Gas Plus Go Station 2 48 2 56 Monday Tuesday 2 50 2 51 Wednesday 2 52 2 46 Thursday 2 57 2 59 Friday 2 55 2 44 Which gas station has more variation based on their range Gas Plus has more variation Go Station has more variation The two gas stations have the same variation There isn t enough information to determine the variation

Solve 571 9 1 and write the solution in interval notation

Adult tickets to the fall play cost 8 and student tickets cost 4 The drama class sold 20 more adult tickets than student tickets to the fall play If the class collected 880 from ticket sales how many adult tickets were sold The drama class Isold adult tickets

s x x 6x 4x 24 Step 2 of 2 Use polynomial division and the quadratic formula if necessary to identify the actual zeros Answer Separate multiple answers with commas Keybo Previous

Consider the following poly f x x 2 x 3 Step 2 of 3 Find the x intercept s at which f crosses the axis Express the intercept s as ordered pair s Answer Select the number of x intercept s at which f crosses the axis Selecting an option will display any text boxes needed to complete your answer O none 01 02 0 3 04

Find the value of the following function at x 3 and x 4 Does the Intermediate Value Theorem guarantee that the function has zero between these two x values Answer f x x 2x 2x 7 f 3 f 4 Does the intermediate Value Theorem guarantee that there is a real zero between 3 and 4 O YES O NO Key Keyboard Shor

In the diagram below a b The measure of angle 4 is 105 find the measure of angle 1 m 1 N J 8 P

15 Find mZQTU V of T 8x 6 4x 14 24 U

Captain Gabriela has a ship the H M S Khan The ship is two furlongs from the dread pirate Daniel and his merciless band of thieves The Captain has probability of hitting the pirate ship The pirate only has 1 1 20 one good eye so he hits the Captain s ship with probability If both fire their cannons at the same time what is the probability that both the pirate and the Captain hit each other s ships