Permutations and Combinations Questions and Answers

Name the property of real numbers illustrated by the equation 2 x 5 2x 10 Distributive Property Associative Property Commutative Property Multiplicative Inverse 1

Her nokta ifti aras ndaki e imi hesaplay n 7 1 2 and 4 4 8 4 2 and 2 5 9 2 4 and 0 2

4 2cosx 1 0 O x 5T 3 0 x 1 O x X 6 7 O x 15 6 7 O x 1 4 of te 0 x 31 O 4 Is a to the equation

1 Find all solutions of the following equation in the interval 0 27 4tan x 4 3 0

2 Evaluate the following expression x 7 10 n where n is a whole number 5 cos 5x 5 cos 5x 1 tan 5x

5 Graph the expression on each side of the equals symbol to determine whether the equation might be an identity csc 0 cot 0 1 cos 0 sin 0 Identity Not an Identity

The following data give the margin of victory for a football championship over 15 years 13 8 3 11 12 33 4 26 8 4 3 3 6 14 3 a Find the mean and median margin of victory b Identify the outlier in the data set If the outlier is eliminated what are the new mean and median a Find the mean and median of the weights The mean is Round to the nearest tenth as needed The median is Type an integer or a decimal b Which if any of the margins of victory would be considered the outlier Select the correct choice below and if necessary fill in the answer box to complete your choice OA The outlier is Type an integer or a decimal OB None of the margins would be considered an outlier Find the mean with the outlier excluded Select the correct choice below and if necessary fill in the answer box to complete your choice OA The mean without the outlier is Round to the nearest tenth as needed OB None of the weights would be considered an outlier Find the median with the outlier excluded Select the correct choice below and if necessary fill in the answer box to complete your choice OA The median without the outlier is Type an integer or a decimal OB None of the weights would be considered an outlier

What do we mean by combinations Explain the meaning of each of the terms in the combinations formula Give an example of its use Choose the correct answer below OA The n represents the number of permutations which includes different orderings The n r xr represents the number of different orderings of n items taken r at a time Dividing n by n r xr determines the number of permutations counting each different ordering which is a combination B The n represents the number of combinations which includes different orderings The n r xr represents the number of different orderings of n items taken r at a time Dividing n by n r xr determines the number of combinations without counting each different ordering which is a permutation OC The n represents the number of permutations not counting different orderings The n r xr represents the number of different orderings of n items taken r at a time Dividing n by n r xr determines the number of permutations counting each different ordering which is a combination OD The n represents the number of permutations which includes different orderings The n r xr represents the number of different orderings of n items taken r at a time Dividing n by n r xr determines the number of permutations without counting each different ordering which is a combination Give an example of its use Select the correct answer below OA The formula can be used when deciding how many ways someone can dial a number on a telephone OB The formula can be used when deciding how many ways the first five letters of the alphabet can be arranged OC The formula can be used when deciding how many ways someone can choose two hats from 10 options D The formula can be used when deciding how many ways someone can choose a vanity license plate

Rangers If you would like to have exactly one player from each position in your starting 9 people in starting line up line up in how many ways could you arrange the line up Be sure to show and explain your work as well as any formulas you use 2 points Player Name John Gray Andrew Heaney Dane Dunning Nathan Eovaldi 1 2 3 4 5 Martin Perez 6 7 8 9 10 11 Brock Burke 12 Cody Bradford 13 Corey seager 14 20 21 Jose Leclerc Josh Sborz Jordan Montgomery Will Smith Max Scherzer Nathaniel Lowe Marcus Semien 15 16 Josh Jung 17 Jonah Heim 18 Sandy Leon 19 Adolis Garcia Leody Taveras Robbie Grossman Travis Jankowski Ezequiel Duran Bubba Thompson 22 23 24 25 Austin Hedges Player s Position Player s Batting Average 000 000 000 000 000 Pitcher Pitcher Pitcher Pitcher Pitcher Pitcher Pitcher Pitcher Pitcher Pitcher Pitcher Pitcher Shortstop First base Second base Third base Catcher Catcher Right Field Center field Left field Left field Shortstop Left field 000 000 000 000 000 000 000 327 262 276 266 258 146 245 266 238 263 276

Kristin Wilson lives in Florence South Carolina and wishes to visit relatives in the following South Carolina cities Columbia Greenville and Charleston In how many ways can she vis each of these cities and return to her home in Florence There are different ways that Kristin can visit each city and return home

Listen Based on the scatter plot choose the best estimate of the correlation coefficient 0 0 5 00 5 00 9 0 0 9

Maggle claims that the function g z 3 4 is the inverse of the function of f x 3x 4 Which statement provides a correct analysis of Maggie s claim A B C D Maggie s claim is correct because if you add 4 to g x and then multiply it by 3 you get x Maggie s claim is correct because when g x is substituted into every occurrence of x in f x f g x x and when x is substituted into every occurrence of x in g x gl Maggie s claim is incorrect because when g x is substituted into every occurrence of x in f x f g x x 8 therefore g x is not the inverse of f x Maggie s claim is incorrect because when g x is substituted into every occurrence of x in f x f g x x therefore g x is not the inverse of f x

A B C D y x

A student was finding solutions to the equation 4 2 5 0 and wrote down these steps Step 1 2 5 Step 2 x 5 4 Step 3 2 5 16 Step 4 2 11 Which statement is an accurate interpretation of the student s work e A B D The student found the correct solution to the original equation 11 x 11 is a solution to the equation in Step 2 but not to the original equation The student made an error in Step 3 The student made an error in Step 1

11 4 7x 1 1 2 6 18 71 A No solution B x 0 6 or x 2 C All real numbers D x 46 4 or x 0 4 2 CUMMULATIVE EXTRA CREDIT Solve each inequality and graph its solution 3 Find each quotient 2 VIAG N A C 10 7 7 10 5 B D 8 7 6 5 4 3 2 1 0 1 2 3 A 15b 2b 20 C 15b 2b 8 4 34 35 10 7 0 3 2 1 0 1 2 3 4 5 4 3 2 1 0 456 6 7 8 Simplify each difference 3 3b3b 1 8b 7b 3 5b b 6b 3b 4 5b B 15b 2b 14 D 15b 2b 20 8b 2 3 4 5 6 05 10 15 20 25 30 35 40 45 50 Simplify each sum 4 n 8n 4n 2 1 n 3n 3n 2n 5n 4n 7n A 7n 12n n 8n 3 B 7n 12n n 8n 4 D 7n 12n n 8n 7 C 7n 12n n 8n 1 Simplify Your answer should contain only positive exponents x y 2x

6 sin3x 1 0 x

Function f x x 6x 3x 26x 24 a Verify the given factors of f x x 3 3 1 6 x 2 1 3 2 1 6 2 Factors x 3 x 2 3 9 m 16 Nice 26 26 X X 24 24 X X

Find the standard deviation for the following 11 13 14 15 17 Round the answer to two 2 decimal places 2 24 1 23 O2 78 3 45

Let q represent the following statement q Chris can sing Symbolically express the statement Chris cannot sing 1 q 2 q 3 q N 4 q

Use the table along with dimensional analysis to convert the given square unit to the square unit indicated 59 cm2 to in 1 in 2 1 ft 1 yd 1 mi2 acre 6 5 cm 0 09 m 0 8 m 2 6 km 0 4 hectare ha 62 5 square inches 65 5 square inches 9 08 square inches 383 5 square inches

Practice 1 If y 12x 10 what is the value of y when x is equal to 4

Graph the image of square ABCD after a dilation with a scale factor of 3 centered at the origin 10 8 6 D 4 104 8 6 4 12 63

Exit Ticket 12 5 1 13x4 2y 11 what is the value of x if y 3 A 3 B 3 C 4 D 7 2 If 2x 4 10 3x what is the value of x a 1 2 b 1 2 c 2 8 d 6 3 If 2 2x 4 x 7 12 what is the value of x a 9 b 1 c 1 d 13 3 4 If 2 3x 6y 5x 10y 6 what is the value of 3x 5 if y 4 A 14 B 37 C 94 D 277

Simplify each expression 3v 5 5v 36v 36 1 A B C D 3 A B 4 2k 8k 10 C 6v 6 5v 36v 39v 4 v 6 5v 6 5v 36v 40v 3 v 6 5v 6 D 5v 36v 39v 5 v 6 5v 6 4v 4v v 6 5v 6 13 4k k 2 k 5 13 k 3k 2 k 5 3k 12k 15k 2 k 1 k 5 6k 24k 29k 4 2 k 1 k 5 2 4 2 5 5 m 5 2m 2 A B C D 4 A B C 25 2m 8m 5 m 5 5m 1 2m 30m 60m 30m 3m 45 3m 16m m 3 D 12m 12 5 m 5 15m 15 2 m 1 m 5 3 2m m 10 2 m 3 m 4 25m 1 20m 40m 30m m 1 12m 4m 5 5 3m 1 44 3m 16m m 2 m 3 m 4

4 4i 3 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Type your answer in the form a bi 2

Find the given power and write the answer in rectangular notation cos 90 isin 90 6 cos 90 isin 90 0 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Type your answer in the form a bl

0 3 23 y 2 3x 5 D y 5x 2 What is the equation of the line 6B y 2x 5 y 5x 23 Dec 6 8 56 US O

7 2x 3y 5x 3 16 3x 6x A C 9 A 5n 5n n 4 n 5 B C D 11 A B 3 5 3 8r r 5 2 r 2 C D 5n 4 2n 3 10n 45n n 5 n 4 7n 2 n 1 2n 1 5 2 2n 3 B 3 7r 3r 1 3 8r D 3r 1 29r 12 7r 2 x 5 r 2 17r 6 41 r 5 r 2 8 3x 3x 5yx 2 5x 8 10 12 8 A v 2 B C D 10 A B C 12 4 2x D 2v 4 3 A B C D 7v 2v 4 3 v 2 8v 8 v 3 v 2 10v 8 3 v 2 8v 11 v 3 v 2 5 2x x 3 10x 17 2x 2x x 3 7x 17 x 2x x 3 9 2x 4 x 4x 17 2x x 3 5 5x 5 x 5x 2 x 6 17x 20 2x 3 x 5 35 7x 2x 3 x 5 x 6 25x 10x x x 6 5x 2 5 r 6 5x 2

Adding Rational Expressions Simplify each expression x 2y x 3y 9x 9x2 A 3 B C D A 2x 2y B C D A 2x 5y 9x 3x 5y 9x 2x 8xy 6y 81x4 B D 5xy 6y 81x4 3y 3x 2x x 2y 2yx y 3x 3 5 2 5 yx 3xy x 2 2x x 2 3y 2y 3x 10x 3y y x 5 15 6x 10x 15x 6y 10y 2x 3 2y 5 4 6 2 2 A C 6 A 3x 4 2 C A b 1 B 3b 2b 3 6b 3b 2b 4 6b 3b D 5a 3b x 9 x 2x x 3 66 2 2x 6 X 2 2x 3 b 2 a 4b Sab 3b 6a 4b b 3 5ba 5a 4b b 3 5ba 3a 5b b a B D 2b 3 b 2b 3 2b 2 b 2b 3 B D 3b a 25a b 3a 12b 15b a 6 x 2x x 3 3x 9x 2 2 x 3

w 2 If log3 325 x 4 Alog3x Blog3z Clog3 w D find A B C D

Calculate the binomial coefficient 15C14

Calculate the binomial coefficient 11C6

Evaluate the expression 15 13 2 15 13 2 Simplify your answer Type an integer or a fraction

Subtract and simplify your answer Do not add spaces in your answer 3 3 3y 15 5y 25 Numerator a Denominator b

etermine intervals on which the function is increasing decreasing and constant On what intervals is the function increasing OA 6 1 OB 3 9 OC 6 1 and 6 9 OD 9 6 and 3 9 On what interval the function decreasing On what interval is the function constant 4 10 40 10

Find the indicated term for the binomial expression 7th term 8 3x y The 7th term is

Use the graph to find the following a f 2 b the domain c any x values for which f x 1 d the range f 2 What is the domain Select the correct choice below and if necessary fill in the answer box es to complete your choice OA x1xs OB x1 x OC x1x OD x1x E The domain is all real numbers 10 8 8 10 8 4 Ay

Simplify each expression b 5 2b 12b 16 1 A 3 b 5 2b b 4 7 2 b 9 24k 16k 3k 1 14b 20b 146 48b 40 6 b 5 b 3 B D b 3 b 1 b 4 27k 18k 27k 9k Find each product 5 7p 3 6p 1 A 16p 64p 64 B 42p 25p 3 C 16p 64p 64 2 4 6 2 40n 56n 35n 49 5n 38n 48 5n 8 4 8n 7 n 6 A B 70m n 9 n 5 C n 6 D 10n n 4 7m 4 49m 28 14m 28 12m 24 6 6k 1 7k 2 A 42k 19k 2 B 4k 16k 12 C 42k 2 5k 2

Which graph is sketched to the right A g x x 1 x 2 x 3 B g x x 1 x 2 x 3 C g x x 3 x 2 x 1

Given the graph below determine whether each statement is true or false Statement 3 is a zero of the function 2 is a zero of the function 1 is a zero of the function 0 is a zero of the function 1 is a zero of the function True False 0000

How is the graph of g x x 3 related to the graph of f x x A The graph of g x is a translation of the graph of f x right 3 units and a reflection across the y axis B The graph of g x is a translation of the graph of f x down 3 units and a reflection across the x axis C The graph of g x is a translation of the graph of f x right 3 units and a reflection across the x axis

How is the graph of g x x 1 related to the graph of f x x A The graph of g x is a translation of the graph of f x down 1 unit B The graph of g x is a translation of the graph of f x up 1 unit C The graph of g x is a translation of the graph of f x right 1 unit

How is the graph of g x 2x related to the graph of f x x

Find the mean for the following group of data items 150 90 120 90 110 The meen is Type an integer or a decimal

A single die is rolled twice The 36 equally likely outcomes are shown to the right Find the probability of getting two numbers whose sum is 6 First Roll Second Roll A 1 1 1 2 1 3 1 4 1 5 1 6 2 1 2 2 2 3 2 4 2 5 2 6 3 1 3 2 3 3 3 4 3 5 3 6 4 1 4 2 4 3 4 4 4 5 4 6 5 1 5 2 5 3 5 4 5 5 5 6 6 1 6 2 6 3 6 4 6 5 6 6 The probability of getting two numbers whose sum is 6 is Type an integer or a simplified fraction 0 www TAPUSTEN

Write the equation of the graph shown below in factored form 5 f x x 2 x 1 x 3 f x x 2 x 1 x 3 f x x 2 x 1 x 3 f x x 2 x 1 x 31 5 0 5

Which of the following describes the function x 1 O The degree of the function is even so the ends of the graph continue in opposite directions Because the leading coefficient is positive the left side of the graph continues down the coordinate plane and the right side continues upward O The degree of the function is even so the ends of the graph continue in the same direction Because the leading coefficient is negative the left side of the graph continues down the coordinate plane and the right side also continues downward O The degree of the function is even so the ends of the graph continue in opposite directions Because the leading coefficient is negative the left side of the graph continues up the coordinate plane and the right side continues downward O The degree of the function is even so the ends of the graph continue in the same direction Because the leading coefficient is positive the left side of the graph continues up the coordinate plane and the right side also continues upward

Construct a truth table for the given statement 9 p q Fill in the truth table P T T F F q T F T LL F q 9 P 9 P q

Step 2 This is a binomial experiment with n 18 trials Let a success be that a student withdraws from the course It is given that 15 of students withdraw Recall the method used to find the probability of an event given a percentage given percentage 100 probability Thus the probability p a student withdraws from the course is as follows given percentage 100 probability p 100 For 2 or fewer students to withdraw from the course means that exactly Select dents withdraw Therefore x will be Select The probability of each x value is f x so the probability that 2 or fewer students withdraw from the course will be 0 1 or 2 2 1 or 2 0 or 1 Submit Skip you cannot come back

1 4 4x 12 4 20 10 5x Topic 6 Mixture 2 20 5 3x 5 10 2 2x 3 10 5 3x 6 16 8 4x