Permutations and Combinations Questions and Answers

Question 1 3 Find the greatest monomial that is a factor of the expression 12f g 15fg 3f g o 3fg o 3g o 6fg o 6f g

Fill in the blanks with the appropriate numbers or expressions related to the following equation V 8 V 5 V 3 54 v 2v 15 a The restrictions on the variable are the smaller number in the first blank b When you If not enter none none You are correct 5 c The solution set of the equation is You are incorrect Ive the equation do you get any traneous solutions If so enter the value of the extraneous solution in the blank 13 10 X You are incorrect and 3 X You are incorrect X Enter Enter the solution set notation If there is more than Open in

7 STEM Connection Hannah is measuring three sheets of metal Sheet A is 1 times as long as Sheet B Sheet C is 2 3 times as long as Sheet A Order the sheets from least length to greatest length ACB 8 Tyler has three dogs of different weights Max Daisy and Charlie 3 as much as 8 Daisy weighs as much as Max Charlie weighs Daisy Who weighs the least How do you know Charlke 9 Hugo is organizing his books from shortest to tallest His math book is 2 times as tall as his science book His reading book as tall as his science book In what order should Hugo organize his books 7 is muth reading science 10 Extend Your Thinking What will happen to the product if a whole number is multiplied by Thee 82 predect answer 15

9 Hugo is organizing his books from shortest to tallest His math book is 2 times as tall as his science book His reading book is as tall as his science book In what order should Hugo organize his books muth reading science 10 Extend Your Thinking What will happen to the product if a whole number is multiplied by DIC answen 15

X X S2 Fill in the blanks with the requested information pertaining to the equation X X x 9 x 4x 3 a The restricted values are Type your answer here X x 2x 3 Write your response here Type your answer here Type your answer here Enter the values from smallest to largest and b Solve the equation Enter the solution set of the equation List solutions in order from smallest to largest separated by a comm

Use the product rule to simplify 63 16x45 y 63 16x4y5 Simplify your answer Type an exact answer using radicals as needed www

Add or subtract as indicated 2 7 3 7 6 7 2 7 3 7 6 7 Simplify your answer Type an exact answer using radicals as needed

Multiply and then simplify if possible 11 6 5 11 6 5 Simplify your answer Type an exact answer using radicals as needed GEN

Simplify the given expression Write the answer with positive exponents Assume that all variables represent positive numbers y 1 1 2 2 y z 14 1 4 11 2 2 y Simplify your answer Type exponential notation with positive exponents Use integers or fractions for any numbers in the expression

Solve the equation and check your solution It is possible that there is NO SOLUTION If y 8 what is the solution 2x 10y 0 Type a response

37 Construction The roof of a house is to extend up 13 5 feet above the ceiling which is 36 feet across If the edge of the roof is to extend 2 feet beyond the side of the house and 1 5 feet below the ceiling find the length of one side of the roof

Find the remaining sides of a 45 45 90 triangle if 49 The shorter sides are each 1 50 The shorter sido

Consider the lantern shown below a Which semiregular polyhedron does the lantern resemble small rhombicosidodecahedron snub dodecahedron truncated icosahedron icosidodecahedron O truncated dodecahedron b The lantern has 90 edges and 60 vertices How many faces does the lantern have

b Obtuse Select all that apply A c Right Select all that apply B B A 73 B

21 It takes the earth 24 hours to make one complete revolution on its axis Through how many degrees does the earth turn in 12 hours

The graph on the right gives the annual per person retail availability of beef chicken and pork in pounds from 2007 to 2012 What is the approximate annual per person retail availability of beef chicken and pork in 2012 The annual per person availability of beef in 2012 is approximately 62 pounds The annual per person availability of chicken in 2012 is approximately pounds G Pounds 70 65 60 55 50 45 beef porke 40 35 2007 2008 2009 2010 2011 2012 Year

Tell whether each figure is convex or concave a b c convex O concave d convex concave convex O concave convex O concave

Ifferent rays share endpoint A as shown in the figure A a How many different angles are formed by the three rays b Describe the types of angles that are formed by the three rays There are two acute angles and one right angle There are two obtuse angles and one right angle O There is one obtuse angle and one acute angle There is one acute angle and one right angle There are two acute angles and two right angles c Describe a special relationship between two of the angles The Select angles Select ales

6 A football team consists of 23 players three goalkeepers eight defenders seven midfielders and five forwards How many different match lineups are possible if we assume that a lineup must consist of exactly 11 players and include exactly one goalkeeper four or five defenders at least three midfielders and at least one forward

3 Let X be the set of all ten letter words that can be obtained by permuting the letters of the word COLLATERAL How many elements does X contain ii How many elements of X begin and end with L iii How many elements of X contain three neighbouring letters L iv How many elements of X contain at least two neighbouring letters L v How many elements of X contain no neighbouring vowel letters letters A E O

1 Let X be the set of all five digit numbers that can be obtained by permu ting the digits of the number 12558 i How many elements does X contain ii How many even numbers are there in X iii How many odd numbers are there in X

3 In how many ways can we put 20 identical silver coins into five coloured boxes so that at most 3 coins go into the blue box at least 4 into red and at most 5 into green The remaining boxes are yellow and black and may contain any number of coins Every box except the red one may also remain empty

2 Assume that a basketball line up must consist of 5 players 2 guards 1 center and 2 forwards A coach has in total 12 players in the team there are 5 guards 2 centers 4 forwards and additionally Peter Williams who can play as center or forward How many 5 player subsets of this 12 element set are acceptable line ups In how many of them does Peter Williams appear

1 Let X be the set of all different eight letter words that can be obtained by permuting the letters of the word DEBUNKED How many elements does X contain In how many of them there are neighbouring identical letters In how many elements of X there are no neighbouring vowels terminology E U are vowel letters while B D K N are consonant letters 2 Assume that a basketball line up must consist of 5 players 2 guards 1 center and 2 forwards A coach has in total 12 players in the team there are 5 guards 2 centers 4 forwards and additionally Peter Williams who can play as center or forward How many 5 player subsets of this 12 element set are acceptable line ups In how many of them does Peter Williams appear 3 In how many ways can we put 20 identical silver coins into five coloured boxes so that at most 3 coins go into the blue box at least 4 into red and at most 5 into green The remaining boxes are yellow and black and may contain any number of coins Every box except the red one may also remain empty 4 How many solutions of the equation a b c d 80 in integers greater than 0 satisfy simultaneously all the following conditions a 30 10 c 40 and a b c d are all even REMARK If your answer is eg 3 56 you don t have to compute the numerical answer 546875 Just write 3 56 as the final answer

What is the least common denominator of rational expressions with the given denominators To enter an exponent use the symbol as in 3x 4 for 3x 4a 6a and 10b Type your answer and submit X X Write your response here

When factoring the given binomial what is the trinomial factor 8x 125 Select an answer and submit For keyboard navigation use the up down arrow keys to select an answer a b C P 4x 10x 25 4x 10x 25 2x 10x 25 2x 2 10x 25 G

68 69 7 3 g x 3 2x 3 3 2 1 y 1 3 123 g x x

7 B 9 1 Write each expression in exponential form 7 5n 8 A 2n C 5n 4 Solve each equation Remember to check for extraneous solutions ANSWER SHOULD BE AN INTEGEROR A FRACTION NO POINTS IF YOU ANSWER AS A DECIMAL 1 1 b 2 6b 6b 8 b Simplify 9 6x 2x A 2 C 12 11 1 B 5n 4 D 5n 5 20 4 4 5 5 4 A B 2x 3x D 2 3 B D 4 5 25 3 5 2 10 10 30x 9 12 6x A 4 105x 5 3x B 27x x 6 C 54 10x 6x 30x D 105 18x 12 12 4 3 3 25 A 3 12 3 2 16 4 4 3 3 5 D 3 5 3 3 B

7 B 9 1 Write each expression in exponential form 7 5n 8 A 2n C 5n 4 Solve each equation Remember to check for extraneous solutions ANSWER SHOULD BE AN INTEGEROR A FRACTION NO POINTS IF YOU ANSWER AS A DECIMAL 1 1 b 2 6b 6b 8 b Simplify 9 6x 2x A 2 C 12 11 1 B 5n 4 D 5n 5 20 4 4 5 5 4 A B 2x 3x D 2 3 B D 4 5 25 3 5 2 10 10 30x 9 12 6x A 4 105x 5 3x B 27x x 6 C 54 10x 6x 30x D 105 18x 12 12 4 3 3 25 A 3 12 3 2 16 4 4 3 3 5 D 3 5 3 3 B

13 2 3 4 A 14 C 2 2 6 13 2 14 6n A 6n C n Write each expression in radical form Simplify 1 16 36n A 6n C 243n 5 15 B Write each expression in exponential form 15 n 5 A 6n C 5n D B n 2 5 2 2 2 2 6 2 B 3n D n D n B 125n D 216n

Slape 1 4 6 0 FIND THE SLOPE OF THE LINEAR FUNCTION IN EACH BOX YOU TRY SLOPE SLOPE 2 3 3 y y 8x 6 SLOPE SLOPE 20 14 8 1 y 268 196 124 40 20 96 12 60

Choose h and k such that the system has a no solution b a unique solution and c many solutions X hx 5 2x 4x k OH The system has a unique solution only when h c Select the correct answer below and fill in the answer box es to complete your choice Type an integer or simplified fraction OA The system has many solutions only when h OB The system has many solutions only when k OC The system has many solutions only when h OD The system has many solutions only when h O E The system has many solutions only when h OF The system has many solutions only when h OG The system has many solutions only when k H The system has many solutions only when h and k and k COOP and h is any real number and k is any real number and k and k and k is any real number and h is any real number and k

Choose the correct answer below OA There is a pivot position in each row of the coefficient matrix The augmented matrix will have nine columns and will not have a row of the form 000000001 so the system is consistent OB There is at least one row of the coefficient matrix that does not have a pivot position This means the augmented matrix which will have nine columns have a row of the form 000000001 so the system is inconsistent OC There is at least one row of the coefficient matrix that does not have a pivot position This means the augmented matrix which will have nine columns 00000001 so the system could be inconsistent have a row of the form i OD There is a pivot position in each row of the coefficient matrix The augmented matrix will have seven columns and will not have a row of the form 0000001 so the system is consistent

Find the general solution of the system whose augmented matrix is given below 1 7 0 1 0 4 0 10 0 8 1 0 00 1 8 3 0 00 0 0 0 Select the correct choice below and if necessary fill in the answer boxes to complete your answer O C X x 0 X3 is free OB X X is free X4 is free X5 is free x X3 is free X5 is free OD The system is inconsistent

Perform the division 4m 10m 6m 3 2m 4 4m 10m 6m 3 2m 4 Simplify your answer Use integers or fractions fa

220 attended the FSU Marist game M 185 attended the FSU Butler game B 190 attended the FSU NC State gandle NCS 100 attended the Marist game and the NC State game 60 attended the NC State game and the Butler game attended the Butler game and the Marist game 30 attended all three of the games 65 Sketch a Venn diagram and answer the questions below M NOS B U

15 x x 2 16 x x 1 17 x x 6 18 x x 9 19 xlx 3 x 3 20 x x 4 x 5 21 x x 1 x 6 22 x x 5 x 7

Survey researchers design and conduct surveys and analyze data Some survey researchers design public opinion surveys Other survey researchers market research analysts design marketing surveys which examine products or services that consumers want need or prefer Most survey researchers work in research firms polling organizations nonprofits corporations colleges and universities and government agencies The majority work full time during regular business hours A bachelor s degree may be sufficient for some entry level positions The median annual wage for survey researchers was 49 760 in May 2014 SOURCE Bureau of Labor and Statistics U S Department of Labor Occupational Outlook Handbook 2016 2017 Edition Survey Researchers Surveys for scientific research cover various fields including government health social sciences and education For example a survey researcher may try to capture information about the prevalence of drug use or disease An anonymous survey of college students was taken to determine behaviors regarding alcohol cigarettes and illegal drugs The results were as follows 894 drank alcohol regularly 665 smoked cigarettes 192 used illegal drugs 424 drank alcohol regularly and smoked cigarettes 114 drank alcohol regularly and used illegal drugs 119 smoked cigarettes and used illegal drugs 97 engaged in all three behaviors 309 engaged in none of the behaviors

A survey was given to 298 people asking whether people like dogs and or cats 186 said they like dogs 123 said they like cats 67 said they don t like cats or dogs How many said they liked both cats and dogs people liked both cats and dogs

The Venn diagram here shows the cardinality of each set Use this to find the cardinality of the given set A C n An BC 8 11 7 5 9 14 B 6 a

Let the Universal Set be S Let A and B are subsets of S Set A contains 29 elements and Set B contains 99 elements Sets A and B have 24 elements in common If there are 24 elements that are in S but not in A nor B how many elements are in S

Let the Universal Set S have 150 elements A and B are subsets of S Set A contains 28 elements and Set B contains 88 elements If Sets A and B have 5 elements in common how many elements are in A but not in B

The Venn diagram here shows the cardinality of each set Use this to find the cardinality of each given set 13 n A n ANC M 5

A quarterback throws an incomplete pass The height of the football at time t is modeled by the equation h t 16t2 40t 7 Rounded to the nearest tenth the solutions to equation when h t 0 feet are 0 2 s and 2 7 s Which solution can be eliminated and why The solution 0 2 s can be eliminated because the pass was not thrown backward The solution 2 7 s can be eliminated because a ball cannot be in the air for that long due to gravity The solution 2 7 s can be eliminated because the pass was thrown backward The solution 0 2 s can be eliminated because time cannot be a negative value

In the last several weeks 74 days saw rain and 39 days saw high winds In that same time period 22 days saw both rain and high winds How many days saw either rain or high winds

Ex 1 If 2 is a root off x 3x 4x 5x 2 find the other roots algebraically

Ex 1 18x 32x

Write the set of points from 3 to 3 but excluding 1 and 3 as a union of interva

Write the set of points from 3 to 3 but excluding 1 and 3 as a union of interva

Which equation represents the vertical asymptote of the graph Ox 8 Oy 8 7 Ox 0 6 LO 5 3 13 14 19 12 11 10 9 8 7 6 5 4 3 2 1 2 2 3 345 5 6 0