Algebra Questions

Suppose that M is an m x m matrix with entries M20 such that 1 M 1 for each of the olumns j 1 m Show that 1 is an igenvalue of Mk for any k EN

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

SAMPLE RIAL PROBLEMS 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

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

During a five day period Marta served a different number of customers at her flower shop each day The mean number of daily customers served during this period was 17 In the following month during the same five day period she served 16 customers per day for four of the days but on the fifth day she served 25 customers What is the difference between the means of the number of customers she served during the two five day periods

Exercises 65 74 Use the graph of f to determine intervals where fis increasing and where f is decreasing 65 3 K 3 1 3 1 1 23 3 3 1 23 2 3 23 123

Exercises 65 74 Use the graph of f to determine intervals where fis increasing and where f is decreasing 65 66 3 3 1 1 321 2 3 321 2 23 2 3 y 23 123 X

67 68 2 1 3 23 2 3 32 3 2 1 23 2 y 3 123 4 123 X

69 70 2 1 T T 1 2 2 2 X

Exercises 93 94 Energy The following graph shows U S Energy consumption Energy millions of Btu 400 350 300 250 200 150 100 50 1970 1990 2010 Year 93 When was energy consumption increasing 94 When was energy consumption decreasing

59 2 1 2 AA 2 172 2 X

Exercises 39 42 Decide whether a line can pass through the data points If it can determine the slope of the like 39 40 41 X y X y X y F 4 1 5 5 2 3 1 NIH 2 3 2 2 7 0 2 1 1 3 11 2 712 3 4 4 15 4 5 5 7

Exercises 31 38 Determine if f is a linear or nonlinear function If f is a linear function determine if f is a constant function Support your answer by graphing f 31 f x 22x 5 32 f x 3x 2 33 f x 1 34 f x 2 35 f x x 1 36 f x 2x 11 37 f x x 1 38 f x x 1

Exercises 5 18 If possible find the slope of the line passing through each pair of points 5 4 6 2 5 6 8 5 3 7 7 1 4 5 2 8 10 4 15 7

A student provided the solution for solving the following equation Click on the part in which an error was made 7x X 3 48 X 3 1 7x x 3 48 1 x 3 7x 48 x 3 7 3 23 1 x 3 x 3 GO 7x 48 1 7x 49 x 7

One roofer can put a new roof on a house three times faster than another Working together they can roof a house in 5 days How many days would it take the faster roofer to put a new roof on a house working alone Round the answer to the nearest tenth Assume the roofs of the houses are similar sizes Type your numeric answer and submit 20 Hint X You are incorrect X Let X represent the number of days the faster roofer carpoof a house The other roofer will take 3x days Think about how much of the roof can be completed each day Then add these together to equal the part of the roof completed in 5

Exercises 1 4 A linear function f can be written in the form f x Identify m and b for the given f x 1 f x 5 2x 2 f x 3 4x 3 f x 8x 4 f x 6

A student provided the following solution for solving the following equation Click on the part in which an error was made 9 x 3 7 x 3 2 x 9 9 7 x 3 x 3 2 x 9 9 x 3 x 3 73 773 x 3 x 3 x 3 x 3 x 3 9 x 3 7 x 3 2 9x 27 7x 21 2 2x 6 2 2x 8 x 4 2

Simplify the product and enter the simplified result in the blank Use to denote an exponent if needed Do not insert spaces in your answer 3x x 4 x 1 3 x 4 x x You are incorrect I X

x 3 3x Select an answer and submit For keyboard navigation use the up down arrow keys to select an answer True or False The expression a b C d is undefined at x 3 True The value 3 satisfies the equation 3x 0 True The value 3 satisfies the equation X 3 0 False The value 3 does not satisfy the equation 3x 0 The correct value is 0 False The expression is defined for all values of X

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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

3 Investigate the restrictions that should be applied to the domain of a cubic function so that it has an inverse Sketch a cubic function g x x 4x 2 Is this a one to one function Explain your answer If the domain is restricted between x a and x b where both a and b are finite real numbers the function becomes one to one Find the largest possible domain a b Use the idea from the cubic function and investigate the domain and range of all the inverse trigonometric functions Use the following as a guideline for investigating other trigonometric functions too Sketch the graph of y sin x Find the largest possible domain for which the inverse can exist Find the domain and range of sin x Sketch both y sin x and y sin 1 x within the restricted domain

Perform the following n 5 conversions on the array 75 80 99 100 50 0 numbers 0 75 corresponds to Roman numeral LXXV 50 X 10 X 10 V 5 Click bar to ope 1 numbers 1 80 corresponds to Roman numeral LXXX L 50 X 10 X 10 X 10 2 numbers 2 99 corresponds to Roman numeral XCIX XC 90 IX 9 3 numbers 3 100 corresponds to Roman numeral C 4 numbers 4 50 corresponds to Roman numeral L Return the array LXXV LXXX XCIX C L as the answer

Hint wwww You are incorrect

Type your answers in all of the blanks and submit X X 2 Enter the appropriate word or expression in each blank Use to denote an exponent a The expressions a b and a b are called b The product a b a b is called the equivalent to Write your response here Write your response here Write your response here c For example x 4 x 4 Write your response here of two squares and when simplified it is Enter the simplified form of the result

2 Enter the appropriate word or phrase in each blank Use to denote an exponent Do not enter spaces in your answer Enter the simplified expressions in parts b and d a The expression a b is called the Write your response here of a binomial Please type your answer to submit b When simplified a b is equivalent to the expression d For example x 4 c This resulting trinomial is called a Write your response here Write your response here Write your response here square trinomial Open in Reading Vie

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

for a cache memory of size 32KB how many cache line does the cache hold for block Size of 32 08 64 byl bolo

5 A trainee technician was required to carry out an analysis of a standard sample containing 31 20 alumina standard deviation 0 22 established by extensive previous analysis The trainee carried out 8 replicates with the following percentage results 31 09 28 85 31 07 31 10 31 09 31 12 I 31 07 31 13 Analyze the data at the 95 CL for gross errors calculate the mean standard deviation and relat standard deviation HINT Rejected values should not be retested nor included in the calculation of the mean SD RSD

3 2 1 3 1 1 2 3 g x 2 x URLISARIO 23 X

11 points Save Dividing people at a party into groups and then selecting two of the groups to interview is an example of which sampling method Enter the le A B C D E F in the answer blank Question 3 A Simple Random D Stratified B Systematic E Convienience C Cluster

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

58 9 3 3 2 1 3 g x 3 2 x 321 1 6 3 1 2 3 g x x 3

Water in a Swimming Pool The line graph represents the gallons of water W in a small swimming pool after x hours a Evaluate W 4 and interpret your result b Determine the domain D of function W and explain what it represents c Determine the range R of function W and explain what it represents y Water gallons 2000 1750 1500 1250 1000 750 500 250 y W x

Electronic Waste As technology advances there are more and more obsolete electronic devices that need to be disposed of The function f x 40x estimates the millions of tons of electronic waste that will accumulate worldwide after x years Evaluate f 5 and interpret the result Source Environmental Protection Agency

31 Height of a Golf Ball A golf ball is hit and its vertical heighth in feet above the ground after t seconds is given by h t 641 161 a What is the initial height of the golf ball b What is the height of the golf ball after 4 seconds c If the golf ball spends the same amount of time going upas coming down after how many seconds does the golf ball reach its maximum height What is the maximum height of the golf ball d Give a reasonable domain D for function h and explain what it represents e Give a reasonable range R for function and explain what it represents

Exercises 125 130 Evaluate the expression for the given function 125 f a 2 for f x 3 4x 126 f a 3 for f x x 2x 127 f a h for f x x x 5 128 f a h for f x 1 4x x 129 f a h f a for f x 2x 3 130 f a h f a for f x x x

Exercises 111 118 Determine if y is a function of x 111 x y 112 y x 1 113 x 1 y 114 x y 7 115 x y 70 116 x 1 y 1 117 x y 2 118 y x

5 3 2 1 3 2 3 123

1 Simplity 1 24x y4 4 A 2xy 3xy C 2y 3x 2 3 3 64v6 A C 16v i B 3y 3x D 2y 2xy B 16 D 1 276 2 2 81m A 49m m

3 13 13 14 15 4 2 3 4 2 B 14 C 2 2 6 D 5 14 6n A on c n Write each expression in radical form 6 2 5 2 2 2 2 6 2 B 3n D Write each expression in exponential form 15 3 m 44

9 V6x V2x A 2 C 12 1 11 5 20 4 4 S 5 A C 4 B 2x 3x D 2 3 B D 4 5 25 3 5 2

9 Simplify 9 6x x 2x W A 2 2 C 12 11 II 11 5 20 4 4 A C 4 B 2x 3x D 2 3 B D 4 5 25 3 5 2 10 12 10 30x 9 12 6x A 4 105x 5 3x B 27x x 6 C 54 10x 6x 30x D V105 18x 12 4 3 3 25 A C 3 12 3 2 16 ENCENSE 4 3 3 B 5 D 3 5 3 3

4 5 Write each expression in exponential form 4 7 6 A 7x C 2x Write each expression in radical form 5 5x A C SK Simplify B 7x D 3x 6 276 A 10006 C 36 B 47 DI B 95 D 2166 2924 SATILI AL ES

10 10 30x19 12 6x A 4105 5 3x B 27xx 6 C 54 10x 6x V30x D 10518c 12 443 3 25 4 3 4 3 3

m 1 3 Simplity 1 24x y A 2xy 3xy C 2y 3x 3 64 9 A C 16v 5 B D B 3y 3x D 2y 2xy 16 1 6 27 A 11 2 7 8 m 2 81m A 49m C m B 27m D m 10

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