Permutations and Combinations Questions and Answers

Find the polynomial 2x 4x 1 for the following values a x 0 b x 2 c x 5 a The value of the polynomial for x 0 is Simplify your answer

Simplify 8y 7y 2y 5 y 8y 6 8y 7y 2y 5 y 8y 6 Do not facto

1 point Jake tosses a coin up in the air and lets it fall on the ground The equation that models the height in feet and time in seconds of the parabola is h t 16t2 24t 6 What is the greatest height the parabola reaches 15 feet 0000 24 feet 16 feet 6 feet

1 point Calculate the rate of change for the quadratic function over the given interval f x x 4x 5 4 x 2 2 00 2 4

16 1 point Convert the function from standard form to vertex form f x x 6x 4 f x x 3 4 Of x x 6 5 Of x x 3 5 Of x x 6 4 Previous

Does the quadratic function have a maximum or minimum Give the value min 4 5 min max 4

1 point The graph of this function will have a maximum f x x 4x 1 True False Previous

Plot the vector field F at the points listed below using a 2D Cartesian Coordinate Grid F Foxx y 1 Show Transcribed Text L

The expression 64 65 is equivalent to Answer 630 63 20 36 30 36

The expression 52 53 is equivalent to Answer 53 250 O 500 O 25

Given x 0 and y 0 select the expression that is equivalent to Answer 8xiy is 64x y15 32xlyi

a Find p 3 p 3 and p 1 p 3 P 3 11 p 1 Mi i 21 b For what value of n does p n 1 4 3 p n 0 063 0 125 0 25 0 5 1 2 1 0 1 2 2 4 3 4 8 16 5 32

3 Let a 3 6 1 1 7 a 1 2 2 3 1 a3 2 4 5 8 4 and b 3 1 2 b 6 2 4 b3 1 2 5 b4 1 3 8 b5 7 1 4 Determine a basis for U V and W where U span a a2 a3 V span b b2 b3 b4 b5 W xe R x a x a x a3 0 The dot in W is the standard dot product A Vector spaces

Relation 1 Domain Range d d Function O Not a function j n S O Function O Not a function C d d b d Relation 3 8 6 6 6 4 8 6 8 Domain Range 4 cloud Relation 2 3 4 O Function O Not a function 8 9 O Function O Not a function sky chair sky chair Relation 4 x 6 s 6 u 6 k 6

Simplify the following expression by combining like terms 3 3 1 5 5x 20 4x 2 5 5x 20 4x 2 Simplify your answer Do not factor Use integers or fractions for any numbers in the expres

mplify each expression by using the Distributive Property to remove parentheses 2 2 X X 22 co intogors or fractions for any numbers in the expression

Simplify each expression by combining like terms 6n 3n 8

12 1 point What is the axis of symmetry for the quadratic function g x 2 x 3 8 y 8 x 3 x 3 y 3 00

In the order of the data given in the following table write a system of linear equations in terms of C and D Ex 1 2 C Ex 5 C C C D D D D 3 21 24 4 y 105 6 265 8 292 8 125 4

Students were asked to simplify the expression sece cose Two students work is given sece Student A Step 1 sece cose Step 2 sece sece Step 1 cos8 1 1 cos8 Step 3 1 cos20 Student B Step 4 sin2e Step 2 Step 3 1 Cose sece cos 8 1 cos e cose sece sin e cos e Step 4 tan 8 All changes Part A Which student simplified the expression incorrectly Explain the errors that were made or the formulas that were misused 5 points Part B Complete the student s solution correctly beginning with the location of the error 5 points

Explain what it means to simplify an algebraic expression Choose the correct answer below O A Rearranging terms using the Commutative Property B Removing all parentheses and combining like terms OC Substituting a numerical value for each variable in the expressio

Evaluate the expression 4 k for k 5 When k 5 4 k 0 Simplify your answer

Simplify the following expression m 5n 2 m 4n 9 2n m 5n 2 m 4n 9 2n

Simplify the following expression by combining like terms 14z 17z 3 8 14z 17z 3 8 Type a simplified expression

Determine the coefficient of The coefficient of 7 b is 7 b 8 Type an integer or a simplified fraction

41 B 1 2 3 4 3 The cylindrical mixing barrel on a cement truck measures 4 yards long and has a radius of 0 8 yards How much cement can the truck hold in its mixing barrel 4 A rectangular fish tank measures 24 inches by 10 inches by 10 inches How much water can the tank hold M 5 7 5 6 7 8 9 10 11 12 zoom in 00 O volume length

B 1 2 3 4 44 Type a response 5 6 7 8 9 10 11 12 10 If New York is 32 degrees what is the temperature in Celsius

5 In 2019 there were 4 120 new cases of breast cancer diagnosed among women in Alabama and 510 new cases diagnosed among women in Alaska Based on these data is it accurate to say that the incidence rate of breast cancer is higher in Alabama than Alaska Why or why not

Factor completely Then solv h x 27 12x y4

1 point Choose the system of equations that best represents the situation I have 30 coins all nickels dimes and quarters worth 4 60 There are two more dimes than quarters How many of each kind of coin do I have n d q 30 05n 10d 25g 4 60 d 2 g 05n 10d 25g 30 05n 10d 25g 4 60 25g 2 10d n d q 4 60 05n 10d 25g 30 q 2 d n d q 30 05n 10d 25g 4 60 q 2 d

12 1 point Solve the system of equations by elimination 3x 2y 16 5x 2y 8 0 0 0 0 O 3 2 3 25 2 5 2 1

10 1 point Solve the system of equations by substitution y 3x 7 6x 2y 12 infinite solutions 1 4 no solution 2 13

9 1 point Solve the system of equations by substitution 3y 6x 24 8 2x y no solution 2 12 0 8 infinite solutions

D ferrets mice birds dogs P turtles pigs F snakes rabbits cats gerbils Last week there were several types of animals at a local animal shelter Let U be the set of the types of animals at the shelter last week During the week some of the animals were treated by the veterinarians on staff Let D be the set of animal types that were treated by Dr Dean Let F be the set of animal types that were treated by Dr Fee Let P be the set of animal types that were treated by Dr Pham Use the Venn diagram to get your answers below Consider this set which is written in descriptive form The set of animal types that were not treated by Dr Fee but were treated by Dr Dean or Dr Pham a Which of these is a correct way to write the set OF n DUP OF N DOP 5 Write the set in roster form OF U DUP OF U DNP birds 0 0 mice cats ferrets gerbils snakes dogs pigs rabbits

In an international food festival Raina can try foods from Korea and Japan She can choose to try foods from one or neither but not both of these countries In the braces below list all the possible sets of countries whose food Raina can try Write each set in your list in roster form If there is more than one set in your list separate them with commas If you need the empty set in your list use the symbol 0 Korea Japan

Serial numbers for a product are to be made using 3 letters followed by 3 digits The letters are to be taken from the first 5 letters of the alphabet with no repeats The digits are taken from the 10 digits 0 1 2 9 with no repeats How many serial numbers can be generated

The lunch special at Trey s Restaurant is a sandwich and a drink There are 4 sandwiches and 2 drinks to choose from How many lunch specials are possible 11 X

childish Remember it is mostly children who consume Nutrine confectionery not teenagers not adults And children love the bunny My son still remembers the advertisement we ran in the 1980s in Chandamama with bunnies holding Nutrine SuperStar Toffees The bunny is our identity We cannot change what we are Ganapathy VP Operations But things change Even customers do The question is can the bunny hop into new confectionary categories Will customers accept the bunny in the mints and gum categories Karthik VP Marketing Introduction Nutrine was developed as the umbrella brand sometimes called the parent or family brand for all confectionery products produced by the Nutrine Confectionery Company NCC All the products it launched initially carried only the name Nutrine on their wrappers To attract its target group of children between the ages of 6 and 13 years Nutrine used a bunny brand character this bunny quickly became part of Nutrine s identity Many middle aged Indian consumers still reminisce about the Nutrine Bunny of their childhood the Bunny advertisements the Bunny teeth they received when they purchased a package of confectionaries such as Kokanaka Cookies But modern kids are different more individualistic more exposed to global media and highly brand and image conscious They understand brands through visual representations Does the bunny on the wrapper still have broad appeal More important is the Background As competition intensified in the confectionery industry in the early part of the twenty first century Nutrine found itself falling behind the competition After intensive negotiations with both Cadbury and Nestl Nutrine finally sold to Godrej Beverages and Foods GBFL in June 2006 In April 2007 GBFL entered into a joint venture with Hershey s But the lack of focus in Nutrine s brand investments between 2003 and 2006 continued to affect the business and its brands The Nutrine portfolio contains products in various confectionery categories but its major brands dominate in three hard boiled candy clairs and toffee Two key brands accounted for a whopping 70 of Nutrine s revenues Nutrine MahaLacto hard boiled candy and Nutrine clairs Unfortunately both key brands were losing substantial market share MahaLacto continued to have a strong brand name independent of its association with Nutrine Despite minimal branding efforts between 2003 and 2007 MahaLacto ranked eighth in a 2007 brand equity survey conducted by the Economic Times behind the chocolate brands Dairy Milk 5 Star KitKat and Perk and heavily advertised brands such as Big Babol and Boomer The GBFL Hershey marketing team had a clear task cut out for it to define a brand roadmap that would arrest declining revenues increase the marketing focus on key brands to enhance sales and build top lines by launching innovative brand extensions into new confectionery categories A key question considered was whether to continue with Nutrine as an umbrella brand if the company chose to make forays into new categories such as mints and gum which includes both bubble gum and chewing gum The details of this case are as of June 1 2007 Appendix 2 displays key brands owned by the Nutrine Confectionary Company Appendix 3 lists all confectionery categories and the key features of each category

dentify the property that justifies the following statement Answer 4x5 4y 4x 5 4y O Commutative Property of Multiplication O Commutative Property of Addition O Distributive Property O Multiplicative Inverse Associative Property of Multiplication O Associative Property of Addition O Multiplicative Identity Additive Inverse

Identify the factors in the following expression Answer 2x y

Select all the symbols from the set that can be placed in the blank to make the following a true statement Answer Less than Greater than 6 6 6 6 Less than or Equal to O2 Greater than or Equal to Keypar Keyboard Shortc

a 12 Determine the Net Rental Income and estimate the market value of the property using the Income Approach Assume state and adopt any variables necessary to arrive at your answer 8 Marks enable you b The Cost Method of valuation is a method of last resort Briefly comment on this statement and indicate which of the valuation methods is the most appropriate to adopt for valuation for the purpose of the sale of a commercial property assuming there is ample evidence or comparable data 12 Marks Answer on separate answer sheet B Q8 State Housing Company SHC wishes to purchase 1 5 ha of freehold land in good residential neighbourhood of Airport East in Accra at a price of GHC 4 500 000 00 Planning permission will be available to subdivide the land and erect 31 detached two storey houses on the land The estimated cost for each house excluding professional design fees is GH 1 000 000 00 The total development period from planning through construction to disposal will take four years including the construction period of 2 years Similarly properties in the neighbourhood have recently been sold for GH 2 500 000 00 each and the current going rents in the same neighbourhood averages GH 20 000 00 per month per unit SHC is happy with 16 per cent return on capital and a developer s profit of 20 per cent Making any assumptions you consider necessary Prepare a development appraisal to advice SHC to take a decision on the viability of the proposed development and express an expert opinion whether or not the houses should be let or sold outright b Assuming SHC is yet to negotiate on the price of land prepare a residual valuation to advise SHC on a reasonable price to pay for the land Assume and state any variable necessary to enable you arrive at your answer 20 Marks Answer on separate answer sheet

10 pts Looking at the data solve for the mean and median If there is an outlier circle that number a Game Score 1 17 2 16 3 16 4 17 5 19 6 15

Determine the angle x in the triangle given below with AB 7 and BC 12 Hint Use the Law of Sines along with a double angle formula a x arccos 2 x arcsin 24 b x arccos 6 d x 2 arccos 6 e Ox arcsin 7 12 c None of the above A B 2x X

19 1 point Your phone plan charges you an initial fee and then a certain amount depending on the amount of data you use They send you periodic updates of your usage and your current bill cost After using 3 GB of data you owe 30 After 5 GB of data you owe 40 What is the initial fee prior to the data usage charge 2 50 15 10 5

16 1 point Which of the following equations represents this line 000 O y 2x 3 y 2x 3 y 2x 3 y 2x 3

10 1 point A daycare center charges a 75 enrollment fee plus 100 per week Write a function C for the cost of daycare after a certain number of weeks w C w 75w 100 C w 100w 75 C w 175w C w 100w 75

8 1 point Which of the following relations represents a function O 3 1 1 4 2 1 0 3 1 3 2 3 1 5 2 5 2 1 0 5 1 3 2 0 4 2 4 3 4 5 4 7

3 Using the data provided above calculate the gastrointestinal GI illness attack in persons who ate the combination of prime rib porterhouse steak Then using the data provided above and your previous calculations for this problem which of the food items or combination of food items is are most likely to contain the bacteria or virus causing this Gl illness Explain your choice Total Number of Persons Who Ate Each Specified Combination of Food Items at Ben s Steakhouse Ate prime rib 172 Ate porterhouse steak Did not eat porterhouse steak 418 Did not eat prime rib 231 105 Total Number of Persons Who Ate Each Specified Combination of Food Items at Ben s Steakhouse and Who Later Became Sick with Gastrointestinal Symptoms Ate prime rib Ate porterhouse steak 145 Did not eat porterhouse steak 139 Did not eat prime rib 182 30

5 Consider a class with 100 enrolled students None of the students were ill at the beginning of the school year On September 30 a total of five students reported having norovirus All continued to be ill on October 1 but all five recovered within 3 days On October 14 another three students developed gastroenteritis All of the students continued to be ill on October 15 but all three recovered five days later In this example assume that a person cannot get norovirus more than once a Calculate the prevalence of norovirus in the class on October 1 b Calculate the prevalence of norovirus in the class on October 30 c Calculate the cumulative incidence of norovirus in the class during the month of October