Permutations and Combinations Questions and Answers

26 9 6m 3 6 1 4m

6 A fruit basket contains 5 apples 19 pears and 6 bananas What percentage of the fruit is a banana

1 Find the exact value of the following logarithmic expression

3 a 8 pts If a and b are positive numbers find the maximum value of f x x 1 x 0 x 1 b 8 pts Find the maximum and minimum values of f x x cot x 2 on the interval T 3 5 3

1 3 Multiply Polynomials Find each product 1 2n 2 n 3 A 2n 6 B 2n 4n 6 C 14n 24 D 14n 62n 24 7 3 7x 8 2x 3 A 6x 31x 30 B 14x 24 C 14x 5x24 D 14x 37x 24 5 5 8x 4 6x x 4 A 21x 38x 41x 6 B 7x 14x 4x 3 C 20x 34x 26x 4 D 48x 32x 28x 16 7 2k 8 6k 5k 8 A 12k 38k 24k 64 B 12k 34k 30k 8 C 10k 44k 12k 16 D 25k 48 34k 9 7b b 4 3b 4b 1 A 21b4 25b b 17b 4 B 21b 4b 4 C 16b4 20b 34b 8b 5 2013

uta Software Multiply Polynomials Find each product 1 2n 2 n 3 A 2n 6 B 2n 4n 6 C 14n 24 D 14n 62n 24 3 7x 8 2x 3 A 6x 31x 30 B 14x 24 C 14x 5x 24 D 14x 37x 24 5 8x 4 6x x 4 A 21x 38x 41x 6 B 7x 14x 4x 3 C 20x 34x 26x 4 D 48x 32x 28x 16 All rights reserved 2 2 2n 5 8n 2 A 16n 36n 10 B 28n 45n 18 C 28n 3n 18 D 28n 18 4 6 4 n 4 2n 7 A 2n n 28 B 2n 28 C 2n 15n 28 D 2n 15n 28 6 8k 7 4k 2k 2 A 42k 78k 60k 24 B 16k 34k k 35 C k 11k 23k 3 D 32k 12k 30k 14

Multiply Polynomials Find each product 1 2n 2 n 3 A 2n 6 B 2n 4n 6 C 14n 24 D 14n 62n 24 2 2 2n 5 8n 2 A 16n 36n10 B 28n 45n 18 C 28n 3n 18 D 28n 18

8 Determine whether the following function is even odd or neither x 1 f x x Some formulas a b a 2ab b b 2a vertex x Even f x f x odd f x f x

Find the composition g f x in simplest form and describe its domain 4 x f x and g x X x 1

h x 3x 18x 12

1 Sketch the graph of each linear inequality 1 y x 3 A B C D 2 22 V y y 2 2 6 x 6 x 4 6 x x 2 2 5x y 5 A B C D 6 4 12 12 y V 4 1 1 X

1 3 6 4 6 3 11 21 11 21 2 3 7 4 7 4 9 15 10 15

Find an expression for the perimeter of the figure 2 li y 1 2 y 2 y y 1 Scanned with CamScanner 1

CA Trea Homework 11 6 Write an expression for each of the following then evaluate for the given variable values 1a Two more than the product of 4 and x 16 Evaluate if x 10 1 c Evaluate if x 2 1d Evaluate if x equals one half

Let p and q represent the following simple statements p I work hard q The taxes are high Write the following compound statement in its symbolic form I work hard and the taxes are high The symbolic form is

The following statement is false r Mars is not the closest planet to Earth Use the representation of r to express the symbolic statement r in words What can you conclude about the resulting verbal statement Choose the statement below that expresses the symbolic statement r in words OA Sometimes Mars is not the closest planet to Earth OB Sometimes Mars is the closest planet to Earth OC Mars is the closest planet to Earth OD It is not Mars that is the closest planet to Earth

Determine whether or not the sentence is a statement Burros are amphibians Is the given sentence a statement A No because the sentence is always false B Yes because the sentence can be either true or false but not both simultaneously OC Yes because the sentence is always true OD No because the sentence can be both true and false simultaneously

Determine the equation of the graph and select the correct answer below 10 4 1 Courtesy of Texas Instruments Oy x 4 1 Oy x 4 1 Oy x 4 1 Oy x 4 1 15 Y 1 5 4606

2a Twelve less than the quotient of x and 10 X 12 10 2b Evaluate if x 20

Rewrite the following radical with a rational exponent 3 7x 3

When a zero root has an even multiplicity the graph When a zero root has an odd multiplicity the graph the the ec bounces on raxis raxis x y

11 use th x x 12 pt Give the equation s of all vertical asymptotes of h x Vertical Asymptotes 10 1 pt Determine the x intercept s of h x Write as an ordered pair x intercepts 11 1 pt Determine the y intercept of h x Write as an ordered pair y intercept h x g x 12 3 pts Determine the horizontal asymptotes of the following functions If there is no horizontal asymptote answer with None 6x h x 12x 1800 3x 19 6x 12x 1800 3x 19 j x 6x 1 12x 1800 3x 19

Answer the constructed response questions completely Include all parts Show all work Write in complete sentences Use the equation builder when necessary Remember Only original work will be accepted Do your own work Do not search the internet for the answer Do not copy and paste work that is not your own Part A A function f x is transformed into the function g x 2 x 4 5 Name and explain in complete sentences the transfor that occurred to the parent cube root function Part B How is the DOMAIN of a cube root function different from the DOMAIN of a square root function Use complet

Let p and q represent the following statements p The chili is spicy q The sour cream is cold Write the compound statement p q in words Choose the correct answer below www OA If the sour cream is not cold then the chili is spicy OB If the chili is not spicy then the sour cream is cold OC The chili is spicy if and only if the sour cream is not cold OD If the chili is spicy then the sour cream is cold

Let p and q represent the following simple statements p This is an octopus q I work hard Write the following compound statement in its symbolic form This is an octopus and I work hard The symbolic form is A

Fill in the blanks A statement is a sentence that is A statement is a sentence that is or true or postive an opinion but not both simultaneously but not both simultaneously

10 23 73 11 8r 42r 36r 51 15r 74 74 74 74 A 444 77 881 B 44r 31 887 C 104 77 887 D 444 33 88r

9 88p 41p 64p 18p 84p 48p 51p 83p A 136p 106p 103p 40p B 136p 106p 13p 40p C 125p 101p 13p 40p D 125 p 106p 13p 40p

Simplify each expression 3 4 3a 7a 7 8a A 5a 17 B 5a 7a 17 C 5a 7a 12 D 5a 7a 11 5 3v 7v4 6v v 8v A 6v4 3v 6v B 6v49v 6v C 6v49v 10v D 6v4 5v 6v 4 6 4 8a a 5a 3a 7a A 5a 11a 2a B 5a 19a 3a C 5a 11a 3a D a 11a 2a 6 4x 7x 3x 7x 6x A 10x 13x 4x B x 13x 4x C x 16x 4x D 3x 13x 4x 7 30 4 145 22 41r 77 26 75r 70r4 A 1855 100 73 41 33 B 895 100r4 73r 41r 33 C 895 100r4 26 41 55 D 895 100 73 41 55

Find the inverse function of the function below f x 5 log x 3

Solve each equation for x If you express your answer as a decimal round to four decimal places a ln x 3 b log3 x 0 2 c log7 x 2 d log x 5 52

Solve for t in the equation below If you give your answer in decimal form round to three decimal places If there is no solution enter DNE If there is more than one answer separate your answers by commas 1 4 In 5t 2 2

Solve for z in the equation below 5 3 11 a Give a representation of the exact answer using logarithms b Give a decimal approximation of the answer rounded to two decimal places

Assignment 8 Problem 16 1 point Let V R2 and let H be the subset of V of all points on the line 3x 2y 6 Is H a subspace of the vector space V 1 Does H contain the zero vector of V choose 2 Is H closed under addition If it is enter CLOSED If it is not enter two vectors in H whose sum is not in H using a comma separated list and syntax such as 1 2 3 4 3 Is H closed under scalar multiplication If it is enter CLOSED If it is not enter a scalar in IR and a vector in H whose product is not in H using a comma separated list and syntax such as 2 3 4 4 Is H a subspace of the vector space V You should be able to justify your answer by writing a complete coherent and detailed proof based on your answers to parts 1 3 choose

3 Which value of x makes 3 x 3 4 1 8 3 6 2 0 4 4 2 17 1 2 true

Find the domain of the function f x x 12 x 13 What is the domain of f A x x is a real number and x 12 OB x x is a real number and x 0 C x x is a real number and x 13 OD x x is a real number

5 Which relation is not a function Explain your answer 1 2 3 A A 2 8 4 10 60 69 69 69 H 2 B B 10 3 8 12 3 C C 12 4

2 The function g x is defined as g x 1 27 2 27 2x 3x The value of g 3 is 3 9 4 45

Graph the given function by making a table of coordinates f x 5x Complete the table of coordinates 2 30 25 20 15 10 5 3 2 1 X y Type integers or fractions Simplify your answers Choose the correct graph below OA 1 2 3 1 X 0 Q Q 1 2 OB 10 5 3 2 1 123 Q Q www 2 forgringringning 5 10 15 20 25 Q OD

Solve the inequality and graph the solution set on real umber line Express the solution set in interval notati 5 5 x 5 x 6 The solution set is Type your answer in interval notation Use integers or fractions for any numbers in the expression Choose the correct graph below O A O C 8 8 6 6 2 2 0 2 6 8 OB D 8 8 6 6 2 2 0 2 2 7 4

8 Solve algebraically for x 2 3 2 x 12 x x 2 5 3 4

Without using a calculator find the exact value of the following expression log 39 log 1 log 18 log 0 0001 3 2 log 39 log 1 10 Jeg 0 0001 Simplify your answer

Practice Aniyah is working at the mall wrapping presents during the holidays She she wraps The function f x 2x represents Aniya s daily earnings for x number of presents wrapped 2 1 Are the values 2 3 10 and 0 5 possible inputs for this situation Explain why or why not No 2 2 Explain why 24 50 is an impossible daily earning amount for Aniyah concert is being held at a local venue Tickets are 25 per person The concert venue has a maximum capacity of 500 people e function f t 25t represents the amount of money raised for t tickets sold 1 Select all the possible values in the domain of f t 0 1 25 3 7 Describe the domain of f t Select all the possible values in the range of f t 25 00 25 525 860 173 12 500

3 f x x 2 2x 1 f g f g fg Domain x 1 x 1 flg x 2 2x 1 g x Domain x 2 x 1 x 2x 1 2x 1 x 1 x 2 X 2x 1 x 1 Domain x 1 x 1 x 1 Domain x 2 2x 1 x 1 2x 1 2x 1 x 2 x 1 x 2x 1 2x 1 x 1 x x 2 2x 1 x 1 X X X 1

Meangru Find the following functions and state the domain of each a f g b f g c fg 1 f x x 2x 1 g x 2x 3 a f g Domain b f g x 2x 1 2x 3 x 4x 2 c fg x 2x 1 2x 3 d flg d f g Domain f x g x x 2x 1 2x 3 Domain

R x 100x R 100 100 100 R 6 6667 e What quantity x maximizes revenue R x 100x b 2a X X R x 150 103 f What is the maximum revenue R x 100x unty of bestonlumom od p x 100 0005 100 0004 16 00 d BS a s Boomed bla 0004 2005 5 x10 R 150 100 150 on A sinsven scha g What price should the company charge to maximize revenue borq inson to bloz z vitias

Follow the steps for graphing a rational function to graph the function R x choice x 9 x 6 3 x 6 OB R x is already in factored form What is the domain of R x Select the correct choice below and if necessary fill in the answer box to complete your choice CA R x x A R x x 3x 54 x 3x 18 OA xx2 Type an integer or a simplified fraction OB xx Type an integer or a simplified fraction C xlx 3 6 Type an integer or a simplified fraction Use a comma to separate answers as needed D The domain is the set of all real numbers Type your answer in factored form Do not simplify Write R x in lowest terms Select the correct choice below and if necessary fill in the answer box to complete your choice x 6 x 3 Simplify your answer 4

2 What is the remainder if f x x 5x 6x 10 is divided by x 4 Remainder 2 pts

EXTRA CREDIT SUM 2 Q2 Sketch the graph of each linear inequality 1 3x y 2 A B C D 6 4 4 2 Y 2 2 4 X 6 x 6 x x 2 2 x 2y 0 A B C D 43 1 4 2 2 16 4 2 V A x X X

10 8x4y 6x 4xy4 6x4 5x y4 6x y 2x 2x y 2x A 6x y 5x y 4 6x y 4xy4 4x 4x B 5x y 5x y4 6x y 4xy 4x 4x C 5x4y4 2x y4 8x y 4xy 4x 4x D 5xy 2x y 6x y 4xy 4x 4x