Permutations and Combinations Questions and Answers

1 For the following stem and leaf plot how many numbers are there between 10 and 19 4 33 3156 2100456 1 00134 01245589 010679 1 005559 217 2

3 Let p and q be the following propositions concerning a positive integer n p n is divisible by 5 and q n is even Which one of the following logical expressions is a correct formalisation of the sentence below n isn t divisible by 5 or it is an odd number but not both P Og O p q OP

6 077 TB MC Qu 02 54 Algo The fo The following account balances were dr Accounts receivable Land

x fx B C D E Coupon rate par value Maturity years annual coupons YTM number of payments F ChickenMan Inc has a 20 year maturity bond with pays interest semi annually The coupon rate is 4 and the yield to maturity Please fill in the range D11 D20 and calculate the PV function and calculate the current yield D21

0 8 1 as a product X E E E3 of elementary matrices 16 E 1 1 16 1 E 0 0 1 8 E3 0 1

The function is defined as follows h x 3x 7 If the graph of his translated vertically upward by 6 units it becomes the graph of a function g Find the expression for g x X S

The cost of renting a car for a day is given by the linear function C x 0 5x 20 where C x is in dollars and x is the number of miles driven Use this information to answer the questions below a Find the cost of driving the car 200 miles The cost is

Partially because of people from a certain country living longer the number with Alzheimer s disease and other dementia is projected to grow each year The table below gives the millions of citizens in the country with Alzheimer s from 2000 and projected to 2050 Complete parts a through e Year 2010 2030 2000 4 2 Number 5 9 8 9 2020 6 8 M SOCCER 2040 11 6 2050 14 4 Q All graphs are shown in 0 50 by 0 20 with xscl 5 and Ysc1 2 viewing rectangles b Find a quadratic function that models y the number of millions of people with Alzheimer s disease or other dementia as a function of x the number of years after 2000 Report the model with four significant digits Out

If f x 4x 4 g x 3x 3x 3 and h x 5x 3 find h 2 h 2 Simplif

1 The number 2018 is used to create six digit positive integers These six digit integers must contain the digits 2018 together and in this order For example 720 186 is allowed but 209 318 and 210 893 are not How many of these six digit integers are divisible by 9 A 28 B 27 C 31 D 34 5 In the triangle each of the numbers 1 2 3 4 5 6 7 8 is placed into a different circle The sums of the numbers on each of the three sides of the triangle are equal to the same number S The sum of all of the different possible values of S is C 66 A 85 D 81 B 99 E 67 E 22

Decomposition of Functions Find f x and g x such that h x f g x Find f x and g x such that h x f g

Evaluate a Composite Function Graphica 10 5 5

Let h x x 3 and g x x 1 Find h g 3 Select the correct choice below and fill in any answer boxes within your cho OA h g 3 Simplify your answer Type an integer or a fraction B The function value does not exist

Solve 44x 2 10 6 Give your answer as an interval If no solutions exists enter No solutions

Priya lives on an island in South Carolina and wants to know its area Priya measures distances across the island at one mile intervals as shown below A B C 2 C D 6 8 5 Use Simpson s rule to approximate the area of the island Area square miles

Betermine whether each x value is a solution or an approximate solution on log x 7 10 a 1 017 Yes No b x 13 Yes No x 10 7 Yes

11 3 3n 3mm 5 Simplify 7 Simplify Your answer should contain only positive exponents 46 9 a 3a 3ab 4x 3xy 3ba 2ba 2b Describe the end behavior of each function 13 f x x x 5x 1 15 f x x 4x 6 2 xy 3x y f x x 2x 2x 3 4 x y 2xy 4x 6 8 xy 2vu 10 12 2x 2y 3yx 2m n 2mn 2 n 14 f x x x 3x 5 16 f x 2x 8x 5 18 f x 2x 8x 4

Multiply the following binomials 4x 5 5x 4 Multiply the following binomials 6x 7 Find the quotient with the remainder 6 791 791 6 Find the quotient with the remainder 575

Find the point that is symmetric to 13 6 with respect to the x axis the y axis and the origin The point symmetric to 13 6 with respect to the x axis is Type an ordered pair

Simplify i85 0 1 Of 01 Question Help Video

Express 2 i in simplest a bi form

Solve the System Give answer as x y z 5x 3y 6z 33 10x 3y 4z 20 20x 3y2z 46 x y z

1 Solve the inequality Graph the solution set and report it in interval notation 4x 92 17 and 4x 9 1

Solve for all values of b in simplest form 13626

4 Write the arithmetic sequence 32 24 16 in the standard form find a

Question 1 28 points Find the Inverse of h x Oh x 2x 3 Oh x 4 4 X Oh x 2 4x 3 Oh x 4x 2 3 N Question 2 16 points Find the Inverse of f x 3x 2 4 x 2 x 2 where x 2

e 2 pts it passes through the point 1 2 and it s parallel to the line y 1 4

Let f x f 3 f 5 f 6 4x 5 x 5 x x 5 Find f 3 f 5 and f 6

23 Use the graph of the parabola to determine its equation in standard form Vertex 3 5 Focus 3 Axis of symmetry

2 Solve the systems x 2y 1 5x 10y 6 2x 7y 3 5x 3y 7 b

We have the following lim 518 f n c implies g n f n if e 0 0 implies g n o f n Implies f n e o g n Proof The proof is left as an exercise

What are all values of side a in the figure to the right such that two triangles can be constructed a a 4 3 b a 8 C a 4 3 d 4 3 a 8 e 8 a 8 3 60

Given the function S x 4 x4 3 a Evaluate S 1 b Evaluate S 5 I Enter an integer or decimal number more Note If the result is undefined input DNE

ETH The partial sum m 2 4 8 128 equals

Identify the vertices and foci of the hyperbola with equation y x 42 32 1 The vertices are The foci are

Which nation from East Asia has invested heavily in small Caribbean countries in order to gain political influence over them O China O Japan North Korea O South Korea

QuestionT 0 sty 6 3 27 10 7 C 1 I 2 10 Give the equation for the ellipse graphed above

12 4 Explain how to solve the equation 8 p

8x 2y 1 0 is the equation of a circle with center h k and radius r for h and k and T 10 Graph the circle 23 3 2 1 2 I 1 2 3 4 5 2 3 4 5 6 7 8 890 10 1 2 3 4 5 6 7 8 9 10

2 Find the center and radius of the circle whose equation is x y 3y 16 0 The center of the circle is The radius of the circle is 3

Find the roots tions using the quadratic formula Rearrange the equations if necessary to get the standard form Be sure to notice if the equation has two one or zero different roots 1 2x 6x 3 0 2 x 4x 3 0 3 3 2x 2x 0 4 5x x 2 0 5x x 2 0 t o 5 6x x x 2 6 4 x 2x x 7 3x 12x 7 8 6x x x 2 x 9 4x 11 9x 0

Gianna builds a solid rectangular prism that has the same volume as Thomas s rectangular prism The bottom layer of Gianna s prism is shown below How many layer s Gianna s rectangular prism have Gianna says 2 layers The bottom layer of the rectangular prism is 10 cubes long and 3 cubes wide So the bottom layer has 10 x 3 30 Gianna s prism has a volume of 60 cubic inches so her prism must have 2 layers 30 x 2 60 True False

The triangles are similar Using the given statement which angle corresponds to ZA LABC ALMN 4 5 A C 6 OLL 6 75 O ZM B 01 N 9 8 M

David Benjamin leased a car to use in his marketing survey business He pays 285 per month for 48 months His deposit was 2 500 He paid a 125 title fee and a 78 license fee What is his total lease cost O 16 180 00 None of the other answers are correct O 16 383 00 13 680 00

Jason and Kendra Adair rent a compact car for 4 days in C 43 95 per day with unlimited miles They also pay a CDW 22 50 per day The Adairs drive 80 miles each day and pay for gasoline What is the total cost to rent the car 358 40 265 80 175 80 324 20

Jim purchased 9 tickets to a concert and spent 65 He purchased some children s tickets and adult tickets The children s tickets cost 5 each and the adult tickets cost 10 each Which system of equation below will determine the number of adult tickets a and the number child tickets c he purchased a c 10 10a Sc 65 a c 585 a c 9 10a 5c 65 a c 9 Sa Sc 74 a c 9 Question 19 3 points Solve the 3 Variable System of Equations 2x 5y 3z 10 3x y 4z 8 5x 2y 72 12 7 1 3 7 1 3 7 1 3 7 1 3

Jackson deposited 5 000 at 3 8 interest rate compounded continuously when he was 18 years old How much will be in the account when he is 40 years old if he made no other deposits or withdrawals 10 000 11 535 60 11 024 91 23 650 87 Question 14 3 points If the rate of an investment is 8 the time is 30 years and the principle is 1 000 which investment would be worth the most Simple Interest Compounded Weekly Com

Question 2 Y of 8 Step 2 of 2 Step 2 of 2 Identify the coordinates of the points A and B on the graph 10 op s 5 300 Enable Zoom Pan X

Solve the following inequality and graph the solution z 9 x 10 0 Choose test values and indicate whether the inequality is true or false in each region Enter the test values from smallest to largest Test Value Inequality False 14 13 12 11 10 9 8 7 6 5 True False 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Clear All Draw Draw the solution above Write the solution as a compound inequality O

Write an equation for the line parallel to the line x 5 9 and passing through 17 5 1 If possible write a formula for a linear function whose graph is the given line The equation of the line parallel to the line x 5 9 and passing through 17 5 1 is Simplify your answer Type an equation