Permutations and Combinations Questions and Answers

Let g x 2x and h x x 2 Find goh 0 goh 0 Simplify your answer

b varies inversely as c If b 6 when c 2 find b when c is 4 b 010

The function f x is a quadratic function and the zeros of f x are 2 and 1 Assume the leading coefficient of f a is 1 Write the equation of the quadratic polynomial in standard form

5 What is an equation of a line that has a slope of and passes through the point 4 3 1 y 3 x 4 y 3 x 4 3 y 3 x 4 4 y 3 x 4 2 6 The value of the x intercept for the graph of 2x 5y 10 is 1 10 2 5 3 5 4 2

24 The second term in an arithmetic sequence is 36 and the fifth term is 54 What is the equation for the nth term of this sequence

fimd a polymnomiall of degree n that has only the givnen zeros x 2 1 n 4

Find the maximum and minimum value of the objective function given z 4x 13y maximum value Z minimum value Z 0 8 24 7 6 010 01

21 Which is equal t A 0 09 B 0 98 9 08 C

X 4 9 PS 19 Use the equation to complete the table d t 3 2 d 43 t 34 25 16 7

5 How many same types of 3 by 2 matrices in reduced row echelon form are there a 1 b 2 c 3 d 4 e

You are in charge of purchases at the student run used book supply program at your college and you must decide how many introductory calculus history and marketing texts should be purchased from students for resale Due to bud limitations you cannot purchase more than 700 of these textbooks each semester There are also shelf space limitations Calculus texts occupy 2 units of shelf space each history books 1 unit each and marketing texts 4 units each an you can spare at most 1 200 units of shelf space for the texts If the used book program makes a profit of 20 on each calculus text 8 on each history text and 16 on each marketing text how many of each type of text should you purchase to maximize profit HINT See Example 3 calculus text s history text s marketing text s What is the maximum profit the program can make in a semester

How many different outfits can I wear if I have 5 shirts 2 neckties 4 pants and 2 sweaters Looks like the previous problem but the dress code has changed and I am permitted to omit the tie and if the weather is warm omit the sweater 180 160 200 220

2 What is the domain of the function f x x 100 The domain is Type your opower in

Baby Ethan wants to arrange 9 blocks in a row How many different arrangements can he make There are ways to arrange the 9 blocks Simplify your answer C

the quotient and remainder using synthet 2x 3 8x 2 6x 2 x 5

Find the inverse of each function 8 f x 3x 1 X 3y 1 1 34 y X 1 3 10 2x 3y 6 12 A C 7 7 B D 9 f x x 5 7 y Which of the following show a graph of a pair of inverses Circle correct choice x y 5 5 X 5 2 x 5 Y 11 f x x 2 14 X 29 2 2 x 2 29 4X 8 34 3 14 x 8 3 13 A 3 C B D k

Name two pairs of congruent angles in the figure Jus

5 5 Given the matrix A and vector b determine the Least Squares solution of Ax b SHOW ALL WORK 1 1 0 1 1 0 10 1 A 1 b 3 00 N

Q5 The game Spin the Spinner has a cost of 7 00 to play one spin The spinner has 8 congruent sections and the sections are numbered 1 3 5 7 9 11 13 and 15 A player chooses one section or number and then spins the spinner The player wins 50 00 if the spinner lands on his her number A What is the player s expected value for one spin Is this a gain or a loss from the player s perspective 3 Assume that 1000 people play the game once What is the expected gain loss for the rganizers of the game

Question 5 18 points Which polynomial function has a y intercept at y 2 and x intercepts at x 1 and 2 2 f x 2x 3x 3x 2 g x x x h x x h x x 6x 12x 8 3

Solve each equation Check your solution 3B 2 4 5 b 5x 3 x 4 8 a

9 In the following figure line MN is parallel to line KP Which pairs of angles are equal Justify your responses Name angles clearly K R P

Here is a list of the main characters in Shakespeare s Romeo and Juliet The first seven characters are male and the last four are female Escalus prince of Verona Paris kinsman to the prince Romeo of Montague Household Mercutio friend of Romeo Benvolio friend of Romeo Tybalt nephew to Lady Capulet Friar Lawrence a Franciscan Lady Montague of Montague Household Lady Capulet of Capulet Household Juliet of Capulet Household Juliet s Nurse A total of 14 male and 12 female actors are available to play these roles How many possible casts are there All roles are to be played by actors of the same gender as the character

12 A radio producer must create a playlist of 6 different songs and 4 different commercials for a radio segment The playlist begins with 3 songs followed by 2 commercials then 3 more songs and 2 more commercials How many different playlists could she create

Points DETAILS WANEFM5 6 3 00 r the given decision algorithm find how many ou Step 1 Alternative 1 1 outcome Alternative 2 4 outcomes outcomes Step 2 Alterna Alterna Alterna

1 point Evaluate the limit x lim x a 6 x a

9 What is the correct statement x A Financial Responsibility plus Deductible equals Total Claim Paid by Insurance Company B Total Injuries minus Deductible equals Money due from Insurance Company C Total Injuries minus Policy Limits equals Financial Responsibility of the Insured D None of the above

7 Solve the differential equation of the form a y x y 2 dy b da C dy dr sec x y 5x 3y 5x 3y 11 dy dr Ax By C using the appropriate substitution

9 points Find the power series for the function f x What is the radius of convergence 1 x at the center x

ons Graph by plotting points y 2x 4 Use the graphing tool to graph the linear e

Find the sum of the first six terms of the geometric sequence 5 15 45 Select one a 365 O b 1 820 c 1 820 d 365

a Find the distance between P and Q b Find the coordinates of the midpoint of the Q P 7 8 10 18 6 4 0

Which of the following relationships is true Select one a sin A cosec A 1 cos A sec A 1 c sec A cot A 1 d sec A cos A 1 b

What is the probability of a person just turning 10 and passing away before the age of 50 Answer with a decimal and not as a

h x x 7 x 1 Question 3 20 points Factor the following polynomial by grouping x x 2x 2 Which of the below is a factor of the polynomial O x 1 O x 2 0 x 2 O x 2 Question 4 20 points Use the graph of f x x 3x 4 to identify the values of x for which f x 0 4 f x 2 5 4 31 2 3 4

Evaluate the given integral over the solid ellipsoid SSJ2lxyz dxdydz to The value of the integral is NING Hint Let x au y bv and z cw Then integrate over an appropriate region in uvw spe

peint Given the graph of f x ato find the following and w Domain of Range of f x

mework Solve the following three part in

nework Solve each inequality analytic follows from the answer to pa a 2x 2 x 2 b 2x 25x 2

Two boxes with given letters are shown Choose a box and draw three letters at random one by one without replacement If the outcome is SOS you win a prize SOS 1 SOSSOS 2 a Which box should you choose b Which box would you choose if the letters are to be

E Writing the equation of a quadratic function given its graph Find the equation of the quadratic function fwhose graph is shown below 4 2 7 11 744 f x

Determine the equation of the polynomials of degree two whose graphs pass through the points 1 14 2 22 3 32 10 marks

HT P 6 S N P NE 94 N ME AR 10 X Graph the lines y 3x 2 and y x 4 What are the slopes of the lines and Are the lines perpendicular 90 apart Use a protractor to verify the angle

ework Solve the following equation an 2x 13 x 13 15

Find an equation of the line Write the equation using function notation Through 2 9 parallel to 5x 2y 7 f x

Composition of two functions Advanced x 2 For the real valued functions f x and g x 4x 13 find the composition fog and specify its domain using interval notation x 1 fog x Domain off g Olol 0 0 6 0 0 0 0 OUD 0 0 0 0 88 8

At a school concert the total value of tickets sold was 4916 Student tickets sold for 7 and adult tickets sola for 11 The number of adult tickets sold was 4 less than 5 times the number of student tickets Find the number of student tickets sold

1 i 1 2 7 2 2 2 k 21 11 For what value of k will the system have no solutions

The one to one function g is defined below g x 7x 1 1 Find g x where g is the inverse of g 1 Also state the domain and range of g in interval notation 1 x 0 g Domain of g 1 Range of g 0 DO 3 0 0 0 OVO 0 0 0 X

3 f x x 45 and g x 3 x 5 6 f x x 8 and g x 4 x 8 1 16 082428 x g bns 2 x a 01