Permutations and Combinations Questions and Answers
Algebra
Permutations and Combinationsb varies inversely as c If b 6 when c 2 find b when c is 4 b 010
Algebra
Permutations and CombinationsThe 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
Algebra
Permutations and Combinations5 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
Algebra
Permutations and Combinations24 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
Algebra
Permutations and Combinationsfimd a polymnomiall of degree n that has only the givnen zeros x 2 1 n 4
Algebra
Permutations and CombinationsFind 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
Algebra
Permutations and CombinationsX 4 9 PS 19 Use the equation to complete the table d t 3 2 d 43 t 34 25 16 7
Algebra
Permutations and Combinations5 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
Algebra
Permutations and CombinationsYou 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
Algebra
Permutations and CombinationsHow 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
Algebra
Permutations and Combinations2 What is the domain of the function f x x 100 The domain is Type your opower in
Algebra
Permutations and CombinationsBaby 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
Algebra
Permutations and CombinationsFind 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
Algebra
Permutations and Combinations5 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
Algebra
Permutations and CombinationsQ5 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
Algebra
Permutations and CombinationsQuestion 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
Algebra
Permutations and Combinations9 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
Algebra
Permutations and CombinationsHere 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
Algebra
Permutations and Combinations12 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
Algebra
Permutations and CombinationsPoints 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
Algebra
Permutations and Combinations9 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
Algebra
Permutations and Combinations7 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
Algebra
Permutations and Combinations9 points Find the power series for the function f x What is the radius of convergence 1 x at the center x
Algebra
Permutations and Combinationsons Graph by plotting points y 2x 4 Use the graphing tool to graph the linear e
Algebra
Permutations and CombinationsFind 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
Algebra
Permutations and Combinationsa 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
Algebra
Permutations and CombinationsWhich 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
Algebra
Permutations and CombinationsWhat 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
Algebra
Permutations and Combinationsh 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
Algebra
Permutations and CombinationsEvaluate 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
Algebra
Permutations and Combinationspeint Given the graph of f x ato find the following and w Domain of Range of f x
Algebra
Permutations and Combinationsnework Solve each inequality analytic follows from the answer to pa a 2x 2 x 2 b 2x 25x 2
Algebra
Permutations and CombinationsTwo 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
Algebra
Permutations and CombinationsE 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
Algebra
Permutations and CombinationsDetermine the equation of the polynomials of degree two whose graphs pass through the points 1 14 2 22 3 32 10 marks
Algebra
Permutations and CombinationsHT 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
Algebra
Permutations and CombinationsFind an equation of the line Write the equation using function notation Through 2 9 parallel to 5x 2y 7 f x
Algebra
Permutations and CombinationsComposition 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
Algebra
Permutations and CombinationsAt 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
Algebra
Permutations and Combinations1 i 1 2 7 2 2 2 k 21 11 For what value of k will the system have no solutions
Algebra
Permutations and CombinationsThe 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
Algebra
Permutations and Combinations3 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