Permutations and Combinations Questions and Answers

12 CHALLENGE PROBLEM Pamela Kruse drives to and from work in her red sports car Her driver rating factor is 4 85 Her insurance coverage includes 100 200 bodily injury and 100 000 property damage She has 50 deductible comprehensive and 50 deductible collision coverage Her car is in age group A and insurance rating group 13 How much more will her annual premium be if she increases the liability coverage to 300 300 100

A Find the slope of the line that passes through the given points B Find the standard form of the equation of the line C Find the slope intercept form of the equation of the line 1 2 and 6 8 A Find the slope of the line that passes through the given points Select the correct choice below and if necessary fill in the answer box to com choice A m Type an integer or a simplified fraction B The slope is not defined

LEARN IT Choosing a Solution Method We ve now discussed three different methods for solving systems of equations Each method has advantages and disadvantages and each method may be simpler to use for a given system of equations Review this chart and then practice selecting what method to use to solve a system of equations When to Use Method Graphing Substitution Elimination Advantages Disadvantages Solution is easy to see Cannot find an exact answer for non integer solutions 1 y 2x 1 y 6 3x Recognizable when first learning Most straightforward Works naturally with standard form equations Can take more time Can be more difficult with fractions Don t have to combine Finding the correct like terms multipliers can be tricky In 00 When graph is already drawn for at least one When the equations are in slope intercept form When one variable is already isolated When one variable has a coefficient of one When the equation starts in standard form When the coefficients of one variable are the same or opposite When the numbers are fractions or inconvenient for substitution For the following problems choose the solving method that you think is most appropriate and state the reasons why you made that choice There may be more than one method that works You do NOT need to solve the problem 2 x 3y 7 2x 3y 11

1 Find the domain of each function using interval notation a f x 5 2x 1 Find the value of x that makes the denominator 0 2x 1 0 add 1 to both sides 2x 1 divide both sides by 2 x 1 2 X so x can be any number except the domain will be ALL REALS Solution

Suppose a line segment from A 1 8 to B 2 4 has internal divisor 13 11 64 12 find the ratio of the division

2 a Describe carefully the action of the rotation group of the regular tetrahedron on its set of faces describing the face orbits for each rotation 4 marks b Use your answer to compute the number of non equivalent ways to colour the faces of a regular tetrahedron using 5 colours where two colourings are equivalent if one can be rotated onto the other Show your working 8 marks c Give a general formula for the number of different coloured tetradheda that can be manufactured using k colours and use your formula to find the minimum number of colours required to produce at least 1 000 different colourings 3 marks

ostitute x 12 x 12 Solve y y In Exercises 1 6 find the sum See Example 1 1 3x 4x 1 2r 3x 2 3 12r5 3x4 2x 5 8x4 3x 4x 1 5 25 7x6 3x 9x 5x5 8x 6x 2x 5 2 5x 4x 2 8x 2x 1 4 8x 3x 1 3x x 7x 1 6 9x4 3x 4x x 7 11x4 9 4x 3x

Find the value s of x for which f x g x 11 f x x 2x g x 2x 12 f x 3x 1 g x x 1

7 If csc 0 13 x 0 3 then the value of cos 20 is a 144 169 b 25 169 c 119 169 d 50 160

r 9r6 4 dx using formula 48 in the table of integrals in the textbook 2 Evaluate

Quadrilateral quadrilateral EFGH is similar to IJKL Find the measure of side KL Round your answer to the nearest tenth if necessary EFGHI J K L 33 23 8

Suppose you have six Virginia quarters and four Pennsylvania quarters in your wallet You randomly choose three quarters What is the probability that all the quarters will be Virginia quarters Your answer should be in fraction form

Which answer choice has the set of numbers ordered correctly from least to greatest O 13 1 71 16 O 3 12 16 1 71 1 71 13 16

Fill in the blanks to complete the descriptions of this linear function X 10 5 0 y The x intercept is at The y intercept is at 5 10

Solve 4x 124 Give your answer as an interval using whole numbers proper fractions or improper fractions

Direction Type your answer in the box below The top four teams in a local tournament move onto the playoffs If 7 teams enter the tournament ho many different combination of teams can make it to the playoffs

10 Simplify each expression by applying the distributive property of division Combine any like terms in your results a 20x 12x 4x b 60x 30x 15x 8x

Perform the indicated operation and simplify 7 6i 3 2i

Which of the following expressions correctly illustrates the Inverse Property of Multiplication 5 i 2 7 7 1 3 2i 4 9i 6 35i 4 9i 4 9i 117 B2i 3 4 2 3 4 D5i 2 1 7i 5i 2 14i

Perform the indicated operation on the expressions below Be sure to simplify your answer 12 13 5x 3xx 4 9 5x 3 x2 2x 8 x 7 4 x 2 x

A typical cross section of a reinforced concrete beam is shown in the figure below Use an effective depth of 600 mm a Determine the required number of 35M rebars corresponding to the balanced condition b Find the corresponding factored moment resistance 100 400 mm 100 600 mm 100 A Given f 25 MPa 400 MPa 0 65 0 85 Es 200 000 MPa

12 Hassan makes two types of carpets The first type costs 3 for wool and 35 per hour for weaving The second type cost 27 for wool and 31 per hour for weaving When are the costs the same How many hours must he weave carpets for the costs to be the same ANS POI 6 213 13 Fatima rents a theatre for a spring concert The theatre charges her 1160 plus 3 per person Fatima plans to charge 11 per person How many tickets must Fatima sell in

7 Sarah is a hairdresser At her salon she charges 15 per woman and I On Saturday she made 5053 and gave 355 haircuts men and women How many women got a haircut How many men got a haircut 8 Martin mows lawns He charges 26 per house and 32 per cottage for this service On Saturday he made 24328 working at 830 houses and cottages How many houses were there How many cottages were there 9 Mike s Garage does oil changes on vehicles For an oil change they charge 32 per car and 46 per truck On Monday the garage made 1620 and did oil changes on 41 cars and trucks How many cars were there How many trucks were there

Find the inverse of the following y log x 3 4 y 2 4 y 2 3 4 y 2 4 3 y 2 4 3

1 Points DETAILS State the property of real numbers being used 6 A B 6A 6B Distributive Property Associative Property of Addition Commutative Property of Addition Commutative Property of Multiplication

What is the domain and range of y e O Domain ALL REALS R Range ALL REALS R Domain ALL REALS R Range y 2 Domain ALL REALS SR Range y 0 Domain x 0 Range ALL REALS O O

Write the equation of a degree 3 polynomial function whose zeros are 5 3 1 and 1 32

Write the following numbers in standard notation a 9 x 103 b 7 7 x 10 5 c 4 99 x 10

Solve 3 sin x cos x in radians to two decimal places for 0 x T O a 0 Ob 0 32 and 3 46 O c 0 32 d There is no solution to this equation for the given interval

f f x Choose an equivalent statement for nif cac csc tan sec chocol sin x

1 2 y x 2 653 2 1 S N www X 2 y 122x 2 2

Find the directional derivatives of the convex function f x max 5x 3 2x 1

If a player spins a blue or yellow and rolls an odd number the player would win 10 Find the probability of this happening O a 1 Odl O d 1

A study of 1000 randomly selected flights of a major airline showed that 820 of the flights arrived on time What is the probability of a randomly selected flight not arriving on time O a 500 1 O b c 4 9 50 d 41 50 Question 19 1 point Which of the following cannot be a probability

Question 2 1 point As Mrs Colby determines the number questions on her upcoming AMDM quiz she decides that she will give a 10 question quiz This quiz will have 4 true false questions and 6 multiple choice questions Each multiple choice question has 5 possible choices A B C D and E How many different ways are there to answer the quiz a 24 b 38 c 240

X TM Pa C Clever Portal Classes A variable needs to be eliminated to solve the system of equations below Choose the correct first step 7x 10y 83 4x 10y 16 Subtract to eliminate y Subtract to eliminate x Add to eliminate x Add to eliminate y

For the function f z f 2 4 4 f 2 f 0 z 3 21 1 1 2 I 2 find each

1 Identify the error Identify the slope and y intercept for the graph below Slope Y intercept 3

Determine the best method to solve each system of equations Then solve the system 2 m 6n 8 3 a b 6 1 x 2y 3 x y 1 m 2n 8 4 4x y 15 x 3y 12 7 4x 2y 10 x 2y 5 10 2a 4b 2 10 4a 46 d 14 c d 2 5 3c 8 x 2y 4x 4y 10 11 4x 10y 6 2x 10y 2 a 2b 7 6 x 2y y 4x 9 28 3t 42 3s 2t 24 12 2x y 3 x y 0

Which table below represents a relation that is not a function E Press the hotspot to select the table that does not represent a function Press the answer box after each selection to save your response X y 0 4 1 3 2 2 1 23 X 0 1 23 2 3 y 4 3 23 2 3 0 1 27 2 1 y 4 321 3 2

Consider the function f x in the interval 5 5 After constructing a fourth order polynomial P which corresponds the approximation of fox by taking 12 equidistant points in 1 5 51 find the value approximate polynomial P r at the point x 99 444 by using MATLAB Your answer 3 1 x O 5 4674e 05 5 5674 05 O 5 5674e 05 O 5 5574e 05 Q 5 5694e 05

Convert the following equation to ope intercept form 28x 4y 40

12 If ke R and the middle term of 2 then value of k is a 3 c 3 b 2 d 4 is 1120 13 The sum of the binomial coefficients of 2x of 2x is equal to 256 The constant term in the expansion is a 1120 b 2110 c 1210 d None of these 14 The sum of the co efficients in the expansion of

Determine which graph represents the inequality given Press the hotspot to select the graph of the inequality Press the answer box after each selection to save your response W Inequality 7 X 9 8 7 6 5 4 9 8 7 6 5 4 9 8 7 6 5 4 4 5 89 2 101 23 4 56 789

D 1 point A polynomial function with a degree of 4 is called a Quartic Function O True O False

Use normal distribution to find the probability 4 2 that the acidity ratio exceeds

If sin 20 cos 20 2 2 cos a then a is equal to

TOTAL COST 20 18 16 14 12 10 8 6 4 2 WINTER CARNIVAL COST 2 4 6 8 10 12 14 16 18 20 OF TICKETS

22 Which table of values below represents a linear relationship X 1 2 3 4 5 X 10 5 0 5 10 X 1 2 4 7 y 1 4 9 16 25 y 10 6 2 6 10 y 1 2 3 A

Question 31 Write the equation in slope intercept form for a line which passes through point 5 6 and 1 2