Permutations and Combinations Questions and Answers

Write the equation of the line in standard form Ax By C for the described Enter in the value for A B and C through 1 6 perpendicular to 3x 5y 1 I x y

Complete the following a The graph of y f x is shown Draw the graph of y f 2x 1 44 ED 5 Segment b The graph of y h x is shown Draw the graph of y h x 3 0 1 X E G

K Graph the piecewise defined function x 1 if x 4 5 if x 4 Choose the correct graph

Find the gradient of the following scalar fiel a V 4x e y b U r cos c T e R sin 0

TrueFun Entertainment sells four types of products radios DVDs video games and CDs The numbers sold for 2021 and 2022 are shown in the double ba graph below Use this graph to answer the questions Number sold 1200 1000 800 600 400 200 0 Radios DVDs Video games CDs Product 2021 2022

Exercise 6 6 3 Show that the plane P s 0 subspace Then explain why we know this is true by some theorem we discussed t0s te R is a subspace of R3 by using only the definition of

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2 st Length of Spring by Weight Attached Length in L L w 6 weight lbs lue in the ordered pair described by the function notation and th

1 24 y 5 x 2 4 15 3 2 1 6 5 4 3 2 1 1 2 3 4 5 6 6 5 4 3 2 6 5 4 3 2 1 1 2 3 4 5 6 O 6 5 3 2 1 6 5 4 3 2 1 1 2 3 4 5 6 6 5 4 3 2 1 2 3 4 5 2 myopenmath com A 2 3 4 5 6 6 6

Distance formula Suppose that P x y and Q x y are points in the Euclidean xy plane Using modern algebra techniques show that the distance between P and Qi 2 2 given by PQ x x y y Include a diagram and explain your reasoning

The graph of y f x is graphed below What is the end behavior of f x 400 350 300 250 200 150 100 50 10 9 8 7 6 5 4 3 2 40 100 150 200 250 300 350 400 1 2 3 4 5 6 7 8 9 10 as x y and as x y as x y and as y as x o y o and as x yx as x y o and as x y

mpute 3 3 3 3 w 2xy 3yz 3xz x st y est z t

3 Find frr 2 0 fzy 2 0 and fyy 2 0 if f x y e sin y

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Complete the square of given quadratic expression Then graph the function using the technique of shifting f x x 8x Complete the square by entering the correct numbers into the expression below f x x

x 3y 4z 14 2x 3y2z 10 3x Y Z 9

When graphing r 9cos 40 the cos 40 0 on the interval AP 46

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Let Pn be the following proposition 2 4 6 2n 2 n 3n 2 Prove by mathematical induction that n is an element for all positive integers

Let z x y z z Y x 10 y z y f x y Y and find the simplest expression for it where f is differentiable and y0 Calculat

A plane flying with a constant speed of 19 km min passes over a ground radar station at an altitude of 7 km and climbs at an angle of 20 degrees what rate in km min is the distance from the plane to the radar station increasing 1 minutes later Your answer kilometers per minute Hint The law of cosines for a triangle is where is the angle between the sides of length a and b c a b 2ab cos 0

Solve the following equation by factoring and using the zero product property x 5x 0 The Factors are Enter using parenthesis around each factor Do not use a comma The Solutions are x Enter numeric values separated by a comma

K Use the graph to evaluate the expressions f fof 1 www fog 3 Round to the nearest whole number as nee gof 1 Round to the nearest whole number as nee

ve the equation of the function whose graph is described he graph of y x is vertically shrunk by applying a factor of Which of the following is the equation of the function 1 y x 3 DA Y DB y DC 13 5 13 5 5 15 and th OLICY

For the following problems let f x 2x 1 and glx x 1 Find the following values Box answers 1 2 2 gf 11 3 g a 4 glx 1 2 2 1 4 13 5 f h x 9 f g x 1 1 1 1 12 6 g f x 10 x a 1 7 f g x 11 g x 8

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42 Which expression is equivalent to 3 O O 16 3 713 3 16 34 1 4

work 1111 Polynomial Functions Homework n list on 1 K For the polynomial function belo that the graph of fresembles for 130 f x 4 x 1 x 9

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3 Refer to the following table which shows the stock market performance of 40 industries from five sectors of the U S economy as of noon on September 11 2015 J Take S to be the set of all 40 industries represented in the table Increased X Decreased Y Financials F 3 Unchanged Z Totals 4 1 8 Manufacturing M 8 Information Technology T Health Care H Utilities U 4 Totals 24 3 10 6 1 3 1 3 1 40 0 5 14 6 7 J Unchanged includes industries that moved by less than 0 1 Source for data Fidelity https eresearch fidelity com a Use symbols to describe the event that an industry neither decreased in value nor was in the information sector How many elements are in this event b Describe the event F U Mn Z in words and compute n FU Mn Z c What percentage of industries that increased in value were utilities industries d What percentage of utilities industries increased in value Hint Similar to Exercises 57 59 and 55 in Section 7 1 of the textbook Solution

1 Your downloaded music files include three symphonies five piano concertos two string quartets and two Chopin ballades You have decided to listen three of these works chosen at random in succession Complete the following sentences a The sample space is the set of b The event that you listen to a symphony followed by a Chopin ballade is the set of

K For the polynomial funct turning points on the gra f x x 2 x 7

P Q T T T F TI FT F F N P Q lowing P Q T T T F T F F Select your conclusion Contradictory V 5 item attempts remaining P QI Q P LL 1 POQIP Q P Q I Q P T T F T 2 Tadictory Can T F F F reate a truth table to determine whether the following statements are contradictory consistent or inconsistent LL P sistent of consistent

A dietitian wishes a patient to have a meal that has 74 grams of protein 106 5 grams of carbohydrates and 430 milligrams of calcium The hospi food service tells the dietitian that the dinner for today is chicken corn and milk Each serving of chicken has 40 grams of protein 45 grams of carbohydrates and 100 milligrams of calcium Each serving of corn has 3 grams of protein 14 grams of carbohydrates and 10 milligrams of calcium Each glass of milk has 8 grams of protein 11 grams of carbohydrates and 260 milligrams of calcium How many servings of each food should the dietitian provide for the patient The patient should have serving s of chicken and serving s of milk Type an integer or a decimal serving s of corn

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Question 5 2 6 15 x x 9x and g x 8x 3 Perform the composition or ope 1 Select the correct choice below and if necessary fill in the n integer or a sim

nework Ques Solve the following inequality graphica x 3 0 7x 4 tom of the given insa

work Question 10 2 4 olve the following inequality 12 4x 11 Select the correct choice below and if necessa Onswer Type your ans real ny plution set is the interval

If f k 9 what is the value of f k The value of f k is 0

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For tx 78 and g06x find the flowing composite functions and state the domain of each a fog b gof c fel 0 g 42x 8 Simply your answer Select the corect choice below and f yanswer boxes within your choice OA The domain of fagh x Type an inequality Upe integers or actions for any numbers in the expression the a beparate answers as eded A B The domain of fog is a real numbers b g 100 42x4 Simply your answer Select the comect choice below and in any answetboes your choice OA The damain of gath Type an inequality Use integers or actions for any numbers in the expression Ube a coma t separate answers asided B The domain of g 980049x 64 Beact the cost choice below and numbers tanower

3 Your broker has suggested that you diversify your investments by splitting your portfolio among tech stocks municipal bond funds industrial stocks and precious metals She suggests six tech stocks four municipal bond funds eight industrial stocks and four precious metals gold silver palladium and platinum You want your portfolio to contain five tech stocks three municipal bond funds and either one industrial stock and two precious metals or no industrial stocks and three precious metals How many different portfolios are possible Hint Similar to Exercise 29 in Section 6 3 of the textbook Solution

Use the synthetic division to divide p x by 1 x p x 3x 8x 7 1 x x 2 3 8 0 7 The quotient of the division is q x The remainder of the division is r x Is 1 x a factor of p x What is p 2 equal to Find it without plugging 2 in the polynomial

The Arab Spring rebellions which began in late 2010 were focused broadly on all of the following EXCEPT O limited opportunities for democracy and free elections O widespread poverty and unemployment among young people O rapidly rising food prices O charges of widespread government corruption

5 3 ints 01 55 58 question 66 Identify whether the following transaction is an Asset So Pald cash for salaries accrued at the end of a prior perk Multiple Choice Asset Source

Gwen and James plan to send their son to university To pay for this they will contribute 8 equal yearly payments to an account bearing interest at the APR of 2 9 compounded annually Five years after their last contribution they will begin the first of five yearly withdrawals of 47 900 to pay the university s bills How large must their yearly contributions be

OP G in this figure ABCD and DEFG are squares Prove that AG E

A poker hand consists of five cards from a standard deck of 52 See the chart preceding Example 8 Find the number of different poker hands of the specified type HINT See Example 8 Straight five cards of consecutive denominations A 2 3 4 5 up through 10 J Q K A not all of the same suit Note that the ace counts either as a 1 or as the denomination above king hands

Let S Barnsley Manchester United Southend Sheffield United Liverpool Maroka Swallows Witbank Aces Royal Tigers Dundee United Lyon be a universal set A Southend Liverpool Maroka Swallows Royal Tigers and B Barnsley Manchester United Southend Find the number indicated HINT See Quick Example on page 410 n An B X 8

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