Permutations and Combinations Questions and Answers

2 A garden s length 1 is five feet longer than the width w If the perimeter is 38 feet choose the best equation for the situation O4w 5 38 O w 5 w 38 O4w 10 38

Use the graph to evaluate each expression a f g 2 b f g 3 c fg 1 d f g 2 6

Use the given table to evaluate each expression in parts a through d if possible a f g 2 b f g 4 c fg 2 d 0 a f g 2 Simplify your answer X 2 0 2 4 f

Let f x 7x 2 and g x 4x 5 Find f g x f g x fg x and f g x 11x 3 Simplify your answer f g x Simplify your answer H x x Give the domain of each

S x 2x f 2x 3 3 1 2x 3 x 1 2 2x 3 3x 3 2x 3 2x 2 x x x 2 5x 5 times the numerator and denominator by x 1

Suppose f and g are inverse If f 3 5 find g 5

Solve the rational inequality and graph the solution set on a real number line Express the solution set in interval notation X 5 30 Move all terms to the left side of the inequality and then define the left side of the inequality as f x Then list the intervals determined by the real zeros of f and the real numbers for which f is undefined Complete the following table Interval Sign Type your answers ir negative se ascending order

What is the solution set of the equation2 2 Note j0 2 O 1 1 o 2 O 1 2 o 1

Kira solved the following radical equation using the steps shown to the right What mistake was made in Kira s work 8 2x x 4 8 2x x 4 2x 8x16 8 0 x 6x 8 0 x 4 x 2 x 4 and 2 A When Kira set the equation equal to zerio she should have gotten 2 10x 24 leading to the solution of x 12 and 2 B When Kira finished solving the radical equation she forgot to check for extraneous solutions which would leave x 4 as the only solution When Kira simplified 4 she should have simplified to get x 16 instead of 8x 16 D When Kira squared both sides to eliminate the radical she should have only squared the side with the radical and not both sides

Solve Be sure to check for any extraneous solutions 2 ln a ln 4 In 16 Ox 8 Ox 8

Solve the following exponential equation 3 27

A Coca cola 5 cents A car 500 bucks These prices may seem cheap but they were not back in the day This is due to inflation In a growing economy most goods and services increase in price over time to the tune of 2 3 each year The key is that workers wages also increase Thus a car may have only cost 500 at some point in the past but the average worker s salary was much much lower back then The inflation formula can be used to predict the future price of a good or service The inflation formula is given by FV PV 1 r t where FV is the future value of the good or service PV is the present value of the good or service r is the inflation rate and t is number of years desired Suppose the average loaf of bread costs 3 94 today and grocery inflation averages 1 75 per year Use the inflation formula to predict what an average loaf of bread will cost 36 years from now Round the solution to the nearest cent Suppose the average gallon of milk costs 3 54 today and milk inflation averages 2 10 per year Use the inflation formula to predict what an average gallon of milk will cost 15 years from now Round the solution to the nearest cent

Multiply Express your solution with positive exponents 2v 3u v 4 A B C 8 u6 4u5 v 8v u5 C

Part B Select the correct solution set for the following inequality 3x 8 3 2x 8 7 6 5 4 3 2 1 1 0 H 0 H 2 3

Which of the following best models the solution set of the given inequality 3 x 3 6 0 1 2 0 0 0 3 4 HH 5 6 1 2 3 4 1 I 5 H 1 2 3 4 5 1 2 3 4 5

13 470 4 5 3k 4 14 4a 16 4x

1 11 4 d 16 5 O 1 5 6 u 22 6 a 11 14

Determine the equation s of the vertical asymptote s if any of the graph of p Also determine the I value s if any where the graph of p has a hole If either does not exist enter DNE P 1 21 19 The equation s of the vertical asymptote s of p are The 7 value s where the graph of p has a hole is are

Express log b OA log b 35 pq 4 7 m b Choose the correct answer below 3 5 pq O D log b 4 7 m b 35 pq OB log b log 3p log5q log4m 7 4 7 m b 3 5 pq OC log b 4 7 m b 35 p q in terms of sums and differences of logarithms 4 7 mb 3 log op 5 logb 4logm 7 log53 5log pq log 4 log bm logb 3 log pq 5 4 logpm 7 logb

9 Solve the inequality set Graph the solution on a numberline 2 3 1 or 9 2 0x 7 2 x 2 or 7 x 2 or 7 all real numbers no solution

Graph both functions using the same set of axes f x 3 f x log 3x Choose the correct graph f x 3 is the solid red line f x log 3x is the dashed blue line O A O C Ay Ay Q O O B O D

Use identities to reduce the expression to a function of a cos x 90 Choose the correct function for cos x 90 OA A sin a OB cos x O C cos OD sin a

Find the exact value of the expression given below cos 105 Rewrite the expression using a sum or difference formula Choose the correct answer below A cos 105 cos 60 45 sin 60 cos 45 cos 60 sin 45 B cos 105 cos 60 45 cos 60 cos 45 sin 60 sin 45 C cos 105 cos 60 45 sin 60 cos 45 cos 60 sin 45 OD cos 105 cos 60 45 cos 60 cos 45 sin 60 sin 45 The exact value of cos 105 is Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all denominators

27 The larger of two numbers is 25 more than the smaller When added together the sum of the larger number and five times the smaller number is 127 What are the two numbers larger number smaller number

15 Convert to standard form y 7x 17 x 16 Solve the inequality set Graph the solution on a numberlin x 13 3 and x 8 4 O 4 O2 10 and x 4 O 10 and x 4 Ox 10 O all real numbers

8 Solve the systems of linear equations using the substitution method x y 2 7y 4x 1 O 5 3 O 7 9 O 5 7 O 7 5 29 Use substitution to solve the system for f Do not round e 0 0 25e f 10

Use negative and fractional exponents to put every answer in the following format constant if any simplified as much as possible multiplied by x raised to an exponent Example 4x3 2x 2 6 x 3x 3x 1 3 3 5 4x4 x 3 4 81 1 3x6 63 2 3x 2x 3x8 3

The radioactive element carbon 14 has a half life of 5750 years A scientist determined that the bones from a mastodon had lost 61 1 of their carbon 14 How old were the bones at the time they were discovered The bones were about years old Round to the nearest integer as needed

13 Given the formula V Ah solve for A V 03 2 3h O V 09 O 3Vh

Find fog x and gof x and the domain of each f x x 17 g x x 17 fog x Simplify your answer

Completely factor and find all zeros of the following polynomial f x x 10z 192 30 Write f as the product of linear factors each with a leading coefficient of 1 f x Find all zeros of f

For problems 13 and 14 use the following information f x 4x 1 g x x 2 Find fog 7 Answer Find gof 7

4r 3k 16 4

Solving Absolute Value Equations Solve each equation 1 3x 9 3 b 5 1 2 3r 9 Date 4 6m 30

Which graph shows the solution set to the compound inequality 2 8 4x and 3x 5 A B C 6 4 20 2 4 6 6 4 202 6 4 6 46 2 4 20

1 2x 2 x 4 2 3x x 7x 3 5x 5x 3x 3x 7 4 2x 4x 16 3x 2x 5 x 5 3x 7 6 4x x 3 5x x 4 7 2x 1 x 4 8 4 2x 9 2x 31 3x x 9

The expression equals y where r the exponent of x is t the exponent of y is 12 5 4 10 x y 4 5

5 Find the exact value of the expression given below COS COS 11x 12 11x 12 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all denominator

Simplify the expression by using an appropriate identity Do not use a calculator cos57 cos33 sin57 sin33 Write the expression using the sum or difference formula for sine or cosine Choose the correct answer below O A cos57 cos33 sin57 sin33 cos 57 33 cos 24 O B cos57 cos33 sin57 sin33 cos 57 33 cos 90 OC cos57 cos33 sin57 sin33 sin 57 33 sin 90 OD cos57 cos33 sin57 sin33 sin 57 33 sin 90

Write the first trigonometric function in terms of the second trigonometric function tan 0 sec 0 Choose the correct answer below OA tan 8 sec 0 1 1 sec 0 O E tan 0 1 sec 0 Question 8 5 1 49 O c tan 8 HW Score 0 0 of 13 p O Points 0 of 1 OB tan 0 1 sec 0 OD tan 0 sec 0 1 OF tan 8 sec 0 1

Question 5 5 Use identities to correctly complete the sentence If cos 0 0 9 and sin 0 0 8 then tan 8 Type an integer or decimal rounded to the nearest hundredth as needed

3 Ethan is writing a customer satisfaction survey for the Brew for You Coffee House he works at He has come up with two versions of the same question Which question creates bias Question 1 How much did you enjoy the cup of coffee you had today Question 2 How would you rate the cup of coffee you had today A Question 1 because it s biased towards a positive answer B Question 2 is biased because the customer has to use a scale to rate the cup of coffee C Neither versions of the question create bias D Both versions of the question create bias

4 Is the survey question below biased Explain your reasoning Do you like animals and would you ever consider owning a dog cat or hamster A Biased because it only lists 3 types of animals B Not biased because people can answer without being swayed one way or and C Biased because two questions are being asked at once D Not biased because people can answer yes or no

C 6 in 6 in What is the perimeter If necessary round to the nearest tent rhes

The numbered disks shown are placed in a box and one disk is selected at random Find the probability of selecting a 3 given that a green disk is selected Find the probability of selecting a 3 given that a green disk is selected Type an integer or a simplified fraction OOOO green green green green OOO green green green blue

Quiz 11 4 11 6 11 7 You are dealt one card from a standard 52 card deck Find the probability of being dealt a five The probability of being dealt a five is Type an integer or a simplified fraction

1 3 ems by substitution Solve each system by substitution 1 2x 7y 1 7x y 20 A 3 1 B Infinite number of solutions C 3 1 D 3 1 3 x 7y 10 3x 7y 2 A 2 4 C 4 2 B 4 2 D 4 2 2 4 2 8x 5y 1 y 3 A 2 3 C 6 3 4 3x 24y 3 x 8y 4 A No solution C 5 5 B 2 3 D 6 3 B 5 6 D 5 6

The table shows the distribution by age of a random sample of 3680 moviegoers ages 12 74 If one moviegoer is randomly selected from this population find the probability expressed as a simplified fraction that the moviegoer is not in the 25 44 age range The probability is Type an integer or a simplified fraction GWWwR Age Distribution of Moviegoers Ages 12 24 25 44 45 64 65 74 Number 550 1300 930 900

work 11 6 Question 1 You are dealt one card from a 52 card deck Find the probability that you are not dealt a two The probability is Type an integer or a fraction Simplify your answer www

A single die is rolled twice The 36 equally likely outcomes are shown to the right Find the probability of getting two numbers whose sum is 8 First Roll The probability of getting two numbers whose sum is 8 is Type an integer or a simplified fraction Second Roll 1 1 1 2 1 3 1 4 1 5 1 6 2 1 2 2 2 3 2 4 2 5 2 6 3 1 3 2 3 3 3 4 3 5 3 6 4 1 4 2 4 3 4 4 4 5 4 6 5 1 5 2 5 3 5 4 5 5 5 6 6 1 6 2 6 3 6 4 6 5 6 6