Permutations and Combinations Questions and Answers

11 a Find the Z transform of 2n 5 sin b Find the inverse Z transform of T n 3a 4 4z 2z 2 23 52 8z 4

Simplify the complex fraction 6 t 6 t 7 7 t 7 7 t

Simplify the complex fraction 5x5 2y6 7x 3xy

Simplify the complex fraction x 9 3x 52 45 9

none of these Question 7 1 point How much force is needed to accelerate a 2 0 kg physics book to an acceleration of 3 0 m s O 1 5 N 6 0 N ON 0 7 N 18 0 N Question 8 1 point A 11 N falling object encounters 4 N of air

Which of the following graphs have the same domain y x y x 4 y x 4 y 4 x

nment rd is drawn from a standard de P king

Check Clear Help Do it Check ACB D ADB Clear Help Do it B ACB O E A B Let A 2n 1 n 0 1 1 2 2 B q q is an odd integer Then mark all that are correct A ACB B ACB C ADB D ADB E A B F None of the above ADB Let A uu is an integer with u 6 B 3 4 5 6 Then mark all that are correct None of the above

According to a study of 200 samples of ground meats the probability that one of the samples was contaminated by salmonella was 30 The probability that a salmonella contaminated sample was contaminated by a strain resistant to at least one antibiotic was 67 and the probability that a salmonella contaminated sample was contamin by a strain resistant to at least three antibiotics was 54 Find the probability that a ground meat sample that was contaminated by an antibiotic resistant strain was contaminated by a strain resistant to at least three antibiotics Round your answer to three decimal places 0 827

Australia and New Zealand were formerly colonies of which country France O The United States O The United Kingdom Great Britain

on 28 Pivot as the shift in American f g of all military ties with Japan so as

Car license plates in Brittany PA consist of 3 different letters in the range A G followed by 4 different The number of possible license plates is CH As above but where the letters but not the digits can repeat Ch

You are at the student cafeteria and trying to decide on a veggie burger combination with 2 toppings and 3 side orders There are 9 different toppings available including mayonnaise hot sauce and some others and I different side orders available including french fries tomatoes tortillas and some others Hint As with everything in life you should use a decision algorithm The number of possible burger combinations is Check Clear Help As above but including mayo and french fries but no tomatoes Check Clear Free Hint

What if we cannot determine the common difference or common ratio very easil function equation by regression Use the appropriate regression on the calculator to find the equation of the following functions Round to the nearest thousandth X Y 6 3 10 18 6 X Y 0 0 35 0 7 2 14 3 4 2 8 5 6

An observer views the space shuttle from a distance of a mi from the launchpad 0 Express the height of the space shut a function of the angle of elevation 6 6 Express the ange of election as a function of the height of the space shutti

1 Knowledge Understanding 8 6 6 marks a Write each of the following as a single power 39 x 34 36 iii 6 6 iv 1 2 25 ii b Evaluate each of the following i 2 2 ii 3 2 3 ii c Simplify each of the following Express all answers with positive exponents if possible 1 2x 7x 45x y z 9x yz 5 x5 5 x5 ii 9 25 iii 2016 x4 26 J0 25

DI 3 points Lesson 17 A savings account pays a 3 nom Any interest earned is deposited in are made 1 Write an expression that re compounded annually 2 If interest is compounded s would be used for each cal

Which city of Central Asia is a prime example of a forward capital O Astana O Kabul O Bishkek

Which animal is used for nomadic pastoralism on the Tibetan Plateau O Yak O Llama O Sheep

A study was conducted of the trend in the design of social robots In a random sample of 108 social robots 61 were built with legs only 21 were built with wheels only 11 were buil with both legs and wheels and 15 were built with neither legs nor wheels Use the rule of complements to find the probability that a randomly selected social robot is designed with either legs or wheels or both The probability is Type an integer or a decimal Round to three decimal places as needed m

ework aspx homeworkld 307285248q eir results are shown in the table What is th

ment he theoretical probability of the ev 3

2 Graph and label both of the curves below Then state their intersection points in other words solve the system of equations shown below y 4 cos x 1 y cos x 4 Intersection Points 2T 10 7 2 3A 2 T x

6 When graphed the line y 14 would not intersect the graph of which of the following functions 1 y 5 cos x 9 3 y 2 sin x 15 2 y 6cos x 10 4 y 3 sin x 20 7 Which of the following functions has a maximum value of 25 1 y 25 sin x 12 3 y 8 cos x 17 2 y 10 cos x 35 4 y 5sin x 15

Write the system of equations corresponding to the given augmented matrix using the variables x and y Then perform the row operation R 4r4 2 on the given augmented mat Which of the following is the system of equations corresponding to the augmented matrix OA OC x 4y 1 4x 4y 9 CIT x 4y 1 4x 4y 9 OB O D 4x 4y 1 4x y 9 Save x 4y 9 4x 4y 1

Solve the system of equations If the system has no solution say that it is inconsistent 3x 3y 5z 5 9x8y 13z 14 3x 4y 7z 5 Select the correct choice below and fill in any answer boxes within your choice OA The solution of the system is x y Simplify your answers and z OB There are infinitely many solutions Using ordered triplets the solution can be written as x y z lx y Simplify your answers Type expressions using z as the variable as needed x y z lx y z any real number OC There are infinitely many solutions Using ordered triplets the solution can be written as x y z x Simplify your answer Type an expression using y and z as the variables as needed OD The system is inconsistent y any real number z any rea

1 Is x 2 y a solution of the given system of equations 3 5x 6y 8 1 3x 4y 2 3 Is the first equation satisfied OYes No

The graph of the function y f x 43 can be obtained from the graph of y f x by one of the following actions O shifting the graph of f x upwards 43 units O shifting the graph of f x downwards 43 units O shifting the graph of f x to the right 43 units O shifting the graph of f x to the left 43 units

Below is the table for the function f x X 1 4 7 13 14 Y 3 5 9 12 15 Choose the one table below which is the inverse function x 8 Y X Y X Y 3 5 9 12 15 1 4 7 13 14 1 3 1 5 3 5 14 15 1 9 1 12 1 15 9 12 15 13 7 4 12 9 45 13

The probability of event A is 0 2 and the probability of event B is 0 6 The probability of event A given event B is 0 4 Which statement is true O Events A and B are independent because P AIB P A O Events A and B are dependent because P AIB P B O Events A and B are dependent because P AIB P A x P B O Events A and B are independent because P A B P B O Events A and B are dependent because P AIB P A

ACT Question 41 of 60 If 10 percent of 50 percent of a number is 30 less than one quarter of the number what is the number O 120 O 160 O 150 O 100 O 130

What is the greatest common factor of 125 50 and 275 O 5 O 25 O 50 O 125 O 275

Question 44 of 60 A student must take one physics one chemistry and one mathematics course during their junior year of high school There are three courses to choose from for physics P1 P2 P3 two courses to choose from for chemistry C1 C2 and two courses to choose from for mathematics M1 M2 How many possible combinations are there for the three physics chemistry and mathematics courses a student could select O24 12 06 07

satellite is cirding a 125 miles above a planet as shown in the figure When the satellite is directly above point B angle A is found to be a 76 3 Use this information to find the radius of the anet Round your answer to the nearest whole number 000 x mi Radion Radn

Kevin randomly selects one card from a standard deck of 52 playing cards What is the probability that the card Kevin selects is a king or a heart O O O O 13 17

Express 0 0000018 in scientific notation O 1 8 x 106 O 18 x 10 7 O 1 8 x 10 5 1 8 x 10 6

Question 3 of 60 Simplify the following expression O O de o seld Ned Reset

the Physics Club executive committee at ESU Enormous State U consists of four members of whom one is designated as chairperson and two as secretaries There are five people available to serve on the committee Which of the following are valid decision algorithms to count the number of possible committees that can be formed The number of possible committees is Check Step 1 Choose a person to exclude from the committee 1 choice O Valid Step 2 Choose a chairperson 1 choice Invalid Step 3 Choose an ordinary member 3 choices Step 1 Choose a person to exclude from the committee 5 choices O Valid Step 2 Choose a chairperson 5 choices Invalid Step 3 Choose an ordinary member 4 choices Step 1 Choose an ordinary member 5 choices O Valid Step 2 Choose a chairperson 4 choices Step 3 Choose a person to exclude from the committee 3 choices Invalid Step 1 Choose a person to exclude from the committee 5 choices O Valid Step 2 Choose a chairperson 4 choices Invalid Step 3 Choose an ordinary member 3 choices Clear Help

Solve for y 2 7 Simplify your answer as much as possible 6 y 0 No solution D O

You take a multiple choice test with 6 questions each of which has 3 choices with one correct choice Hint You can enter the answers as either numbers or formulas as in 5 6 7 or in 7 4 The number of possible filled out answer sheets is Check Clear Help Check Clear Help The number of those that have every single answer wrong is Now let s look at a situation that calls for combining both principles The following is similar to Example 1 in Finite Mathematics

A party rental company has chairs and tables for rent The total cost to rent 2 chairs and 5 tables is 53 The total cost to rent 8 chairs and 3 tables is 42 What is the cost to rent each chair and each table Cost to rent each chair s Cost to rent each table s X S

A plant is already 14 00 meters tall and it will grow 25 centimeters every month The plant s height H in meters after x months is given by the following function H x 14 00 0 25x What is the plant s height after 15 months meters

Find the y intercept and x intercept of the line 3x 9y 10 y intercept x intercept 00 X 08 S

certain substance decomposes according to a continuous exponential decay model To begin an experiment the initial amount of the substance is 320 kg fter 5 hours 240 kg of the substance is left a Lett be the time in hours since the beginning of the experiment and let y be the amount of the substance in kg at time t Write a formula relating y to t Use exact expressions to fill in the missing parts of the formula Do not use approximations y 0 0 b How much of the substance is left 23 hours after the beginning of the experiment Do not round any intermediate computations and round your answer to the nearest whole number kg 00 X DinG 5

12 12x 29x 14 13 18x 14 122 15 4x 17x 4 16 12x2 8x 39 17 4x 23x 33 15x7 47x 40

240 50x 6 6x 7x 10 7 10x 37x 7 8 8x 30x27 9 30x2 31x 44 10 30x 103x 51 11 2x 17x 30

1 3x 4x 7 2 6x 5x 4 3 10x 59x 22 4 5x 32x 35

ROBLEM SOLVING A bag contains 12 movie tickets and 8 concert tickets You randomly choose 1 ticket and do not replace Then you randomly choose another ticket Find the probability that both events A and B will occur Round your answer to the hearest tenths place Event A The first ticket is a concert ticket Event B The second ticket is a concert ticket About

Dg Select one 12 18 31 Exponential Functions and Equations Question 3 The amount of money in Tomas s bank accoun follows the equation y 5000 1 1 where t is a unit of 2 years Which equation represents the approximate monthly interest rate 18 O y 5000 9 850 Z O y 5000 1 004 O y 5000 9 850 24 O y 5000 1 004 24t 24

NUMBER SENSE Events A and B are independent Let P B 0 4 and P A and B 0 13 Find P A Write your answer as a decimal rounded to the thousandths place D 1