Permutations and Combinations Questions and Answers

Use the following The Grad Committee at a particular high school is made up 5 of students and 4 teachers At the graduation ceremony the entire Grad Committee will be sitting on the stage in a single row of 9 chairs 21 How many different seating arrangements are possible if none of the students can sit beside each other 345600 mation to answer the next question 2880 360000

Credit score of students at Aritona State University has a normal diatribution The mean of the Credit Score of Arisona State Univernity Students is 750 and its rtandard deviation is 60 What proportion of Arizona State Ualversity Students have Credit Seores which more than 624 but less than 7687 44 66 50

Given f x 2x and g x 5x 1 find the following expression a fog 4 b gof 2 c fof 1 c fof 1 d gog 0 a fog 4 Simplify your answer b gof 2 Simplify your answer c f of 1 Simplify your answer d gog 0 Simplify your power

One measure of living standards in country A is given by the following formula L t 8 4e0 16t In this formula t is the number of years since 1982 Find L to the nearest hundredth for each year a 1989 b 1996 c 2005 a Find L for 1989 L 0 Round to the nearest hundredth as needed b Find L for 1996 L Round to the nearest hundredth as needed c Find L for 2005 L 0 Round to the nearest hundredth as needed

x y z 3 2x y z 11 x y z 7 The solution set is 0D Simplify your answer

Determine the correct partial fraction decomposition for Provide your answer below 2y 4y 7 2y 1 y2 2y 5

using a graph table and equation and describe the relat between each form using function notation 3 Determine whether each table represents a function Select Function or Not a Function for each Lesson 3 2 1 2 point Table X 2 y 5 3 y 2 X y XU X 1 7 y 4 11 23 2 7 3 6 8 2 4 9 22 8 35 73 10 11 3 12 8 7 12 3 1 12 Function 0 0 Not a Function 0

This exercise uses the radioactive delay model The half life of cesium 137 is 30 years Suppose we have a 14 g sample a Find a function m t mo2 h that models the mass remaining after t years m t b Find a function m t moet that models the mass remaining after t years Round your r value to four decimal pla m t c How much of the sample will remain after 72 years Round your answer to one decimal place d After how many years will only 3 g of the sample remain Round your answer to the nearest whole number

Applicat 4 Sketch the graph of a polynomial function f x that has a zero of order 3 a zero of order 2 two zeros of order 1 and a negative leading coefficient 12 marks a Determine a possible equation for f x in factored form www www www

Question 2 Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively i 1 ii 2 iii 0 5 4 3 iv 1 1 v vi 4 1 11 4 4 Answer i 1 1 4 Let the polynomial be ax bx c and its zeroes bea and B a B 1 b 4 a a 1 4 a If a 4 then b 1 c 4 4 C Therefore the quadratic polynomial is 4x x 4 ii 2 11 3 a Let the polynomial be ax bx c and its zeroes bea and B a B 3 2 b 3 a 1 3 a If a 3 then b 3 2 c 1

The confidence interval is given CI P 2x P 1 P n To construct a 95 confidence interual 2 1 96

Q 38 If for some real number a 4 is 1 18 2 14 3 0 4 16 limx o sin2x a sinx x3 exists Then value of a a

Write an equation and solve Salma is flying a kite It is 30 ft from her horizontally and it is 40 ft above her hand How long is the kite string 30 ft The kite string is 40 ft ft long 0 0 4

The accompanying data table lists measured amounts of chest compression mm from car crash tests Also shown are the SPSS results from analysis of variance Assume that we plan to use a 0 05 significance level to test the claim that the different car sizes have the same mean amount of chest compression Click here to view the table of chest deceleration measurements Click here to view the table of analysis of variance results What is the value of the test statistic The test statistic is Round to two decimal places as needed Chest Deceleration Measurements Small 31 29 28 Midsize 32 27 32 Large SUV 24 31 33 26 32 25 23 26 31 26 25 30 35 26 39 27 31 21 26 25 26 19 29 34 30 34 39 22 33 34 Print Done 34 26 34 20 22 22 26 24 31 35 29 26 CIL ANOVA results CHEST Sum of Squares 223 750 Between Groups Within 860 167 Groups Total 1083 917 df 3 44 47 ANOVA Mean Square 74 583 19 549 F 3 815 Sig 016 X

oblem 2 Referring to the same integral functional I u in the problem above the associated Euler Lagrange equation ca be written in the form h x u x h x u x 1 h x u x x u x Find the function h x

se mathematical induction to give a detailed proof that the formula is true for all natural numbers n our work should be legible and all your logic should be clear and justified 1 3 2 4 3 5 n n 2 n n 1 2n 7 6

A boat sails on a bearing of 75 for 134 miles and then turns and sails 220 miles on a bearing of 194 Find the distance of the boat from its starting point The distance is miles Round to the nearest integer as needed

When raising a monomial to a power the coefficient is number of the times the exponent indicates by itself the

The Archie Carr National Wildlife Refuge near Melbourne Beach was established to protect habitat at the most significant area for loggerhead sea turtle nesting in the world and the most significant area for green turtle nesting in North America Biologists working at the refuge need to estimate the clutch size number of eggs per nest for this year s loggerhead sea turtle nesting season A recent survey of 10 nests yielded the following data 16 11 Determine the point estimate and the sample standard deviation s for these data Round the solutions to four decimal places if necessary 11 125 113 119 94 100 96 99 120 117 121 An 80 confidence interval is given by Using an 80 confidence level determine the margin of error E and a 80 confidence interval for the average clutch size of loggerhead sea turtles at the Archie Carr National Wildlife Refuge this season Report the confidence interval using interval notation Round solutions to two decimal places if necessary The margin of error is given by E

Solve the following logarithmic equation using a calculator if necessary to evaluate the logarithm Write your answer as a fraction or round you answer to one decimal place In e 13 8

ve the following elementary exponential equation 4 4x 13 27 33 8

Solve the system of equations by elimination 8x 3y 6z 2 4x 9y 4z 18 12x 3y 8z 2

14 6 7 8 9 20 21 B 3 A 1 17 C 5 D 7

0 11 4 pi Write the order pair on the unit circle related to coterminal angle found Sin 8 Cos 0 tan 0 csc 0 sec 8 cot e

42 5 n n 1 n C A 5 B 6 C 7 D 8 E 9

ich is the equation for a line with a y intercept has a slope of 3 Oy 3x 2 Oy 3x 1 Oy 3x 7 Oy 3x 2

The behaviour of tides in a fishing community can be modelled using the function h 3 sin 30 t 4 5 where h represents the height of the tide in metres at t hours after midnight When will the tide will be 6m within 24 hours Note There may be more than one answer 5 marks

Use the method of elimination to solve the following system of equations If the system is dependent express the solution set in terms of one of the variables Leav fractional answers in fraction form Answer 2x 3y 5 10x15y 25 Selecting an option will display any text boxes needed to complete your answer Only One Solution 43 O Inconsistent System O Dependent System Ke Keyboard Sho

Half of your baseball card collection got wet and was ruined You bought 17 cards to replace some that were lost How many did you begin with if you now have 33

Submit Answer 5 Points DETAILS Let y 4x 5 x Find dy X BERRAPCALC7 3 R 064

Use synthetic division to divide f x x 7x 20x 96 by x 8 Use the result to find all zeros of f 8 3 4 8 3 4 8 3 4 8 3 4

16 x 2f x 2 x f x 2 x f x 2 flor g x the functions whose graphs are shown on the left and right respectively Click the image to enlarge Which of the following best describes the relationship between f and g

Divide the polynomials Express numbers using integers or simplified fractions Check your answer by multiplication 6x 5x x 8x 6 x DO

Solve for x Show all of your work log2 x 5 4

compound inequality 37 5z 7 23 equality and express your answer in int ical values

Determine the exponential regression of the data below using either a calculator or spreadsheet progra 25 4 19 22 12 38 9 48 4 58 2 67 Select the correct answer below O f x 107 819 1 117 O f x 107 819 1 117 Of x 107 819 1 117 O f x 107 819 1 117

factor the following polynomial function completely Use the Conjugate Roots Theorem if applicable x x6 6x4 31x 36 Answer 4 Points

Solve for x H Y 115 95 W H r 5 X

Select the correct answer below t ln 3 O t 2 ln O t 0 5 ln Ot 2ln 11 O t 0 5 ln

Decide whether the function is one to one y 2 x 3 7 Is the given function one to one O No Vos

Country C decides to reduce their 10 5 billion debt by a decay factor of 0 985 each year This can be modeled by the equation A 10 5 0 985 Estimate the debt after 8 years Round to the nearest hundredth and do not round until the final calculation Provide your answer below billion

You are considering a movie club membership The company charges 2 per movie that you buy each month plus a monthly membership fee of 12 If C represents the total cost of the membership in a month and M represents the number of movies you buy write an equation that represents the relationship between M and C Provide your answer below C M

Farley invests 9 300 into an account with a 1 6 interest rate that is compounded monthly How much money will be in this account after 3 years Round your answer to the nearest cent Do NOT round until you have calculated the final answer Provide your answer below

Sama has twice as many dimes as she has quarters and 17 more nickels than quarters She has in total 65 coins How many of each coin does she have How much money in dollars and cents is it worth it

9 The domain of f x is x 2 5 If the transformation f x 9 2 is applied then the new domain of the function is A 2 4 O A OB O C D B x2 2 C x 10 D x 12

4 Which graph has a domain of x 2 5 and a range of y 2 A B C O A C B D

Upper Bound for the Error Using Linear Approximation Suppose that f is a function such that f is bounded on some interval centered at x a that is there exist positive real numbers K and u such that f z K for all az in I a u a u Then for every ro I we have that Efa ro Lfa zo f xo Ko al e Use the upper bound for the error in linear approximation to find an interval of the form T 6 6 contained in I 1 1 guaranteeing that Ero zo 1 whenever zo T

1 4 12 20 28 84 A 484 B 492 C 500 D 508

A mutual fund manager wishes to purchase a property that s been valued at 1 5 million She has 200 000 in cash to use as a deposit and she will require a mortgage for the rest The annual interest rate on the loan is 2 45 and the loan is for 25 years Calculate the monthly payments Round your answer to the nearest cent Do NOT round until you have calculated the final answer Provide your answer below

When a raindrop falls it increases in size and so its mass at time t is a function of t namely m t The rate of growth of the mass is km t for some positive constant k When we apply Newton s law of motion to the raindrop we get mv gm where v is the velocity of the raindrop directed downward and t is the acceleration due to gravity The terminal velocity of the raindrop is lim v t t18 Find an expression for the terminal velocity in terms of g and k lim v t t18