Permutations and Combinations Questions and Answers

Consider the two functions below Function 1 f x g x 2x Function 2 h x h x x Which has a larger average rate of change from x 1 to x 0 Og x Oh x Neither because they both have an equal average rate of change over the interval

The function h x 3x 4 is graphed at the right What is the average rate of change for the function h x from x 0 to x 2 04 10 0 6 4 3 2 f h x 3 4 21 2 3 Asymptote y 4 S

30 Solve a 5 4x 3 5 c 2e x 13 b 64 4 x 16 d e x ex 6 0

Compute 6 28 10 8 30 10 Express your answer to three digits View Available Hint s Hint 1 How to approach the problem 10 OP 9 20 1011 1013

43 50 Difference Quotient Find f a f a h and the f a h f a difference quotient where h 0 h f a 3a 2 44 f x 3x 2

3 Divide using synthetic division Express the answer as 3x 2x x 4 x 1 r x 1 x q x d x

Find the zeros of the polynomial by following the steps below Make a list of the POSSIBLE RATIONAL ZEROS From the list above pick a value and use synthetic division to check if indeed it IS a zero Rewrite in Factor Form and repeat process with NEW POLYNOMIAL f x 2x 7x 10x 24 The polynomial can have at most The zeros of the polynomial are

me evel 4 D Determine the height of tower in m corred to one decimal place to most sob 895 m

you would like to have 72000 available in 15 years There are two options Account A has a rate of 5 5 compounded once a year Account B has a rate of 5 compounded daily How much would you have to deposit in each account to reach your goal

Find the center and radius of the circle Write the standard form of the equation The center of the circle is h k Type an ordered pair The radius of the circle is r irelo in standard form is 2 Ay 6 3 0 3 2

Find an equation of the line L

2 Given parallelogram XYZW X 2m 8 Y X 1 W 3m 1 Z a Find x b Find m 5m 2

Graph the set xx 5 on the number line Then write the set using interval notation 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 X

Using the table write the given traditional Chinese numeral as a Hindu Arabic numeral A 1 B 2 3 4 5 6 t At 3 7 7 8 9 10 100 1000 0 PRO

1 6 5 4 3 2 1 f 5 4 3 2 f x graphs 1 g x f g 5 a a 1 g f 2 f f 4 1 2 3 2 3 4 5 5 X X expre

The final questions relate to this parallelogram mA 35 AB 30in AD 65in Remember that diagonals of a parallelogram are bisectors not perpendicular unless it is a rhombus opposite sides like A and C of a parallelogram are congruent 30 mZB Type a response 31 mZA mZB mZC mZD Type a response FERRED U

4 In each expression what cancels if anything 8 5m 8 a b C d 5m m 5 8 5m 5m 8 m 5 5m

Find the logarithm log4 64

The area of a rectangle is 20ab7 8a b 6ab The length of one side of the rectangle is 2a b a What is the length of the other side of the rectangle 2 marks

The movement of the progress may answer Solve x 20x O x 4 5 10 O x 10 4 5 O x 10 80 O x 20 10 80

nswer Which of the following radical expressions has an absolute value symbol in its simplified form O 16x 32x5 O O 64x6 8x O

points Consider the functions f x x 2 g x 3x What is the value of f g 2 8 10 12 14 Question 2 22 points If f x x 5and g x x Find f g 8 50 4

If f x 2x 1 and g x x Find g f 3 049 19 7 13

A student is trying to use long division at the right to solve the following 3x3 4x2 x 1 x 1 What value should go in the box next 3x x 1 3x 4x x 1 3x 3x O 2x 2x O 7x 7x 7x x

M x 33 K 2x 12 L Solve for x Then use that value of x to find JK 25 Use you answer for x to find JK The length JK A Type a response

J14 2x 0 M 5x 7 Solve for x Then use that value of x to find JK 22 Solve for x Type a response

Radar Detectors Radar detectors are either powered by their own battery or plug into the cigarette lighter socket All radar detectors come in three models no frills standard and fancy In addition detectors powered by their own batteries detect either radar or laser or both whereas the plug in types come in models that detect either radar or laser but not both How many different radar detectors can you buy choices

In a class of students the following data table summarizes how many students passed a test and complete the homework due the day of the test What is the probability that a student chosen randomly from the class did not complete the homework Completed the homework Passed the test Failed the test 11 7

Let f x 2 and g x x 1 find a fog x b gof x c fog 3 d gof 3

7 2 10l 23 8 7 10 24 8 9 31 25 5 91 7 51

A bacteria culture initially contains 2500 bacteria and doubles every half hour Find the size of the baterial population after 100 minutes Find the size of the baterial population after 8 hours

At the beginning of an experiment a scientist has 312 grams of radioactive goo After 90 minutes her sample has decayed to 19 5 grams What is the half life of the goo in minutes Find a formula for G t the amount of goo remaining at time t G t How many grams of goo will remain after 59 minutes

The number of bacteria in a culture is given by the function n t 1000g0 15t where t is measured in hours a What is the relative rate of growth of this bacterium population Your answer is 15 b What is the initial population of the culture at t 0 Of percent Your answer is 1000 OF c How many bacteria will the culture contain at time t 5 Your answer is 2080

BUHARLAN CANTARE montre LENN Solve the following rational inequality PRESO 2 2 72 9 State your answer using interval notation Use U for union and oo for oo 12027700 OFFRES EMAMANERALN ENTRA TAKEN TO OUTE CRED WHEBBEN 0 PRO MENPITEKEEN EFENDER UMAHAN TE WASHER M MANTELORANT HOMEPA ANTOREN WEEK BUT

answer Which of the relations given by the following sets of ordered pairs is a function O 5 4 4 3 3 2 4 5 2 1 O 2 4 2 6 2 8 2 10 2 12 O 0 3 6 8 3 5 0 3 7 11 O 8 1 4 1 3 5 0 4 1 2

long division See Example 1 2 3x 14x 5 x 5 4 7x x x x 1 C 10x3 5x 1 2x 4x x 2 8 0 5x4 5x 1 x 3x 2 n See Examples 2 and 3 10 4x 13x 5 x 2 12 x 1 x 14 2x3 5x 8x 15 x 3 16 x4 4x 16x 35 x 5 expressions Justify your answers 19 x x 3 x 2

x 2 x 1 1 4x x 2x 3 3x 0 8 x x 1 x 2 3 4 7x x x x 1 ivide using synthetic division See Examples 2 and 3 x 4 x 20 x 5 6 10x 5x2 1 2x 4x x 2 8 0 5x 5x 1 x 3x 2 10 4x 13x 5 x 2 12 x 1 x 14 2x 5x 8x 15 x 3 16 x4 4x 16x 35 x 5 GES

Find the quotient and remainder using synthetic division The quotient is The remainder is 24 8x 43x 8 x 3

Find the quotient and remainder using long division for The quotient is The remainder is I 5x 12 x 3

Cost Revenue Profit For these problems will represent the number of items and y will represent the money The fixed costs for a certain item are 220 per week The cost to produce each item is 15 per item Using this information what is the cost equation Give your answer in slope intercept form y The retailer intends to sell each item for 20 item Using this information what is the revenue equation Give your answer in slope intercept form y If in this week 49 items are made and all items are sold in the week what are the total costs to the retailer 4 Cost S What is the revenue from selling 49 items Revenue S Finally what is the profit for this retailer Profit S Box 1 2 Enter your answer as an expression Example 3x 2 1 x 5 a b c

11 You rent an 8 passenger van for a week to transport 8 people to a convention in a city 1 240 miles away The rate is 399 00 a week with 1 500 free miles and 0 25 per additional mile The CDW fee is 165 00 for the week and the estimated gasoline cost is 600 00 Determine the round trip cost a for total rental b per mile and c per person

Graph each function f x 12 4 X 2 4 3 2 1 6 X

Which investment would be worth the most after 15 years An initial investment of 5000 compounded semi annually at a rate of 6 after 15 years An initial investment of 5000 compounded quarterly at a rate of 5 9 after 15 years An initial investment of 5000 compounded continuously at a rate of 5 8 after 15 years Question 5 3 6 points Consider the function h x 4x 2 Determine the asymptote for the function h x Oy 1 Oy 2 09 3 0 4 Question 6 3 6 points Which function below has a range of f x 4 f x 4 f x 2 4 f x 4 2 3

Use the quadratic formula a quadratic equation 2 x 4 0 3 0 O 3 X 0 T 1ti 15 1 17 1 17 2 1 iv 15 2 b b 4ac 20 to find the solution to the following

Solve the following equation for x log2 x log3 2 2 In the blank list the solution to this problem just the number only Question 4 15 points Solve the following equation for x log 2x 7 3 In the

Solve the equation 5 2 7 28 0 108 X 2 XN 6 201 Ox 21 Question 4 15 points Solve the following equation for x e 1 494 In the blank list the approximate solution to this problem to one decimal pla the number only e g if the answer was 6 524 you would just put 6 5

Simplify each expression write your answer with positive exponents only 24x 6x3 24y7 6x 16x y22 16y22 01 Question 2 20 points Simplify 3 2 18x

Identify the asymptotes domain and range o f x 5 X 2 f x 4 2 20 2

Let f x 2 1 If g x is the graph of f x shifted down 1 units and left 2 units write a formula for g x g x Enter as sqrt x

If 85 is added to a number the result is 45 less than three times the number Find the number