Permutations and Combinations Questions and Answers

Solve the inequality x 14 5x 8 or x Enter

A pair of standard dice are rolled Find the probability of rolling a sum of 10 with these dice P D D 10 Be sure to reduce

Determine the domain of the variable x in the given expression x 13 X 10 Choose the correct domain below OA The domain is x x Use a comma to separate answers as needed B The domain is the set of all real numbers

0 3 A 1 0 10 se the graph to find a The numbers if any at which f has a local maximum What are these local maxima b The numbers if any at which f has a local minimum What are these local minima a Select the correct choice below and fill in any answer boxes within your choice A The value s of x at which f has a local maximum is are x Type an integer Use a comma to separate answers as needed OB There are no values of x at which f has a local maximum

In a popular online role playing game players can create detailed designs for their character s costumes or appearance Meena sets up a website where players can buy and sell these costumes online Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below 53 visitors purchased no costume 151 visitors purchased exactly one costume 22 visitors purchased more than one costume Based on these results express the probability that the next person will purchase exactly one costume as a percent to the nearest whole number

For f x x 1 and g x 1 6x find the following a fog x b gof x c f f x d f x f f x

For the given graph determine whether the line has a slope that is positive negative 0 or undefined a 10 SNect negative positive The slope S b 5 y 10 10 10 X

Of all the different permutations of the letters in the word STOP if you choose one at random what is the probability that it will start with the letter P Be sure and reduce your answer Enter

Let V be a finite dimensional and nonteivial vector space and S be a subspace of V show that if dim S dim V then S V

Oh x ln x 2 3 Oh x ln x 3 2 Oh x ln x 2 3 Oh x ln x 3 2 Question 20 Select the logarithmic equation after a vertical compression by a factor of 13 and a reflecti the y axis Oh x log x Of x log x log x g x

Identify key features of the graph of f x log5 Select all that apply 5 0 5 This image cannot be easily described If you need an explanation of this image please ask your teacher help 5 There is an x intercept at 1 0 and no y intercept The domain is and the range is 0 00 The domain is 0 and the range is 0 00 There is a horizontal asymptote at y 0 There is a y intercept at 0 1 and no x intercept The function is increasing There is a vertical asymptote at x 0 The function is decreasing

Kyle is using composition of functions to determine if these two functions are inverses of each other He does g f x Select the choice that shows what that would look like f x 6 1 g x log x 1 O f g x 6 log x Of g x 6log x 1 1 O f g x 6x 1 log x 1 Of g x log 6 1 1

L 0711 1 1 1 1 2 2 19 1 3 3 14 21

Find all the missing elements Round to the nearest tenth C B a A C b A B a 4 b 5 c 7 C

Find the slope and y intercept of the line Graph the line x 7 Select the correct choice below and if necessary fill in the answer box to complete your choice OA Slope Type an integer or a simplified fraction OB The slope is undefined

44 Which graph represents the following equation y x 1 A B C D 5 LO n

SEXY uplinjaneTi 38 Find the x intercepts of the function y x 3x 10 A 5 0 and 2 0 C 0 5 and 0 2 B 5 0 and 2 0 A 10 0 39 Find the y intercept of the function y x 3x 10 D the function has no x intercepts atinu hign 0 ander B 5 0 C 0 10 D 0 10

Solve by graphing and then select the correct number line 5 2 6 1 8 7 8 7 4 7 8 4 2 4 2 4 2

Solve and graph the answer on a number line x 6 4 7 O O O 6 0 0 6 12 12

Consider the number line below Select the two choices below that could be used to describe this number line if you were writing an absolute value inequality 8 7 6 5 or Ogreater than less than or equal to and less than greater than or equal to 3 2 1 0 1 2 3 4

Select the equation or inequality that could be represented by this number line 2 O 3 1 x O x 2 1 O x 4 3 C x 1 2 0 2 4 5

In Minecraft diamond ore can be found anywhere within 5 blocks of Y level 11 Complete the absolute value inequality to describe where diamond ore can be found Ox 5 11 Ox 5 11 Ox 11 5 Ox 11 5

Given the graph select the correct transformation of f x x 5 2 8 5 0 5 10 Of x x 8 2 Of x x 2 8 Of x x8 2 Of x x2 8 5 This image cannot be easily described If you need an explanation of this image please ask your teach for help

Let f 1 1 2 7 2 5 0 6 Find a f 1 and b f 2 a f 1

Let g x x x 4 Find and simplify g 2 The value of the function is Type an integer or a fraction

Determine whether the three points are collinear 0 4 3 9 2 0 Are the three points collinear O Yes No

For the point P 13 9 and Q 8 6 find the distance d P Q and the coordinates of the midpoint M of the segment PQ What is the distance Simplify your answer Type an exact answer using radicals as need

What is the length of AC Round to the nearest tenth 10 5 m O 12 3 m 18 3 m 21 4 m

X 60 4 N 30 Given right triangle XYZ what is the value of tan Y 01 1 201 2 3

Use tiles to find 29 28 57 1 56

Select the correct answer The Breaker s Manufacturing Company makes 80 of a particular sensor the Cartin Company makes 15 of them and the Flutes Company makes the other 5 The sensors made by Breaker s have a 4 defect rate the Cartin sensors have a 6 defect rate and the Flutes sensors have a 9 defect rate If a sensor is randomly selected from the general population of all sensors what is the probability that it is defective given that it was made by Breaker s A B 0 04 O D 0 05 C 0 15 0 80

Suppose the number of strawberries a plant produces is normally distributed with a mean of 15 and a standard deviation of 2 strawberries Find the probability a given plant produced between 15 and 19 strawberries Probability of between 15 and 17 was 34 Probability of between 17 and 19 was 13 5 9 2 35 11 13 5 34 13 15 P 34 17 13 5 19 2 35 Enter 21

6 9 D 12 15 18 21 Question 4 1 point To use the Cosine Law to solve for an unknown angle you must know a two sides and the angle opposite one of the sides b two angles and the side contained between the two angles c two sides and the angle contained between the two sides d all three sides e none of the above Question 5 1 point The vertex of the parabola defined by the equation y 5 x 2 4 is a 5 4 Ob 2 4 c 2 4 d 5 2 e none of the above Question 6 1 point The count

Find mBCD in circle A 61 60 A 2

22 Find AB D C 4 x B 5 x 6 A Find the measure of the line segment indicated Assume that lines which appear tangent are tangent

Line Segments about Circles Solve for x 10 X 7 6

The cost to produce x units of wire is C 10x 400 while the revenue is R 20x Find the interval where the product will at least break even Select the correct choice below and if necessary fill in the answer box to complete your choice OA The interval where the product will at least break even is in interval notation OB The product will never break even Type your answer

10x4 17x 3 0 The solution set is Simplify your answer including any radicals and i as needed Use integers or frac for any numbers in the expression Use a comma to separate answers as needed

Decide what values of the variable cannot possibly be solutions for the equation Do not solve 1 x 2 1 X 1 1 x x 2 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solutions cannot include Type an integer or a fraction Use a comma to separate answers as needed B There are no numbers that would have to be rejected as potential solutions

Find the product of the polynomials 12 3x 2x 5x 13 2x 5 x 7

Multiply 14 14 14 14 Simplify your answer Type your answer in the form a bi Type an exact answer L radicals as needed

Two sides of a triangle have the same length The third side measures 3 m less than twice the common length The perimeter of the triangle is 17 m What are the lengths of the three sides What is the length of the two sides that have the same length m

Solve the following formula for the specified variable B m s k for s Simplify your answer

Find the exact value without using a calculator log4 1 1024

Fill in each box below with an integer or a reduced fraction a log 4 2 can be written in the form 24 B where A and B b log 3125 5 can be written in the form 50 D where C and D

7 There are 10 yellow 5 blue 8 red and 7 green marbles in a bag A marble is chosen at random not replaced then another marble is chosen Find each probability 30 29 29 87 2 P yellow then green 10 10 3 3 3 9 33 7 b P both not red

Express as a single logarithm and simplify log36 log31 5 O a 1 b 0 c 2 d log 7 5

Solve for the x in the equation log2 x 2 log 2 x 1 4 a x 3 b x 2 O c x 2 3 d x 0

13 16 19 23 26 www 29 33 ww Listen Which of the following is the graph of the piecewise function C a L O a b Od 100 O d 100 1000 1000 7 C x C x 100 x s a 100 100 60 60 80 100 140 100 120 120 1 30 140 140 140 The 160

Derek and Tim run in a straight line Their positions d with respect to the starting point at t seconds are modelled by the following functions Derek d t A Tim d t t 8 t 1 At what time were Derek and Tim at the same position a t 5 seconds and t 2 seconds b t 5 seconds c t 2 seconds