Permutations and Combinations Questions and Answers

A bag contains 36 red blocks 48 green blocks 22 yellow blocks and 19 purple blocks You pick one block from the bag at random Find the theoretical probability Write your answer as a fraction in simplest form in the form a b P green or yellow

8 Suppose is the function given by f x 2 4x 3 Determine 30

Which sampling method puts the population into groups and then only selects sample members from a few of the groups Answer by typing the letter in front of each word Do not type the word A Stratified B Systematic C Simple Random D Cluster

Part 1 of 3 A study shows that water usage is normally distributed with an average shower using 17 8 gal with a standard deviation of 2 3 gal Find each 1 decimal answer The percent of showers that use between 10 9 and 24 7 gal Part 2 of 3 010 X The percent of showers that use more than 22 4 gal OC 15

Consider the following planes 5x y z 5 15x 3y 5z 25 e Find the engle in degrees between the two planes Round your answer to two decimal places 45 25 X b Find a set of parametric equations for the line of intersection of the planes Use t for the parameter Enter your answers as a comma separated list of equ x y 5 5z 5

15 through 4 4 and 0 3 17 through 2 4 and 1 3 16 through 0 4 and 1 4 18 through 0 4 and 0 1

5 Let X be the set of all different nine letter words that can be obtained by permuting the letters of the word AAABBCCCE How many elements does X contain In how many elements of X there are no neighbouring vowels terminology A E are vowel letters while B C are consonant letters

A homogenous system with two equations and three variables must hav infinitely many solutions Select one Of False

let W x x 1 x1 x2 are real numbers then W a subspace of R3 Select one O True

find value values of m will the system be inconsistent mx 1 m y 1 1 m x my 3 Select one O a m 1 2 b m 2 c m 1 2 d m 1

Find m G 3x 2 K H

What is the shortest interval in which a periodic function will complete one cycle Ob a period A C a B bd a wavelength c Question 21 1 point an action d an event b a Given triangle ABC above if DA 38 and b 4 47 cm determine a to the nearest hundredth a 5 67 cm b 7 26 cm c 3 52 cm d 2 75 cm

Use the Y screen to write the equation being solved Then use the table to solv Plot1 Plot2 Plot3 X Y Yt 2 X 3 Y2 2 3 2X Y3 AY4 Y5 Y6 Y7 O C 2 X 3 2 3 2X 2 O D 2 X 3 0 and 2 3 2X 0 OE 2 X 3 2 3 2X 3 OF 2 X 3 2 3 2X 0 O G 2 X 3 2 3 2X 3 2 1 3 X 3 12 10 8 6 4 110 Y 2 Part 1 of 2 18 14 10 840 6 2 6

Identify Types Of Slope Worksheet 4 What type of slope does the line on the graph below have K E EL14 14 13 T TE 30 13 14 O Positive slope O Zero Slope O Negative slope

1 2023 Kuta Software LLC All rights reserved Solving Quadratics a 1 Solve each equation by factoring 1 7x 3x 0 A 4 27 8 7 C 1 55 7n 52n 21 9 3 3 3p 14p 27 3 A 2 7 6 B A 7 9 12 8 C 7 3n 2n A B C D 4 D B D B D 9 29n 52n 32 8n A B 131 D 37 43 3 48 2 4 6 8 10 2 3b 206 32 0 A C 4 5x 27x 31 3 A B 6 2p 15p 18 A 1 1 C D 5 B D B 7 1 3 8 8 9x 45x28 2x A D 3 5 B B D D 225 6 3 7 25 10 a 7a 25 5 3a A 4 4 6 5 6

Let v 1 3 0 6 2 Then there exists a vector w such that w 1 and v 1 v w and there exists a vector u such that u 1 1 and v v u Then w 5 and u 4 The number of different w that do the above trick is Note If the number is infinite write X in the space and the number of different u that do the trick is

Part 1 of 2 Rewrite the function to make it easy to graph using transformations of its parent function Describe the graph y 25x 75 y Simplify your answer C

Create a new post where you analyze two functions over an interval a Create two functions using the following guidelines 1 one is represented as an equation one as a table ii key features including intercepts maxima minimum and average rates of change can be found from the functions you create iii the functions must be quadratic exponential radical or cubic functions b Choose an interval over which to analyze and compare the two functions 1 State the interval you are using ii Compare the intercepts of the two functions lii Compare the maxima and minima of the two functions iv Compare the average rates of change of the two functions 2 Choose another student s functions to review Comment on whether you think the student s comparisons are correct Be sure to include calculations or other reasoning to support your answer

Lucas is walking on a circular path modeled by the equation x 6 2 y 5 2 36 and Neal is walking on another circular path modeled by the equation x 9 2 y 5 81 where their distances are given in meters What is the maximum distance between the walkers at any given time O 15 meters 20 meters 25 meters O 30 meters

How many distinct four digit numbers can be formed by the digits 1 2 3 4 5 5 5 8 6 Select one DOO a 560 b 840 C 360 d 606 e 280 f 486 9 650

if X 30 100 j 1 then the sample mean will be Select one a 40 b 60 0000 c 30 d 50

The value of Correlation Coefficient od values 5 Select one O a 0 80 b 0 92 d 0 904 3 14

if the following table is the probability distribution of random variable X X 0 1 P X X 0 1 Then the mean of X i e E X is Select one 2 0 4 b 4 75 C 1 85 3 0 25 4 0 05

6 x 16x 60

A phone company charges its customers 50 or the first 500 minutes used each month For any additional minutes used over the 500 the customer is charged an additional 10 per minute Find the piecewise function that describes this situation O 50 1m m 500 m 500 O f x f x f x 50 f x 50 50 1m 50 50 m 500 m 500 50 1 m500 f50 1 m 500 m 500 m 500 m 500 m 500

Given a normal distribution with mean 90 and standard deviation 20 use the 68 95 99 7 Rule or 34 13 5 2 35 0 15 to find the percent of the population for each of the following Less than 90 Above 150 Less than 70 Above 50 Between 70 and 130 What z score would be associated with a data value of 40

X X 2 According to a poll 56 of voters are likely to vote for the incumbent The poll has a 3 margin of error The margin of error means that the difference between the actual percent of voters and the percent determined by the poll is 3 Write and solve an absolute value equation to find the least and the greatest percent of voters X likely to vote for the incumbent a The absolute value equation that represents this situation is your answer Write your response here b Solve the equation Based on the equation there can be between Type your answer here Type your answer here A of voters that vote for the incumbent Do not enter any spaces in and Open in Reading View

x 1 2 X Type a response Solve each equation and check your solution 130 1

Here is a table and a graph that show the number of coffee shops worldwide that the company Coffee Brew had in its first 10 years between 1987 and 1997 The growth in the number of Poimebige eritio enthe growth in the number of stores was roughly exponential F number of coffee shops 1 000 500 5 years since 1987 V signes 10 Snch Cup 193 year 1987 1988 1989 1990 1991 1992 1993 36 stres 1994 1995 1996 1997 Part I Find the average rate of change for each period of time Show your reasoning 1987 and 1990 1987 and 1993 number of stores wom 17 33 55 84 116 165 272 425 677 1015 1412 36 Stors 1987 and 1997 126 41795 Make some observations about the rates of change you calculated by comparing each period of time

What are the domain and range of the function f x OD X E R x 4 R y R y 0 OD x R x 4 R y e R y 2 E OD x R x 4 R y e R y 2 OD x ER x 2 R y R y 0 E x 6x 8 x 4

Find the volume of the prism by counting the number of unit cubes

Give the dimensions of the different rectangular prisms that can be constructed using exactly 8 unit cubes Select all that apply 8 by 8 by 8 4 by 8 by 4 1 by 8 by 8 1 by 2 by 4 1 by 1 by 1 2 by 2 by 2 1 by 1 by 8 What is the volume of each prism 3

Answer saved Marked out of 1 00 Price of bond has a a Can t decide b Positive Oc Negative O d No relation Clear my choice relation with the maturity

2x 5y 15 a Find the slope and y intercept if possible of the equation of the line algebraically Use a graphing utility to verify you answer If an answer is undefined enter UNDEFINED Enter NONE if there is no y intercept slope 2 5 y intercept x y b Sketch the line by hand Use a graphing utility to verify your answer S No Solution 0 3 10 9 8 7 6 10 9 8 7 6 5 13 1 4 2 3 4 5 6 7 8 2 6 7 8 9 10 Clear All Delete Fill Graph Layers Line 1 Point 1 Point 2

to each following statements Explain A Street adresses are a a zip code B 10g x 3 105x 1093 C false The function function function of 9 cx 2 is an odd d the graph of the function f x 8x bx where b c and d are real humbers may have 9x Intercepts cx d an e The function h x 2x 3 has oblique Slant asymptote SX 4 fe The circle x 9 4 25 has 5 cente at the point 0 4 and a radius of 5

Work required Determine the polynomial function whose graph passes through the following points 2 5 3 2 4 5 If you do not need a term in your answer enter zero as the coefficient in the blank provided p z 2 4 x X

check your solution 3x 4 x 10

3 1 A tension test was performed on a steel specimen having an original diameter of 0 503 in and gage length of 2 00 in The data is listed in the table Plot the stress strain diagram and determine approximately the modulus of elasticity the yield stress the ultimate stress and the fracture stress Use a scale of 1 in 20 ksi and 1 in 0 05 in in Redraw the elastic region using the same stress scale but a strain scale of 1 in 0 001 in in Load kip Elongation in 0 0 1 50 0 0005 4 60 0 0015 8 00 0 0025 11 00 0 0035 11 80 0 0050 11 80 12 00 16 60 20 00 21 50 19 50 18 50 0 0080 0 0200 0 0400 0 1000 0 2800 0 4000 0 4600

Lauren is going to a carnival that has games and rides Each game costs 2 and each ride costs 4 75 Lauren spent 50 altogether at the carnival and the number of rides she went on is 2 more than the number of games she played Write a system of equations that could be used to determine the number of games Lauren played and the number of rides Lauren went on Define the variables that you use to write the system

7 The path that a football takes can be described by the equation h in meters of the football at time t in seconds a Graph the function b What does the y intercept represent c What does the x intercept represent 16t 1024 can be used 8 The equation h t to determine h the height of a ball dropped from a level of 1024 feet for any time t measured in seconds How long will it take the ball to hit the ground a 8 seconds c 64 seconds b 8 seconds d 1024 seconds 10 The graph of quadratic function g is shown on the grid to the right The coordinates of the x intercepts the y intercept and the vertex are integers What is the maximum value of g Range d How high is the football after 3 seconds e After how many seconds will the ball be at least 20 meters high f About what time does the football hit the ground g Domain a 40 mph c 60 mph 10 y 35 5 30 5 25 10 20 15 10 9 The equation below represents d the stopping distance in feet of a car and s the speed of the care in miles per hour 5 What is the speed of the car if the stopping distance is 120 feet 25t 0 10 5t where his the height d 0 05s s b 50mph d 70 mph 5 5 10 X

Simplify 1 13 13 A 2 13 C 4 13 3 1 54 2 6 3 27 B 5 13 D 3 13 A 4 6 9 3 6 9 3 B C 6 6 D 4 6 55 2 2 2 2 A 2 2 C 8 V 8 2 B 4 v D 6V 6 2 7 3 2 3 2 2 3 A 6 2 2 3 B 9 2 2 3 C 9 2 2 3 D 9 2 9 9 12 8 12 7 22 12 6 A 52 3 7 22 12 6 B 34 3 7 22 12 6 C 52 3 D 52 3 12 6 2 4 6 8 10 2 2 3 18 A 0 C 9 2 4 2 2 54 3 3 2 3 A 6 6 6 3 B 6 6 8 3 C 6 6 5 3 D 6 6 7 3 6 2 3 3 A 2 3 C 4 3 B 11 2 D 10 2 8 B 0 D 3 2 6 2 3 2 3 A 2 6 8 3 B 2 6 2 3 C 2 6 6 3 D 2 6 4 3 10 2 17 4 17 11 12 5 A 6 17 11 12 5 B 11 12 5 C 2 17 11 12 5 D V 11 24 5

Solve the equations and check your solution It is possible to have NO SOLUTION 3 1 x 10 4 Type a response 15 5 2

Find the volume of the composite solid which has a square base 6 1 11 6

Type your answers in all of the blanks and submit X X 22 In blank a enter conditional equation contradiction or identity In blank b enter the numerical solution all real numbers or no solution 3 2x 1 2 3x 2 a The equation is a n Write your response here b Solution Write your response here

1 Addition and multiplication properties of equality Homework Unanswered Due Today 11 59 PM Fill in the Blanks Type your answers in all of the blanks and submit X X Q To solve the equation x 7 5 we must add The resulting equation is X Type your answer here Type your answer here The solution set of the equation is Write your response here to each side of the equation Enter the answer using solution set notation The

Select all equations that are linear equations i Multiple answers Multiple answers are accepted for this question 5 Determine which equations are linear Homework Unanswered Due Today 11 59 PM Select one or more answers and submit For keyboard navigation SHOW MORE a C d 5I5 X X5 1 1 T 3 2x 3 2x x 3 4 x 2 x 2 3

Select the equation that results after simplifying the left side of the equation 4 3 2x x 3 6 Select an answer and submit For keyboard navigation use the up down arrow keys to select an answer DJ b 9x 15 6 C 9x 9 6 d 7x 9 6 7x 15 6

Factoring A Sum Difference of Cubes Factor each completely 1 x 125 as x bc5 3 x 64 X 5 5X 25 example 5 x 27 7 1 a 9 x 27 11 8x 27 Name 2 a 64 4 u 8 6 125 x 8 a 125 10 x 1 12 27u 125 Date

ion has a minimum value of of t is the horizontal translati ollowing graph is a translation 21 8x 8x 21 59x Date lem Solving C on f x 2 x 3 4 Complete 2 The dratic Functions 19 7x 2x 0 17 7 7k 6k 3 3 Class 15 3r 16r 7 5 13 4k 8k 3 3 5K

Question 1 6 Which of the following expressions is a factor of 2y 11y 5 O 2y 1 O2y 5 O 5y 1 o 2y 10