Permutations and Combinations Questions and Answers

Points 0 of 1 A fair coin is tossed 2 times in succession The set of equally likely outcomes is HH HT TH TT Find the probability of getting a head on the first toss The probability of getting a head on the first toss is Type an integer or a simplified fraction

Solve the inequality algebraically x 6 X 3 The solution is

1 12 1 12 4 69 4 Simplify your answer Type a whole number or a fraction

Subtract and simplify 7 8 7 8 5 8 5 8 Simplify your answer Type a fraction

11 HW When the student wrote Determine whether the following statement makes sense or does not make sense and explain the reasoning 5 5 2 10 E 6 6 2 12 Choose the correct answer below Question 7 R2 2 117 fff9 the student is not changing the value of because the student is multiplying by 1 GREEN OA The statement does not make sense because the numerators of 12 5 6 10 and are greater than 1 HW Score 0 O Points 0 of 1 OB The statement makes sense because the student multiplied the numerator and denominator of 5 6 by the same nonzero number 2 5 10 and are less than the denominators 12 6 OC The statement makes sense because the numerators of OD The statement does not make sense because 5 10 and 6 12

Partner Practice 1 The price of an item was 500 one week and then decreases to 350 What was the percent decrease 500 350 C X X 100 X C 500

Analyze the graph of the function 2 x X 12 R x 2 x x 6 B There is no horizontal or oblique asymptote d Choose the correct graph for R x below O A 8 6 4 3 2 Q B 8 6 4 22 3 2 Q O C 8 6 13 2 Q Ly O D E

Suppose you attend a fundraiser where each person in attendance is given a ball each with a different number The balls are numbered 1 through x Each person in attendance 1 places his or her ball in an urn After dinner a ball is chosen at random from the urn The probability that your ball is selected is Therefore the probability that your ball is not X 1 chosen is 1 Graph 1 X A 1 Graph P x 1 P x 0 0 20 40 60 Q 1 using transformations 1 AY 0 20 40 60 Q 1 Ay 0 20 40 60 1 0 0 20 40 60 Comment on the likelihood of your ball not being chosen as x increases Choose the correct answer below O A The likelihood of your ball not being chosen decreases very quickly and approaches 0 as the number of attendees x increases O B The likelihood of your ball not being chosen increases very quickly and approaches 1 as the number of attendees x increases OC The likelihood of your ball not being chosen increases very quickly and approaches above 1 as the number of attendees x increases The lib ll Q

Analyze the graph of the function 3 x 27 H x 2 x 100 A x 10 10 Use a comma to separate answers as needed Type an integer or a fraction OB There is no vertical asymptote c What is the equation of the horizontal or oblique asymptote of H x Select the correct choice below any answer boxes within your choice O A y Simplify your answer OB There is no horizontal or oblique asymptote

The light vehicle market share in percent in a particular country for pickup trucks is shown in the graph Let x 0 represent 1995 x 4 represent 1999 and so on a Use the points on the graph to write equations for the line segments in the intervals 0 4 and 4 8 b Define this graph as a piecewise defined function f x Percent Ay Pickup Truck Market Share 45 43 0 424 41 39 37 35 33 31 1995 1997 4 39 7 8 32 1 1999 2001 2003 Year Q a The equation for the line segment in the interval 0 4 is y 0 675x 42 4 Simplify your answer Use integers or decimals for any numbers in the expression The equation for the line segment in the interval 4 8 is y Simplify your answer Use integers or decimals for any numbers in the expression

Step 3 Defining your variables 2 pts Identify your independent and dependent variables using appropriate symbols to state them Let the independent variable represents the time in years and the dependent variable represents the cost in dollars variable T time years Independen Dependent variable P Dollars Step 4 Average rate of Change 4 pts Compute the average rate of change per year of the cost over each time period Just fill in the result don t show the calculation X Time Line Price dollars Y 1970 0 20 1980 0 50 2003 2 00 2009 2 25 2013 2 50 2015 2 75 2009 2013 10159 Average rate of change XXXXXXXXXXXXX t 0 0 03 0 06 5 00 4 6 0 12 Do these values suggest a linear trend Explain Yes because the table shows a Positive trend Over time as well as the rate of approximately the same slupe Change Step 5 Linear Modeling 6 pts Assuming that the trend is linear generate a linear model To make the calculation easier rescale the time values for 2009 through 2015 in the above table Let 2009 be the year 0 y axis X ans P dollars 2 25 2 50 2 75 S

Solve the equation Check for possible extraneous solutions logg 8 log 3 1 O X 11 no solution x 6 x 3

Graph Mean Of Leaves 20 15 10 5 0 9 8 10 12

The Mars company says that before the introduction of purple yellow candies made up 20 of their plain M M s red another 20 and orange blue and green each made up 10 The rest were brown Complete parts a and b b Assume you have an infinite supply of M M s from which to draw Suppose you pick three M M s in a row 1 What is the probability that they are all brown 2 What is the probability that the third one is the first one that is blue 3 What is the probability that none are orange 4 What is the probability that at least one is red 1 The probability of picking three brown M M s is Type an integer or a decimal Do not round 2 The probability of the third one being the first blue one is Type an integer or a decimal Do not round 3 The probability that none are orange is Type an integer or a decimal Do not round 4 The probability of at least one red M M is Type an integer or a decimal Do not round Submit test

The solution set is MEIER Use a comma to separate answers as needed

For the series below a find the series radius and interval of convergence For what values of x does the series converge b absolutely c conditionally 49x D 1 Type a company my you awe Use eyes analyse expression OB The series converges only at x Type an integer or a simplified fraction C The series converges for all values of x b For what values of x does the series converge absolutely Select the correct choice below and if necessary fill in the answer box to complete your choice OA The series converges absolutely for Type a compound inequality Simplify your answer Use integers or fractions for any numbers in the expression OB The series converges absolutely at x Type an integer or a simplified fraction OC The series converges absolutely for all values of x c For what values of x does the series converge conditionally Select the correct choice below and if necessary fill in the answer box to complete your choice OA The series converges conditionally for Type a compound inequality Simplify your answer Use integers or fractions for any numbers in the expression OB The series converges conditionally at x Type an integer or a simplified fraction Use a comma to separate answers as needed OC There is no value of x for which the series converges condi

Consider the solid obtained by rotating the region bounded by the given curves about the specified line y x 1 y 0 x 6 about the x axis Set up an integral that can be used to determine the volume V of the solid v f 1 2x10 20 20 Jav dx X Find the volume of the solid 92 7 x 4

Simplify function cotx CSC x 1 cot x csc x 1 to a single trig 2cot x csc x 1 csc x Preview

Write an equation for the line parallel to g x 6x 4 and passing through the point 4 3 Write the answer in slope intercept form help equations

Francisco claimed that the equation x 8x 0 cannot be solved by the quadratic formula since there is no value for c Is he corre Select the correct choice below and if necessary fill in the answer box to complete your choice A He is incorrect because c OB He is correct

4 Jupiter weighs 1 898 000 000 000 tons If 1 0 ton is equal to 2000 lbs and 2 5 lbs equals 1 0 Couric How much does Jupiter weigh in Couric

Using complete sentences and correct mathematical terminology answer the following questions A gardener noticed a rainbow through the arch of the stream of water while he was watering his garden He wondered the height of the rainbow and decided he could use the stream of water to determine it The time t the water is in the air is measured in seconds and the water s height w t is measured in inches above the ground The function that represents this relationship is w t 4 9t 15t 23 1 Correctly interpret the following calculations within the context of the given scenario above i w 0 4 9 0 15 0 23 23 h ii a 4 9 b 15 15 2 4 9 2a C 23 1 53

Mazsolate Mean 82 Median 84 Mode 78 alculate the upper and lower boundary for possible outliers Press nach hotspot Label the corresponding number below with the data or calculation Veasure of Dreven Range 30 IQR 40 65 68 74 78 78 78 84 84 88 89 91 94 95 IQR Outliers Median 1 5

Five less than a number is less than or equal to 6 times the number What inequality can be written to represent this statement O O O O 5 n 6n 5 n 6n n n 5 6n 5 6n

Fill in the blanks to correctly complete the sentence below The graph of y sin is obtained by shifting the graph of y sin x unit s to the

m R x 1 2 f x h f x h 1 1 x h x h x x h x x h h simplify and rationalize the nur x x h h x x h x x h x x h h x x h x x h 1 x x h x x

Evaluate wi6 164

Simplest form 54

28 Evaluate 16 N w

2 Charlie would like to make at least 200 washing cars this summer He charges 10 per car Write an inequality to represent Charlie s goal amount use w for the number of cars washed Type a response

Annual revenue billions for the Boeing Corporation from 1990 to 2002 is given by R t 1 t 2 2 80 Annual revenue billions that Boeing made just from sales of its 737 airplane in the same period is given by A t 0 22 t 8 30 Note t 0 is January 1 1990 In what year and month was annual revenue excluding sales of 737s at a minimum March Xo November 1996 What was that minimum revenue in billion year 52 x 56 9 nearest 0 1 billion year

93 Construct a probability plot that will allow you to assess the plausibility of the lognormal distribution as a model for the rainfall data of Exercise 83 in Chapter 1 EXERCISE 83 FROM CHAPTER 1 83 Consider numerical observations x x It is frequently of interest to know whether the x s are at least approxi mately symmetrically distributed about some value If n is at least moderately large the extent of symmetry can be assessed from a stem and leaf display or histogram However if n is not very large such pictures are not par ticularly informative Consider the following alternative Let y denote the smallest x y the second smallest x and so on Then plot the following pairs as points on a two dimensional coordinate system y x X Y 1 X X y y 2 X X There are n 2 points when n is even and n 1 2 when n is odd a What does this plot look like when there is perfect symmetry in the data What does it look like when observations stretch out more above the median than below it a long upper tail b The accompanying data on rainfall acre feet from 26 seeded clouds is taken from the article A Bayesian Analysis of a Multiplicative Treatment Effect in Weather Modification Technometrics 1975 161 166 Construct the plot and comment on the extent of symmetry or nature of departure from symmetry 4 1 7 7 17 5 31 4 32 7 40 6 92 4 115 3 118 3 119 0 129 6 198 6 200 7 242 5 255 0 274 7 274 7 302 8 334 1 430 0 489 1 703 4 978 0 1656 0 1697 8 2745 6

8 10 of the students in the school play some sort of sport Out of the athletes 30 play more than one sport If there are 600 students in the school how many play exactly one sport

9 For a group project the members of the group have to read a 200 page book They split it up by chapter between the four members of the group If Martina reads 30 of the book how many pages do the other members of the group read

7 In a recent survey of some people 333 of them were women 432 of them were men and the remaining were children If 90 of the people surveyed are adults how many children took part in the survey

5 Jim bought strawberries and blueberries He froze 30 of the strawberries he purchased and 50 of the blueberries he purchased If he purchased 9 pound of strawberries and 12 pounds of blueberries how many total pounds of fruit did he freeze

4 40 people are asked whether they have a dog or a cat 12 respond that they have a cat only 6 respond that they have a dog only and 10 respond that they have both What percent of the people surveyed had neither a dog nor a cat

3 Melinda has red blue and black pens 10 of her pens are blue 30 are black and the rest are red If she has 15 black pens how many blue pens does she have

1 Leslie gets a check for 200 for a week of babysitting She spends 80 on concert tickets and spends the rest on a new outfit for the concert What percent of her money did she spend on clothes

all potential rational zeros x 5 7x 28 Which of the following choices lists all the potential O A 11 12 4 7 14 28 OB 1 2 4 OC 7 14 28 OD 0 11 12 4 7 14 28

Solve 4x 5y 13 for y

7 A bag of candy contains red and blue candy 40 of the candy is red If there are 20 pieces of red candy in the bag how many pieces of blue candy are in the bag

1 Language Acquisition Almost all humans acquire at least one language before the age of five Although people gain vocabulary throughout their lifetimes even young children are able to understand and produce complex sentences with complicated meanings How do children accomplish this remarkable feat in such a short amount of time Do adults learn language differently from children Linguistic researchers have long debated the answers to these questions but most agree that both nature and nurture are involved in language acquisition They disagree however about how much linguistic knowledge children have from birth and thus whether genetics or experience is more important in language acquisition How do the second and third paragraphs work together They present a scientific debate and then discuss what all linguists agree on They present a specific theory and then propose a novel study to prove it They present a general argument and then explain a specific theory They present a general arqument and then disprove a counterargument

X is a normally distributed random variable with mean 46 and standard deviation 12 What is the probability that X is between 21 and 71 Write your answer as a decimal rounded to the nearest thousandth

Identify the domain and range of y x 4 Domain Range x 0 x 0 x 4 x 4 y 0 y 0 H

Given the inequality 3r 2 r 4 23r 4x 9 state if the given graph is correct If not explain how you would change it 3 2 1 0

1 Describe the domain of the following functions Show all work a f x c E x e R x X g T x 1 1 2 x x 2 2t 1 et sin x b S x d C x f L x h N x 2 x x cos x log x x 2x 4 x In x 1

billions of dollars a Estimate the value of the country s exports in 2008 and 2022 b What is the doubling time for the value of the country s exports a The value of the country s exports in 2008 is 1 7 billion Simplify your answer Round to the nearest tenth as needed Do not include the symbol in your answer The value of the country s exports in 2022 is 3 1 billion Simplify your answer Round to the nearest tenth as needed Do not include the symbol in your answer b The doubling time is approximately years Simplify your answer Round to the nearest integer as needed be approxim

7 Simplify a 4 b 6 3 c 5 1 d e 8 4

Verify the identity 1 sin t 5 cos t 36 sin t cos t 36 cos t 1 sin t 5 cos t 36 sin t cos t 6 cos t 36 cos t cos t