(15 points) Suppose R is a relation on a set A={1,2,3,4,5,6} such that (1,2),(2,1),(1,3)∈R. Determine if the following properties hold for R. Justify your answer. a) Reflexive b) Symmetric c) Transitive 8. (6 points) A group contains 19 firefighters and 16 police officers. a) In how many ways can 12 individuals from this group be chosen for a committee? b) In how many ways can a president, vice president, and secretary be chosen from this group such that all three are police officers? 9. (6 points) A group contains k men and k women, where k is a positive integer. How many ways are there to arrange these people in a
Answers
9. the number of ways to arrange k men and k women in a group is (2k)!.
a) To determine if the relation R is reflexive, we need to check if (a, a) ∈ R for all elements a ∈ A.
In this case, the relation R does not contain any pairs of the form (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), or (6, 6). Therefore, (a, a) ∈ R is not true for all elements a ∈ A, and thus the relation R is not reflexive.
b) To determine if the relation R is symmetric, we need to check if whenever (a, b) ∈ R, then (b, a) ∈ R.
In this case, we have (1, 2) and (2, 1) ∈ R, but we don't have (2, 1) ∈ R. Therefore, the relation R is not symmetric.
c) To determine if the relation R is transitive, we need to check if whenever (a, b) ∈ R and (b, c) ∈ R, then (a, c) ∈ R.
In this case, we have (1, 2) and (2, 1) ∈ R, but we don't have (1, 1) ∈ R. Therefore, the relation R is not transitive.
To summarize:
a) The relation R is not reflexive.
b) The relation R is not symmetric.
c) The relation R is not transitive.
8. a) To choose 12 individuals from a group of 19 firefighters and 16 police officers, we can use the combination formula. The number of ways to choose 12 individuals from a group of 35 individuals is given by:
C(35, 12) = 35! / (12!(35-12)!)
Simplifying the expression, we find:
C(35, 12) = 35! / (12!23!)
b) To choose a president, vice president, and secretary from the group of 16 police officers, we can use the permutation formula. The number of ways to choose these three positions is given by:
P(16, 3) = 16! / (16-3)!
Simplifying the expression, we find:
P(16, 3) = 16! / 13!
9. To arrange k men and k women in a group, we can consider them as separate entities. The total number of people is 2k.
The number of ways to arrange 2k people is given by the factorial of 2k:
(2k)!
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Related Questions
What are the 5 algebraic properties of equality?
Answers
The five algebraic properties of equality are: Reflexive, Symmetric, Transitive, Addition, and Multiplication properties
Reflexive property: For any real number a, a = a.Symmetric property: For any real numbers a and b, if a = b, then b = a.Transitive property: For any real numbers a, b, and c, if a = b and b = c, then a = c.Addition property of equality: For any real numbers a, b, and c, if a = b, then a + c = b + c.Multiplication property of equality: For any real numbers a, b, and c, if a = b, then a * c = b * c.These properties are the foundation of algebraic manipulation and are used to solve equations and simplify expressions.
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Pls help me !!!!!!!!!!
Answers
Answer:
1. (a+b)²/a.b/(a+b)(a-b)
Find the zero of the linear function by graphing f(x)=2x+3 and verify your answer algebraically
Answers
Answer:
(-1.5, 0) or -1.5
Step-by-step explanation:
The answer if -1.5 because the line hits the x-axis one time and hits it at the point of -1.5. The slope of the line is 2 and the y-intercept is 3, when graphed, you should also see when the line hits the x-axis
10TH GRADE MATH PROBLEM
Please answer: What is m∠KNL?
Answers
Answer:
74
Step-by-step explanation:
5x+2=3x+42
2x+2=42
2x=40
x=20
3(20)+14=74
How many digits will be in the quotient?
39 4,641
Answers
Answer:
the answer is 119 so three digits
Step-by-step explanation:
Answer:
3 digits
Step-by-step explanation:
4641/39=119
Determine the limit. limx→1(x−1)29−x
Answers
The limit of the expression as x approaches 1 is 1/28.
To determine the limit of the expression as x approaches 1, we can simplify it algebraically.
Given expression: (x - 1)/(29 - x)
Let's factor out a negative sign from the denominator to make it easier to work with: (x - 1)/(-(x - 29))
Now, we can cancel out the common factor of (x - 1) in the numerator and denominator: -1/(x - 29)
As x approaches 1, the expression (x - 29) approaches (1 - 29) = -28. Therefore, the limit is: limx→1 (x - 1)/(29 - x) = -1/(-28) = 1/28
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Economic growth typically results in rising standards of living and prosperity. However, it also invites negative externalities such as environmental degradation due to over- exploiting of natural resources. As such, the world is confronted with the dilemma of growth versus environmental sustainability. Developing a model explaining the disparity of economic development concentrating on drivers such as tourism sustainability, technological innovation and the quality of leadership would be important not only to facilitate future economic growth in developing countries, but also to the environmental and sociocultural sustainability which ultimately lead to global sustainable development. The present research objective is to develop and test framework of sustainable development by considering the elements of tourism, technological innovation, and national leadership. This further would facilitate growth, environmental and socio-cultural sustainability. Understanding the integration of these dimensions would enable the building of a Sustainable Development Framework (SDF) that would provide better insight in promoting the SDGS agenda. Ultimately, growth and environmental sustainability can be achieved which will benefit the society, the economy, and nations and of course for future sustainable policy recommendation. Based on the issue above, you are required to propose relevant econometric approaches with the aims to test sustainable development by considering the elements of tourism, technological innovation, and national leadership. Question 1 [10 marks] [CLO2] Based on the scenario above, a. Propose an appropriate model specification based on the scenario above. [4 marks] used in the [4 marks] [2 marks] b. Justify the selection of the dependent and independent variables model. c. Justify the selection of the sample period.
Answers
According to the given information, the sample period should be from 2010-2020.
a) Model specification
The model specification based on the scenario above is as follows:
SDF= f(T, TI, NL)
Where: SDF= Sustainable Development Framework
T= Tourism
TI= Technological innovation
NL= National leadership
b) Justification for the selection of the dependent and independent variables model:
Dependent variable: The dependent variable in this model is Sustainable Development Framework (SDF). The model seeks to develop a framework for sustainable development that would facilitate growth, environmental and socio-cultural sustainability.
Independent variables:
The independent variables are tourism sustainability, technological innovation, and quality of leadership. These variables drive economic development. The inclusion of tourism sustainability reflects its importance in the global economy and its potential to drive growth.
The inclusion of technological innovation reflects its potential to enhance productivity and create new industries. The inclusion of national leadership reflects the role of governance in promoting sustainable development and managing negative externalities.
c) Justification for the selection of the sample period:
The sample period should be selected based on the availability of data for the variables of interest. Ideally, the period should be long enough to capture trends and patterns in the data. However, it should not be too long that the data becomes obsolete or no longer relevant.
Additionally, the period should also reflect the context and relevance of the research question. Therefore, the sample period for this study should cover the last decade to capture the trends and patterns in the data and reflect the relevance of the research question.
The sample period should be from 2010-2020.
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Gianna buys ice cream and onions at the store.
• She pays a total of $27.97.
She pays a total of $4.17 for the ice cream.
• She buys 7 bags of onions that each cost the same amount.
How much does each bag of onions cost?
Answers
Answer:
$3.40
Step-by-step explanation:
\(27.97 - 4.17\)
\(23.8\)
and
\(23.8 \div 7\)
\(3.40\)
to check your answer you will need to times 3.40 with 7
\(3.40 \times 7\)
\(23.8\)
coach mac finds a new practice court for the basketball team. if the width of the rectangular lot is 16 feet less than the length, and the perimeter is 160 feet, what are the dimensions of the new practice court?
perimeter of rectangle = 2W + 2L
first complete these equations: 160 = ?W + ? L ; W = L - ?
Answers
The dimensions of the new practice court is 45.5 feet by 29.5 feet.
The equations should be completed as 160 = 2W + 2L; W = L - 16
How to calculate the perimeter of a rectangle?Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;
P = 2(L + W) or P = 2L + 2W
Where:
P represents the perimeter of a rectangle.L represents the length of a rectangle.W represents the width of a rectangle.Since the width of the rectangular lot is 16 feet less than the length, we have:
W = L - 16
Substituting the given parameters into the perimeter formula, we have;
160 = 2L + 2W
160 = 2(L - 16) + 2L
160 = 2L - 32 + 2L
160 = 4L - 32
4L = 182
L = 45.5 feet.
For the width, we have:
W = L - 16
W = 45.5 - 16
W = 29.5 feet.
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(4x^4y)^2
i need help
Answers
Answer:
16x⁸y²
Step-by-step explanation:
Answer:
16x^8y^2
Step-by-step explanation:
what you do is simplify the expression
HELPPPPPPPPPPPPPPFHXBBXBSBSBDF
Answers
Answer:
it's B
Step-by-step explanation:
A gardener planted a newly sprouted oak tree that was just 3.5 inches tall. The sapling grew 12 inches each year.
Write an equation that shows how the sapling's height in inches, y, depends on the number of years since it was planted, x.
Answers
Answer:
y = 12x + 3.5--------------------------------------
Initial height is the y-intercept of the line.
Yearly growth rate is the slope.
So we have:
m = 12, b = 3.5.The equation of the line with these constants is:
y = mx + by = 12x + 3.5Rewrite the function by completing the square. f(x)=x^{2}+16x-46
Answers
x^2 + 16 - 46 = x^2 + 16 + 8^2 - 46 - 8^2 = (x + 8)^2 - 110
Answer:
\(f(x)=(x+8)^{2}-110\)
Step-by-step explanation:
\(f(x)=x^{2}+16x-46 \\=x^{2}+2\times 8\times x-46 \\=x^{2}+16x+8^2-8^2-46 \\=(x+8)^{2}-64-46\\f(x)=(x+8)^{2}-110\)
Illustrate on a number line the solution set of each pair of simultaneous inequalities. x>-2;-4 <x <2
Answers
The intersection region will be between -2 <x <2 or x ∈ (-2, 2) if the two inequalities are x>-2 and -4 <x <2
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than, known as inequality.
We have two inequalities:
x>-2 and
-4 <x <2
or
x ∈ ( -2, ∞) and x ∈ (-4, 2)
The intersection region will be(from the graph)
x ∈ (-2, 2)
Thus, the intersection region will be between -2 <x <2 or x ∈ (-2, 2) if the two inequalities are x>-2 and -4 <x <2
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if you start at 6,4 and move 4 units left, and 2 units down, what point will you end up on
Answers
Answer:
2,2
Step-by-step explanation:
Answer:
2,3
Step-by-step explanation:
Draw it on a coordinate grid...
PLEASE HELP!!!!!!!!
How do I write these in Slope y-intercept form example: y=1/2x-5
7) 2x - y = 3
8) 2x+4y = 8
9) 3x-5y=10
10) 3x-1/2y=2
Answers
Answer:
The answers would be:
7) y=-0.5x+2
8) y=-0.5x+2
9) y=0.6x-2
10) y=6x-4
Step-by-step explanation:
Help me with this question.
Answers
Answer:
The equation for the nth term of the arithmetic sequence is:
\(a_{n} = a + (n-1)d\\\)
The \(a_{30}\) is 140
Step-by-step explanation:
"a" represents the first term which is -5.
"d" represents the common difference which is 5.
To find the common difference, just subtract the 2nd and 1st term.
0 - (-5) = 5
Now put the values in the equation:
\(a_{n} = a + (n - 1)d\\a_{n} = (-5) + (n - 1)5\)
We are finding the 30th term so just put 30 to the "n" to help us find the 30th term of the sequence.
\(a_{30} = -5 + (30-1)5\\a_{30} = -5 + (29)5\\a_{30} = -5 + 145\\a_{30} = 140\)
So the 30th term is 140
Describe the relationship between the angles!! HELP ME PLZ
Answers
Answer:
1. alternate exterior angles
2. co-interior angles
3. corresponding angles
4. alternate interior angles
5. corresponding angles
6. co-interior angles
two times the sum of a number and 7
Answers
Answer:
2(x+7)
Step-by-step explanation:
i hope this helps
a pollster wishes to estimate the number of left-handed scientists. how large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 4%? a previous study indicates that the proportion of left-handed scientists is 8%.
Answers
If a pollster wishes to estimate the number of left-handed scientists. The sample that is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 4% is: 176.71.
How to find the sample?Using this formula to find the sample
n =Z²π (1-π) ÷ e²
Where:
n =sample size =?
Z = Z -score for 95% confidence level =1.960
π = Population proportion = 0.08
e = Margin of error = 0.04
Let plug in the formula
n = 1.96² × 0.08 × (1 - 0.08) ÷ 0.04²
n = 3.8416× 0.08 × 0.92 ÷ 0.0016
n = 176.71
Therefore the sample is 176.71.
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For the first week of January, Kim Walker worked 45.25 hours. Kim earns 10.90 an hour. Her employer pays overtime for all hours worked in excess of 40 hours per week and pays 1.5 times the hourly rate for overtime hours.
Answers
Answer:
Gross pay when she works 46 hours a week = 532 dollars per week
Step-by-step explanation:
Complete question
Find gross pay when she works 46 hours a week
Solution
For working hours less than or equal to 40 hours, kim earns 10.90 per hour
For working hours higher than the basic 40 hours of working, the per hour rate increases by 1.5 time = 1.5 *10.90 = 16 dollars per hour
Gross pay for 46 working hours = 40 *10.90 + 6*16 = 532 dollars per week
If the question is right I will mark brainliest and give 20 points
Answers
In general form, the equation is 8x² + 30x - 2x = 0.
In factored form, the equation is 4x(2x + 7) = 0.
To solve the equation 8x² + 30x = 2x, we can rearrange it to bring all the terms to one side:
8x² + 30x - 2x = 0
Combining like terms:
8x² + 28x = 0
Now, let's factor out the common factor of 4x:
4x(2x + 7) = 0
To find the solution set, we set each factor equal to zero and solve for x:
4x = 0 -> x = 0
2x + 7 = 0
2x = -7
x = -7/2
Therefore, the solution set for the equation is {0, -7/2}.
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HELP ASAP A certain breand of nuts costs $3.20 for 16 ounces what is the unit rate
round to nearest hundredth show me how your raio should be set up
Answers
Answer:
$0.20 : 1 ounce
The nuts cost 20 cents per ounce.
Step-by-step explanation:
First, set up the ratio
$3.20 : 16 ounces [cost : weight]
Next, to find the price per ounce, divide each side by 16
$3.20 / 16: 16 ounces / 16
$0.20 : 1 ounce
How to calculate theta 2 d2 and first angle i will give 16 brainly points and maybe a bonus
Answers
The term "first angle" is also unclear and could have different interpretations depending on the context.
To calculate θ2, d2, and the first angle, we need more context or specific information about the problem. The variables θ2 and d2 are not universally defined and can vary depending on the problem or equation you are referring to. The term "first angle" is also unclear and could have different interpretations depending on the context.
If you can provide additional details, equations, or specify the problem you are trying to solve, I will be happy to assist you in calculating θ2, d2, and the first angle accurately. Providing specific information will enable me to provide a detailed and tailored explanation to help you solve the problem effectively.
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What is the coefficient in this expression: 5x + 3 = 8
Answers
Answer:
5x
Step-by-step explanation:
coefficients always have letters while constant does not
HELP WILL GIVE BRAINLY PLZ DONT SKIP
Half of a class took Form A of a test, and half took Form B. Of the students who took form B, 39% passed. What is the probability that a randomly
chosen student took Form B and did not pass? Show ur work/explain in words what you did
A. 0.055
B 0.195
C. 0.305
D. 0.390
Answers
Answer:
C. 0.305
Step-by-step explanation:
100 - 39 = 61
.5 x .61 = .305
30.5%
A flagpole makes a 15-foot long shadow. The angle of elevation with the end of the shadow and the ground
makes a 65° angle. What is the height of the flagpole?
Answers
Answer:
12.5988 feet.
Step-by-step explanation:
Length of shadow = 15 feet.
Height of flagpole = A.
We know the angle of elevation is 40∘. Using this angle and the tangent ratio, we can find A.
Hope this helps! :)
Add.
(56² − 3b + 2) + (26 — 4)
What is the answer? Enter your answer in the blanks.
Answers
Answer:
The correct answer is 5b²-b-2
0.09+27/100=?/100+27/100
Answers
Answer:
x = 9
Step-by-step explanation:
0.09+27/100=x/100+27/100
0.09=x/100
9=x
Answer: 0.36
Step-by-step explanation:
0.09+(27÷100)= 0.36
(27* 100)= 0.27
Don’t know need help
Answers
I think that the answer would be 14