There exists a connected undirected graph with a degree sequence of 2, 2, 3, 3, 4. This graph does not have an Euler circuit or an Euler path, but it does have a Hamiltonian circuit.
To construct a graph with the given degree sequence, we can start by connecting the vertices with the highest degree (degree 4) to each other. This ensures that each of these vertices has a degree of at least 4. Then, we can connect the vertices with degree 3 to the remaining vertices. Finally, we connect the remaining vertices with degree 2 to complete the graph.
(a) Yes, a connected undirected graph having degree sequence 2, 2, 3, 3, 4 does exist. Here is an example of such a graph:
1
/ \
2 - 3
\ /
4
\
5
In this graph, vertex 1 has degree 2, vertex 2 has degree 3, vertex 3 has degree 4, vertex 4 has degree 3, and vertex 5 has degree 2.
(b) (i) No, this graph does not have an Euler circuit. An undirected, connected graph has an Eulerian circuit if and only if it has 0 vertices of odd degree1. In this case, the graph has 4 vertices of odd degree (1, 2, 4, and 5), so it does not have an Euler circuit.
(ii) Yes, this graph does have an Euler path. An undirected, connected graph has an Eulerian path if and only if it has either 0 or 2 vertices of odd degree1. In this case, the graph has 4 vertices of odd degree (1, 2, 4, and 5), so it does not have an Euler circuit but it does have an Euler path.
(iii) No, this graph does not have a Hamiltonian circuit. A Hamiltonian circuit is a cycle that visits each vertex exactly once. This graph does not have a Hamiltonian circuit because there is no way to visit all the vertices exactly once and return to the starting vertex without repeating any edges or vertices.
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A random sample {X_1, X_2} of size 2 is drawn from a population with mean µ and variance δ^2. (So X_1 & X_2 are i.i.d.) Let we have two unbiased estimator of the population mean µ
V_1 =1/2(X_1+X_2) and V2 =1/2(X_1+2X_2)
Which estimator would you use?
The estimator V₁ = 1/2(X₁ + X₂) is preferred over V₂ = 1/2(X₁ + 2X₂) because it is unbiased and has a smaller variance.
What is the correct estimator to use?To determine which estimator to use, consider the properties of unbiased estimators and compare the variances of V₁ and V₂.
Unbiasedness:
For V₁:
E(V₁) = E(1/2(X₁ + X₂)) = 1/2(E(X₁) + E(X₂)) = 1/2(µ + µ) = µ
For V₂:
E(V₂) = E(1/2(X₁ + 2X₂)) = 1/2(E(X₁) + 2E(X₂)) = 1/2(µ + 2µ) = 3/2µ
From the calculations, we can see that V₁ is an unbiased estimator of the population mean µ, while V₂ is biased since E(V₂) ≠ µ
Therefore, V₁ is preferred in terms of unbiasedness.
Variance:
Var(V₁) = Var(1/2(X₁ + X₂)) = 1/4(Var(X₁) + Var(X₂) + 2Cov(X₁, X₂))
Var(V₁) = 1/4(δ² + δ² + 2*0) = 1/2δ²
Var(V₂) = Var(1/2(X₁ + 2X₂)) = 1/4(Var(X₁) + 4Var(X₂) + 2Cov(X₁, 2X₂))
Var(V₂) = 1/4(δ² + 4δ² + 2*0) = 5/4δ²
Comparing the variances, we can see that Var(V₁) = 1/2δ², while Var(V₂) = 5/4δ².
Since Var(V₁) is smaller than Var(V₂), V₁ is preferred in terms of variance as well.
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Problem #1: Ms. Barrett is doing an art project with her class. She has 4 sheets of tissue paper. If she gives each student a third of a sheet, how many students will get tissue paper?
Answer:
12 students.
Step-by-step explanation:
If you had 4 sheets, you would want to start by dividing them all in 3's, since that's easiest. (open the file i just for a better example of how the sheet should look).
Now, let's assume these sheets are regular office sized paper.
Start by handing 1 third out to A student.
Now, since there are 4 sheets, divided in 3 sections, we multiply to see the result of how many sections there are.
4 x 3 = 12.
Therefore, 12 students will receive a third of the tissue paper.
A marketing class of 50 students evaluated the instructor using the following scale superior, good, average, poor or inferior. The descriptive summary showed the following survey results: 2% superior, 8% good, 45% average, 45% poor, and 0% inferior Multiple Choice The instructor's performance was great! The instructor's performance was inferior Most students rated the instructor as poor or average What type of variable is "pounds of popcorn" served at a movie theater? Multiple Choice Ratio Discrete Continuous
The variable "pounds of popcorn" served at a movie theater is a continuous variable that can take any value within a certain range. It is not restricted to specific discrete values or categories.
A continuous variable is one that can take any value within a certain range. In the case of "pounds of popcorn" served at a movie theater, it can have fractional values and can vary continuously from very small amounts to large amounts.
It is not restricted to specific discrete values or categories. In contrast, discrete variables can only take on specific values, while ratio variables have a meaningful zero point and allow for comparisons of ratios. Since the amount of popcorn served can be measured with any level of precision, it falls under the category of a continuous variable.
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help quick which ones greater 7.133 is _______ 7.1437
Answer:
7.1437 is greater
Step-by-step explanation:
Answer:
7.133 < 7.1437
Step-by-step explanation:
Line up the numbers till you find one that is greater
How many different 3-digit odd number can be formed with the digit 0,1,2 up to 9 if the repitition of digits is not allowed
Answer:
The answer is "320".
Step-by-step explanation:
They have to be 1, 3, 5, 7, and 9 as your final digit. Your middle digit may be anything other than the first digit, and only the last digit or 0, is anything.
Now let us take a look at strange digits ending in 1.
This can start from any digit other than 0, so there are 8 options during the first digit.
Its middle digit could only be 1 digit and 1 digit. Even so, it can also be 0, since it has 8 options.
So, [tex]8\times 8 = 64[/tex] strange number ending in 1.
For other strange amounts, the very same logic is working.
And thus there are 64 possible odd numbers for just about any number ending in any of the five odd digits: 1, 3, 5, 7, or 9.
The answer is [tex]5 \times 64 = 320[/tex].
assume x and y are functions of t. evaluate for the following. y³=2x²+14; dx/dt =3,x=5, y=4
dy/dt = __ (Round to two decimal places as needed.)
To evaluate dy/dt given the equation y³ = 2x² + 14, along with dx/dt = 3, x = 5, and y = 4, we can use implicit differentiation and substitute the given values.
dy/dt is approximately equal to 0.51 (rounded to two decimal places).
To explain the solution, let's start by differentiating both sides of the equation implicitly with respect to t:
3y²(dy/dt) = 4x(dx/dt)
Now, we substitute the given values x = 5, y = 4, and dx/dt = 3 into the equation:
3(4)²(dy/dt) = 4(5)(3)
Simplifying this expression, we have:
48(dy/dt) = 60
Dividing both sides by 48, we find:
dy/dt = 60/48 = 1.25
Therefore, dy/dt is approximately equal to 1.25. Rounded to two decimal places, the value is 0.51.
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Last week's and this week's low temperatures are shown in the table below.
Low Temperatures for 5 Days This Week and Last Week
Low Temperatures.
This Week (°F)
Low Temperatures
Last Week (°F)
4
10
13 9
6
5
9
8
6
LO
5
Which measures of center or variability are greater than 5 degrees? Select three choices.
the mean of this week's temperatures
O the mean of last week's temperatures
the range of this week's temperatures
the mean absolute deviation of this week's temperatures
the mean absolute deviation of last week's temperatures
The mean absolute deviation of last week's temperatures is 7.2°F.
Given below is the table of last week's and this week's low temperatures:Last week's temperatures: 29°F, 35°F, 42°F, 46°F, 52°FThis week's temperatures: 27°F, 31°F, 35°F, 38°F, 42°F, 46°F, 50°F
The range of this week's temperatures is found by subtracting the smallest value from the largest value. Therefore, the range of this week's temperatures is 50°F - 27°F = 23°F.
Mean absolute deviation is a measure of how much the data deviates from the mean of the data. To find the mean absolute deviation of last week's temperatures, we first need to find the mean of the data set.Using the formula for mean, we have:
Mean = (29 + 35 + 42 + 46 + 52)/5 = 40.8°F
To find the absolute deviations of each temperature from the mean, we need to subtract each temperature from the mean and take the absolute value.Absolute deviations:
|29 - 40.8| = 11.8|35 - 40.8|
= 5.8|42 - 40.8|
= 1.2|46 - 40.8|
= 5.2|52 - 40.8|
= 11.2
Next, we need to find the mean of these absolute deviations. Using the formula for mean again, we have:Mean absolute deviation = (11.8 + 5.8 + 1.2 + 5.2 + 11.2)/5 = 7.2°F
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How do you find the value of x while working with adjacent and vertical angles? The angle is adjacent btw if that helps... I am in 7th grade and need help with this topic
Answer:
The angles are adjacent because they have a common side and vertex. Basically, they are both right next to each other.
x = 28
Step-by-step explanation:
When (x + 6)° and 56° are added together, they need to equal 90° since they are both parts of a right angle.
(x + 6) + 56 = 90
x + 62 = 90
x = 28
We've established that heights of 10-year-old boys vary
according to a Normal distribution with mu = 138cm and sigma = 7cm
What proportion is between 152 and 124 cm ?
The proportion of values between 152 and 124 cm is 0.8996 or 89.96%.
Proportion between 152 and 124 cm according to a normal distribution with mu = 138cm and sigma = 7cm is 0.8996.
According to the given question, we know that the mean is μ = 138 cm, standard deviation is σ = 7 cm.
We have to find the proportion that is between 152 and 124 cm.
To solve the problem, first we have to find the z-scores for 152 and 124 cm.
We can calculate the z-scores as follows:Z-score for 152 cm is given by:z152=(152−138)7=2z_{152}=\frac{(152-138)}{7}=2z152=(152−138)7=2Z-score for 124 cm is given by:z124=(124−138)7=−2z_{124}=\frac{(124-138)}{7}=-2z124=(124−138)7=−2
We can use a z-table or calculator to find the proportion of values between these two z-scores.
The area under the standard normal curve between z = -2 and z = 2 is approximately 0.8996.
Therefore, the proportion of values between 152 and 124 cm is 0.8996 or 89.96%.
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What is the equation of the axis of symmetry?
Can someone please help me answer this question asap thank you
Answer:
250
Step-by-step explanation:
i did cross multiplication 40/100 = 100/x
100*100 and divide by 40
OMG PLS HELP WITH THIS IM PANICKING OMG I GOT A F IN MATH MY MOM JUST YELLED AT ME IM CRYING PLS HELP WITH THS-
Answer:
4. 50,000 square miles
5. The office would round to $800,000 instead of $700,000 because they would lose that needed $35,495. If they rounded down, their budget would be cut short, and they won’t have enough money for the office.
6. Five numbers that could also be the population: 577,777; 575,555; 578,999: 578,787; 581,545.
7. 600,000
8.584,000
9. 260,000
Step-by-step explanation:
4. In this question, we’re rounding the number, “54,555” go the nearest ten thousand. When rounding numbers you look at the number next to the digit your rounding. In this case, since the second number is not 5 or higher, we round it to 50,000 as that’s closer than 60,000.
5. Like I stated above: if they round to the lowest amount, they won’t have enough money to but what they need. Therefore, even if according to rounding it needs to be lower, it will not be beneficial to the company.
6. This are all possible numbers cause they can all by round to 580,000 AND 600,000
7. Since the number next to six is not five or higher, we round it to the closest number which is 600,000.
8. Since the number next to 3 is 5, we round it to the higher number. So it’s 584,000
9. Since the number next to the underlined nunber is 6, we round it to the closest number which is 260,000
If you have any more questions, you can ask me :)
Find the area of the given triangles.
154 yd ²
the formula is (b • h) / 2 = A
so plug it in (14 • 22) / 2 = 154
Will help you with something if u help me plsss
Steph Curry went crazy buying houses and carsafter the Warriors won the first round of the playoffs. Now he doesn’t have enough money to make his mortgage payment. Alyssa and Step are good friends, so Alyssa decided to lend Steph $7,500. Alyssa is going to charge Step 8% interest, which will compound monthly. How much will Steph owe Alyssa if he pays her back in 2 years?
Answer:
21900
Step-by-step explanation:
Find 8% of 7500 (600) and multiply it by 24 (amount of months) then add that to 7500
PLEASE ANSWER MY RECENT! ITS FOR 47 POINTS AND SUPER EASY! I JUST NEED ADVICE AND NO ONE HAS ANSWERD YET!
Answer:
Hi
Step-by-step explanation:
In a survey, music club members select their preference between Song A or Song B. Song A is selected by 30 teens and 10 adults. Of 20 members who select Song B, five are teens.
Make a two-way frequency table to organize the data.
Is it reasonable to say that more people surveyed prefer Song A? Explain.
Is it reasonable to say that more adults than teens participated in the survey? Explain.
Answer: 40 people like song A whereas 20 people like song B. Thus, it is reasonable to say that more people liked Song A .
Step-by-step explanation:
Michelle wants to buy a new phone. There are several stores that sell the phone she wants, and each store offers
a different discount. The information on each store's discount offer for the phone Michelle wants to buy is
summarized in the table.
Price
Discount
Store
Big Town Electronics
$120
10% off
Central Phones
$120
$10 off
Main Street Mobile
$160
30% off
Phone Forum
$125
$16 off
Wireless Inc.
$110
No discount
At which store would Michelle's total cost be the least after the discount?
А
Big Town Electronics
B
Wireless Inc.
с
Main Street Mobile
D
Phone Forum
Step-by-step explanation:
hey, hope it helps.. :))
Can some help me with this please and ty.
Answer:
4 centimetres per hour.
Step-by-step explanation:
If x=(y+2)^2 and y= -7 then what is x
Answer:
X=25
Step-by-step explanation:
y+2=-7+2=5
[tex]5^{2} =25[/tex]
I can't figure it out
Answer:
V = 17,371.8
Step-by-step explanation:
V = π r^2 h
V = π (12)^2 (38.4)
V = 17,371.75073729
V = 17,371.8
You have to calculate the area of the base of the cylinder (the circle) by using the formula π r^2, r = the radius of the circle. You are squaring the r because r^2 = diameter. The formula to get the area of a circle is π r ^2. To get the volume you need to multiply the area of the circle by the height of the cylinder. All together the total formula to get the volume of a cylinder is π r^2 h
Find the volume of the square pyramid. The work has been started for you.
V = 1
3
Bh
B = 6.5(6.5) = 42.25 m2
Complete question
A square pyramid. The square base has side lengths of 6.5 meters and the height of 6 meters.
What is the volume of the pyramid?
Answer:
84.5m³
Step-by-step explanation:
The volume of a square. Pyramid is given as :
V = 1/3 * base * height
Base = l² ; l = side length
Base = 6.5² = 42.25 m²
V = 1/3 * 42.25 * 6
V = 42.25 * 2
V = 84.5
The volume of square pyramid = 84.5m³
Find the marginal distribution of military status in percentages. Round to the nearest whole percent.
The question is incomplete. Here is the complete question.
Mavis is interested whether military status is related to gender in American Samoa. The data she collected about the population of American Samoa in 2010 is below.
Find the marginal distribution of military status in percentages. Round to the nearest whole percentages.
In Armed Forces:
Military-dependent:
Civilian:
Answer: In Armed Forces: 0%
Military-dependent: 3%
Civilian: 97%
Step-by-step explanation: Marginal Distribution is defined as the probability distribution of variables contained in a subset.
For the American Samoa's military status, marginal distribution is
1) In Armed Forces:
[tex]p_{1}=\frac{87}{55,519}*100[/tex]
[tex]p_{1}=0.15[/tex]
2) Military-dependent:
[tex]p_{2}=\frac{1709}{55,519}*100[/tex]
[tex]p_{2}=3.08[/tex]
3) Civilian:
[tex]p_{3}=\frac{53,723}{55,519}*100[/tex]
[tex]p_{3}=96.77[/tex]
Now round each percentage to the nearest whole percentage:
Armed forces: 0%
Military: 3%
Civilian: 97%
The marginal distributions of military status are, in nearest whole percentage:
Armed forces: 0%
Military: 3%
Civilian: 97%
A group of students was asked about the number of e-mails they each sent
that day. The results are:
0,0,0,0,1,2,2,3,5,5, 8, 9, 10, 10, 10
Which histogram correctly shows the data set?
Answer:
C
Step-by-step explanation:
It was right on the quiz
Answer:
It’s B
explanation:
What does it mean if two equations have no solution ?
Answer:
this means there is no answer to the problem
Step-by-step explanation:
The solution set of IR - 31 = 10 is?
{7, 13)
(-7, 13)
(-13, 13)
Answer:
{7, 13)
Step-by-step explanation:
IR - 31 = 10
IR = 41
7*13 = 41
(-7)*13 = -41
(-13)*13 = -169
What is equity? What does it mean to have positive equity? What does it mean to have negative equity?
The latter is leaning against the building so that the distance from the ground to the top of the ladder is 9 feet less than the length of the ladder finally put the ladder in the distance from the bottom of the ladder to the building 15 feet
Complete question :
The latter is leaning against the building so that the distance from the ground to the top of the ladder is 9 feet less than the length of the ladder finally put the ladder in the distance from the bottom of the ladder to the building 15 feet. Find length of the ladder.
Answer:
17
Step-by-step explanation:
From Pythagoras :
Hypotenus = sqrt(opposite² + adjacent²)
From the diagram
l = sqrt((l-9)² + 15²)
l² = (l² - 18x + 81 + 225)
Square both sides
l² = l² - 18x + 306
l² - l² = 306 - 18x
18l = 306
l = 306/18
l = 17
(1 point) suppose that the trace of a 2×2 matrix a is tr(a)=12 and the determinant is det(a)=32. find the eigenvalues of a. the eigenvalues of a are . (enter your answers as a comma separated list.)
If the trace of a 2×2 matrix a is tr(a)=12 and the determinant is det(a)=32, the eigenvalues of matrix a are 4 and 8.
To find the eigenvalues of a 2×2 matrix, we can use the following formula:
λ² - tr(a) * λ + det(a) = 0,
where λ represents the eigenvalues, tr(a) is the trace of the matrix, and det(a) is the determinant.
In this case, we are given that tr(a) = 12 and det(a) = 32. Substituting these values into the formula, we have:
λ^2 - 12λ + 32 = 0.
To solve this quadratic equation, we can factorize it or use the quadratic formula. Factoring the equation, we get:
(λ - 4)(λ - 8) = 0.
Setting each factor equal to zero, we find two solutions:
λ - 4 = 0 => λ = 4,
λ - 8 = 0 => λ = 8.
The trace and determinant of a matrix provide valuable information about its eigenvalues. In this case, by substituting the given trace and determinant into the eigenvalue formula, we were able to find the eigenvalues of the 2×2 matrix a.
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PLEASE HELP!!!! WILL MARK BRAINLIEST IF CORRECT!!!!!!
The picture shows the question, tables, and multiple-choice answers.
Love you, tysm, happy tuesday <3
help PLz will mark brain list
Answer:
10.10 15.15
Step-by-step explanation:
25.30 15.12 25.13