No, such a simple directed graph with at least three vertices and the property that deg+(v) + deg¯(v) = 1 cannot exist.
The property deg+(v) + deg¯(v) = 1 implies that for every vertex v in the graph, the sum of its in-degree (deg¯(v)) and out-degree (deg+(v)) is equal to 1. In a directed graph, the in-degree of a vertex represents the number of incoming edges, while the out-degree represents the number of outgoing edges.
If we consider a graph with at least three vertices, let's say v1, v2, and v3, and apply the given property, we would have:
deg+(v1) + deg¯(v1) = 1
deg+(v2) + deg¯(v2) = 1
deg+(v3) + deg¯(v3) = 1
However, this leads to a contradiction. In a directed graph, the sum of in-degrees and out-degrees of all vertices is always equal. Therefore, if we sum up the equations above, we would get:
deg+(v1) + deg+(v2) + deg+(v3) + deg¯(v1) + deg¯(v2) + deg¯(v3) = 3
Since each term on the left-hand side of the equation is at least 1 (due to the property), the sum would be at least 6. This contradicts the fact that the sum should be equal to 3.
Hence, a simple directed graph with at least three vertices and the property deg+(v) + deg¯(v) = 1 cannot exist.
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[5 points) X is places in an account which carries a nominal annual interest rate of 2.5% compounded monthly. After five years, the accumulated value is places in an account which earns a nominal annual interest rate of 3.2% compounded quarterly. The value of this account in eight years is $10,000. Find X.
The initial value of X can be determined using compound interest calculations. X is invested in an account with a nominal annual interest rate of 2.5%, compounded on a monthly basis, for a period of five years. After the initial period, X is then transferred to another account with a nominal annual interest rate of 3.2%, compounded on a quarterly basis, for a total duration of eight years. The approximate value of X at the end of this investment period is $6,573.83.
To solve for X, we will substitute the first equation into the second equation and solve for X. Let's proceed with the calculations:
The first equation is: FV = X(1 + 0.025/12)^(12*5)
The second equation is: $10,000 = X(1 + 0.032/4)^(48)(1 + 0.025/12)^(125)
We can substitute the first equation into the second equation:
$10,000 = [X(1 + 0.025/12)^(125)] * (1 + 0.032/4)^(48)
$10,000 = X * (1 + 0.025/12)^(125) * (1 + 0.032/4)^(48)
Now we can simplify the equation:
$10,000 = X * (1.002083)^60 * (1.008)^32
Divide both sides of the equation by [(1.002083)^60 * (1.008)^32] to solve for X:
X = $10,000 / [(1.002083)^60 * (1.008)^32]
Using a calculator, we can find the value of X:
X ≈ $10,000 / (1.138877 * 1.335893)
X ≈ $10,000 / 1.521364
X ≈ $6,573.83
Therefore, the value of X is approximately $6,573.83.
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4 out of the 80 students at a school assembly were first-grade students. What percentage of the students at the assembly were first-graders?
Answer:5
Step-by-step explanation:
Answer:
5 percent
Step-by-step explanation:
4/80 = 5 percent
HELPPPPPPPPPPPPP meeeee please
Step-by-step explanation:
5. 4b = b + b + b + b (A)
4b = 2b + 2b (C)
6. 111 = 14a
a = 111/14
a = 7.92
#CMIIWA delivery company purchases a $20,000 van. The value of the van depreciates at a rate of 19% per year. How many years will it take before the van is worth half its original purchase price? Round to the nearest tenth of a year.
A 1.7 years
B 4.0 years
C 3.3 years
Factor 8b^3 – 4b^2 a - 18b + 9a completely.
Answer:
85
Step-by-step explanation:
Answer:
(2b-a)x(2b-3)x(2b+3)
Step-by-step explanation:
Can someone help me on this I’m struggling to figure it out...
Answer:
It's D
Step-by-step explanation:
Find the measure of the exterior angle.
What is the mode of the data set? {102, 102, 100, 94, 102} Enter your answer in the box.
Answer:
102
Step-by-step explanation:
The mode is the number that appears the most in the data set. 102 appears 3 times while the others only once
What is the value of b for b' - 36/64
A car salesman sells cars with prices ranging from $5,000 to $45,000. The box plot shows the distribution of the numbers of cars he expects to sell over the next 10 years.
The salesman has observed that many students are looking for cars that cost less than $5,000. If he decides to also deal in cars that cost less than $5,000 and projects selling 200 of them over the next 10 years, how will the distribution be affected?
A. The mean and the median will be the same.
B. The median will shift to the right.
C. The mean will shift to the left.
D. The mean will shift to the right.
Simplify each radical expression, if possible 3v/7-5^4v/7
Answer:
cannot be simplified
Step -by-step explanation:
[tex]3\sqrt{7} - 5\sqrt[4]{7} \\[/tex]
The indexes are not the same so the radicals cannot be combined.
cannot be simplified
-6x - 14 > 10 what is the answer to this problem, please helt
Answer:
Inequality Form:
x < - 4
Interval Notation:
( − ∞ , − 4 )
Step-by-step explanation:
what is the true solution to 3 l n 2 l n 8 = 2 l n (4 x)x = 1x = 2x = 4x = 8
The true solution to the equation is x ≈ 0.688. By simplifying the equation and solving for x, we find the approximate value.
To find the true solution to the equation 3ln(2ln8) = 2ln(4x)x = 1x = 2x = 4x = 8, we need to simplify the equation and solve for x.
First, let's break down the equation step by step:
3ln(2ln8) = 2ln(4x)x = 1x = 2x = 4x = 8
By simplifying each expression, we have:
3ln(ln8) = 2ln(4x)x = x = 2x = 4x = 8
Now, let's focus on the middle expression, 2ln(4x)x. Using the properties of logarithms, we can rewrite it as:
ln((4x)^2) = x
Simplifying further:
ln(16x^2) = x
Exponentiating both sides:
16x^2 = e^x
This is a transcendental equation that cannot be solved algebraically. However, using numerical methods or a graphing calculator, we find the approximate solution:
x ≈ 0.688
Therefore, the true solution to the equation is x ≈ 0.688.
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Consider the function represented in the table.
Which point of the given function corresponds with the
minimum value of its inverse function?
X
-10-20
3 8
0
-2.
5 8
4.5-6
A (-20, 8)
B (-10,3)
C (0, -2)
D (8,-6)
HELPPP
Answer:
The real answer is (-20, 8).
Step-by-step explanation:
I just did the unit test practice or whatever and used the answer above and got it wrong. This is the correct answer.
I need help with this helpppp :(
Answer:
Domain: (-∞,+∞)
Range: (-∞,1)
y-intercept: (0,2)
Asymptote: I am not sure (sorry) I know they can be solved using the equation n(x)=0
Step-by-step explanation:
Domain: the set of all x-values
- this graph has arrows which means the domain is from -∞ to +∞ (-∞,+∞)
Range: the set of all y-values
- the graph extend continuously on the negative side so -∞ and it stops at 1 on the positive side (-∞,1)
Y-intercept: this point is where the graph crosses the y-axis, this is at (0,2)
What is the ratio of yellow butterflies to total butterflies? Choose the correct option
Answer:2/3
Step-by-step explanation: there is 2 yellow out of 3 butterfiles
Assuming that the sample variances are continuous measurements, find the probability that a random sample of 30 observations, from a normal population with variance 92= 5, will have a sample variance of s2 that is a) greater than 7.338; b) between 2.766 and 7.883.
a) chi-square = (30-1) * 7.338 / 5 = 42.456 b) The probability of having a sample variance between 2.766 and 7.883 is the difference between the cumulative probabilities of chi-square2 and chi-square1.
Answer to the aforemention questionsTo find the probability in both cases, we need to use the chi-square distribution with n-1 degrees of freedom, where n is the sample size.
a) To find the probability that the sample variance is greater than 7.338, we need to find the upper tail probability of the chi-square distribution.
The chi-square statistic is calculated as:
chi-square = (n-1) * s^2 / sigma^2
In this case, n = 30, s^2 = 7.338, and sigma^2 = 5.
chi-square = (30-1) * 7.338 / 5 = 42.456
b) To find the probability that the sample variance is between 2.766 and 7.883, we need to find the cumulative probability within that range.
First, we calculate the chi-square statistics for both values:
chi-square1 = (30-1) * 2.766 / 5 = 15.359
chi-square2 = (30-1) * 7.883 / 5 = 43.179
The probability of having a sample variance between 2.766 and 7.883 is the difference between the cumulative probabilities of chi-square2 and chi-square1.
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The longest run way at an airport has the shape of a rectangle and an area of 1,573,000 sq ft. This run way is 130 feet wide. How long is the run way?
Answer:
12,100 feet
Step-by-step explanation:
The longest run way at an airport has the shape of a rectangle and an area of 1,573,000 sq ft. This run way is 130 feet wide. How long is the run way?
The area of a rectangle = Length × Width
Width = 130 feet
Area = 1,573,000 sq ft
The Length = Area/Width
= 1,573,000 sq ft/130 feet
= 12,100 feet
Therefore, the runaway is 12,100 feet long.
what is a shape that has no sides the same length that is a quadrilateral
Answer:
Step-by-st
Bitly: URL Shortener - Short URLs & Custom Free Link ...bitlep explanation:
In a large population of college-educated adults, the mean IQ is 112 with standard deviation 50.62. Suppose 30 adults from this population are randomly selected for a market research campaign. The distribution of the sample mean IQ is: a. approximately Normal, with mean 112 and standard deviation 1.443. b. approximately Normal, with mean 112 and standard deviation 4.564. c. approximately Normal, with mean equal to the observed value of the sample mean and standard deviation 25. d. approximately Normal, with mean 112 and standard deviation 9.241.
Given: Population mean IQ = 112Population standard deviation IQ = 50.62Sample size (n) = 30To find: Distribution of the sample mean IQ
The Central Limit Theorem states that for a large sample size, the distribution of sample means will be approximately Normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size . Let's calculate the standard deviation of the sample mean IQ:
Standard deviation of sample mean IQ = (Population standard deviation IQ) / √n= 50.62 / √30= 9.241 (approx.)Therefore, the distribution of the sample mean IQ is approximately Normal, with mean 112 and standard deviation 9.241. The correct option is (d).
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Which of the expressions below is equal to 10x+30? Select all that apply.
Which of the following statement(s) with regard to a data set's measures of Central Tendency, Dispersion, and Paired Observations is(are) TRUE?
In a very small set of data, i.e. small n, the Sample Standard Deviation is generally smaller than its Population Standard Deviation.
It is possible for the value of the Correlation between a set of paired observations to be greater than 1.
Unlike STDEV.P Excel function for calculating a Population Standard Deviation, Excel has no direct functions for calculating the Range and Midrange values of a data set.
Mode and Range are both measures of central tendency.
In a set of paired observations of X and Y, if the Correlation is 0.75, then as the values of X increases (decreases), the values of Y also generally increases (decreases) in the same direction.
In a very large set of data, i.e. large n, the Standard Deviation is a better measurement than Range.
It is possible for Median of a data set to have a value that is not equal to any of the values in the data set.
The statements that are TRUE with regard to a data set's measures of Central Tendency, Dispersion, and Paired Observations are the following:In a very small set of data, i.e. small n, the Sample Standard Deviation is generally smaller than its Population Standard Deviation.
It is possible for the value of the Correlation between a set of paired observations to be greater than 1.In a set of paired observations of X and Y, if the Correlation is 0.75, then as the values of X increases (decreases), the values of Y also generally increases (decreases) in the same direction.In a very large set of data, i.e. large n, the Standard Deviation is a better measurement than Range.Why these statements are true?In a very small set of data, the Sample Standard Deviation is generally smaller than its Population Standard Deviation because when the sample size is smaller, there is less dispersion and thus the value of the sample standard deviation is generally smaller than that of the population standard deviation.It is possible for the value of the Correlation between a set of paired observations to be greater than 1 because the correlation coefficient r ranges from -1 to 1, inclusive of both endpoints.
However, it is practically impossible to get a value of r outside this range in a real dataset.In a set of paired observations of X and Y, if the Correlation is 0.75, then as the values of X increases (decreases), the values of Y also generally increases (decreases) in the same direction. This is because 0.75 is a strong positive correlation indicating that as the value of one variable increases, the value of the other variable also increases.In a very large set of data, i.e. large n, the Standard Deviation is a better measurement than Range because the standard deviation takes into account all values in the dataset and is less sensitive to outliers as compared to the range. On the other hand, the range only considers the minimum and maximum values of the dataset and thus is less informative.
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HELP ASAP!!! question in picture!!!
Answer:
Y=3x-17
Step-by-step explanation:
I graphed it
please help me .......
Answer:
A
Step-by-step explanation:
Flow many years after the tree is planted does the model predict the tree will reach a height of 65 feet?
B
this is the answer
PLEASE HELP!
The blank of y in 17y is 17.
Its either term, variable or coefficient
In the term, 17y 17 is the coefficient of 17y.
What are coefficients and like terms?A quantity or number that is combined with a variable is known as a coefficient. The variable is often multiplied by an integer, which is then printed next to it.
Terms that have the same variables raised to the same power are referred to as like terms. The only difference is in the numerical coefficients.
The term 17y together is a variable, In 17y 'y' is also a variable.
In front of 'y' the constant number is 17 and it is called the coefficient of 'y'.
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(3/2)^4= in fraction form help pls
Answer:
81/16
Step-by-step explanation:
Help me with this asp please
The x-coordinate of the endpoint of the line segment is 2.
The y-coordinate of the endpoint is -6.
To find the x-coordinate of the endpoint of the line segment, we can use the midpoint formula.
Given that one endpoint is at (10, 12) and the midpoint is at (6, 9), we can denote the coordinates of the other endpoint as (x, y).
Using the midpoint formula, we have:
x-coordinate of the endpoint = 2 * x-coordinate of the midpoint - x-coordinate of the known endpoint
x = 2 * 6 - 10
x = 12 - 10
x = 2
To find the y-coordinate of the endpoint of the line segment, we can use the midpoint formula. We know that the midpoint of the line segment is (6, 9) and one endpoint is (10, 12).
Let the coordinates of the other endpoint be (x, y). Using the midpoint formula, we can set up the following equation:
(10 + x) / 2 = 6
Simplifying the equation, we have:
10 + x = 12
Subtracting 10 from both sides:
x = 2
Therefore, the x-coordinate of the endpoint is 2. Now, we need to find the y-coordinate. Since we know that the endpoint is (2, y), we can use the given endpoint (10, 12) to find the y-coordinate:
12 + y / 2 = 9
Subtracting 12 from both sides:
y / 2 = -3
Multiplying both sides by 2:
y = -6
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Jackson Brothers Auto Dealers sells two brands: Honda and GMC. Over the last 3 months, they have sold 175 autos. The company makes $300 profit on each GMC sold and $450 profit on each Honda. If the company has made $60,750 profit in that time, how many of each type of car have they sold?
Let x be the number of GMC sold
Let y be the number of Honda soldAccording to the given data, we can form the following equations: x+y = 175 ............ (1)300x + 450y = 60,750 ............ (2)
Multiplying equation (1) by 300 on both sides, we get:300x + 300y = 52,500Subtracting this equation from equation (2), we get:150y = 8,250Solving for y, we get:y = 55Substituting the value of y in equation (1),
we get:x + 55 = 175x = 120Therefore, the number of GMCs sold is 120 and the number of Hondas sold is 55.
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The company have sold 50 GMC and 125 Honda for this profit.
Let the number of GMC sold be x and the number of Honda sold be y.
Then:
[tex]x + y = 175[/tex]----------------------(1)
GMC: Profit on one car sold = $300
Therefore, the total profit on x GMC cars sold = $300x
Honda: Profit on one car sold = $450
Therefore, the total profit on y Honda cars sold = $450y
Total profit on x GMC and y Honda sold = $60,750
Therefore, we can write:
[tex]300x + 450y = 60,750[/tex]----------------(2)
Multiplying (1) by 450 and subtracting it from (2) multiplied by 100, we get:
[tex]-150x = 7,500⇒ x = 50[/tex]
Substituting the value of x in (1), we get:
[tex]y = 175 - 50= 125[/tex]
Therefore, the number of GMC sold is 50 and the number of Honda sold is 125.
They have sold 50 GMC and 125 Honda.
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What is the distance between A(7, 4) and B(2, −8)?
Answer:
The distance would 13 square units
Step-by-step explanation:
Well follow the formula
=√(2−1)^2+(2−1)^2
Plug in everything and solve, remeber to follow order of operations