Lemma 1 Let g = (V, E, w) be a weighted, directed graph with designated root r e V. Let E' = {me(u): u E (V \ {r})}. Then, either T = (V, E') is an RDMST of g rooted at r or T contains a cycle. Lemma 2 Let g = (V, E, w) be a weighted, directed graph with designated root reV. Consider the weight function w': E → R+ defined as follows for each edge e = (u, v): w'le) = w(e) - m(u). Then, T = (V, E') is an RDMST of g = (V, E, W) rooted at r if and only if T is an RDMST of g = (V, E, w') rooted at r.
Lemma 1 states that in a weighted, directed graph with a designated root, if we create a new set of edges E' by removing edges from the root to each vertex except itself.
Lemma 1 introduces the concept of an RDMST (Rooted Directed Minimum Spanning Tree) in a weighted, directed graph and highlights the relationship between the set of edges E' and the existence of cycles in the resulting graph T. It states that if T is not an RDMST, it must contain a cycle, indicating that removing certain edges from the root to other vertices can lead to cycles.
Lemma 2 focuses on the weight function w' and its impact on determining an RDMST. It states that the resulting graph T is an RDMST rooted at the designated root in the original graph if and only if it is an RDMST rooted at the designated root in the graph with the modified weight function w'. This lemma demonstrates that adjusting the weights of the edges based on the weights of the vertices preserves the property of being an RDMST.
Overall, these two lemmas provide insights into the properties and characteristics of RDMSTs in weighted, directed graphs and offer a foundation for understanding their existence and construction.
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Please help me with this
Answer:
x=8
Step-by-step explanation:
The ratio of a side of PQRS to the corresponding side in TUVW. is 6:4=3:2.
The ratio of RS:VW=3:2. RS=12, and VW=x. 12:x=3:2. 3 multiplied by 4 is 12, so 2 multiplied by 4 is x. So, the makes x=8.
Question is in picture
Answer: 1.7
Step-by-step explanation: We can use the pythagorean theorem!
A² + B² = C²
1² + B² = 2²
1 + B² = 4
4 - 1 = B²
3 = B²
√3 = B
1.7 = B
Hope this helps :)
Solve for x , assume all segments that appear tangent are tangent.
Answer:
Step-by-step explanation:
x = 5
The value of x in the given angle is 5.
What is circle?A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent. A circle is also known as the location of points that are evenly spaced apart from the centre. The radius of a circle is measured from the centre to the edge.
Labelling the figure,
We have,
Measure of complete angle of circle = 360 degree
∠ABC = 360 - (81 + 74)
= 205 degree
Now from figure,
∠APE = (205 - 81 )/2
= 62 degree
Since we know that,
∠APE = 17x - 23
Therefore,
17x - 23 = 62
17x = 85
x = 5 degree,
Hence,
Required value is 5.
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Is (2, 3) a solution to the equation y = x - 1?
yes or no
and pls explain for i can lead this already
Answer: No
Step-by-step explanation: Because if you substitute the 2 for x and 3 for y it is not equal
9. Let H be the set of all vectors of the form 3s. Find a 2s vector v in R3 such that H that H is a subspace of IR 3? Span {v). Why does this show 2t 10. Let H be the set of all vectors of the form 0.Show that H is a subspace of R3. (U'se the method of Exercise 9.) 11. Let W be the set of ali vectors of the formb where b and c are arbitrary. Find vectors u and v such that W Span (u, v. Why does this show that W is a subspace of R3? St 2s-t 4t 12 Let W be the set of all vectors of the form Show that W is a subspace of R4. (Use the method/of Exercise 11.)
9. H is a subspace of R3 as it contains a 2s vector [0, 2s, 0].
10. H is a subspace of R3 as it consists of the zero vector [0, 0, 0].
11. W is a subspace of R3 as it is spanned by the vectors [1,0,0] and [1,1,0].
12.W is a subspace of R4 as it is spanned by the vectors [1,2,0,0] and [0,-1,4,0].
9. To find a 2s vector v in R3 such that H is a subspace of R3, we can choose v = [0, 2s, 0]. This vector satisfies the condition of H being a subspace since it is of the form 2s, and any scalar multiple of v will also be of the form 2s, which is within H. Therefore, H is a subspace of R3.
0. Let H be the set of all vectors of the form [0, 0, 0]. To show that H is a subspace of R3, we can use the method from Exercise 9. By choosing v = [0, 0, 0],
we can see that H is closed under scalar multiplication and addition, as any scalar multiple or sum of the zero vector will still result in the zero vector. Therefore, H is a subspace of R3.
11. Let W be the set of all vectors of the form [b, c, 0], where b and c are arbitrary. To show that W is a subspace of R3, we need to find vectors u and v such that W is spanned by (u, v).
We can choose u = [1, 0, 0] and v = [0, 1, 0]. Any vector in W can be expressed as a linear combination of u and v, and therefore W is spanned by (u, v). This shows that W is a subspace of R3.
12. Let W be the set of all vectors of the form [s, 2s - t, 4t] in R4. To show that W is a subspace of R4, we can use the method from Exercise 11. By choosing u = [1, 2, 0, 0] and v = [0, -1, 4, 0],
we can observe that any vector in W can be expressed as a linear combination of u and v. Hence, W is spanned by (u, v), indicating that W is a subspace of R4.
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Nita is making pizza.
She needs 3/4 cup of cheese to make one whole pizza .
She has 3/8
Nita can make exactly one whole pizza or less than or more than
Answer:
Less than
Step-by-step explanation:
To see how 3/4 compares to 3/8, give em the same denominator. The simplest way is to multiply 3/4 by 2. Multiply each the numerator and denominator by 2. That gives you 6/8. She needs 6/8 but only has 3/8, so less than a pizza.
Solve the initial value problem below using the method of Laplace transforms. y" - 12y' + 72y = 40 e 4 y(0) = 1, y'(0) = 10
To solve the given initial value problem using the method of Laplace transforms, we need to perform the following steps:
Step 1: Take the Laplace transform of both sides of the given differential equation.
Step 2: Solve for the Laplace transform of y.
Step 3: Take the inverse Laplace transform to obtain y.
Step 4: Use the initial conditions to find the constants in the solution obtained in Step 3.1.
Taking the Laplace transform of both sides of the given differential equation: L{y" - 12y' + 72y} = L{40e⁴}L{y" - 12y' + 72y} = 40L{e⁴}.
Taking Laplace transform of y" term L{y"} - 12L{y'} + 72L{y} = 40L{e⁴}.
Using the Laplace transform property of derivatives,
we get:s²Y(s) - sy(0) - y'(0) - 12[sY(s) - y(0)] + 72Y(s) = 40/(s - 4)
Simplifying the above equation, we get: s²Y(s) - s - 10 - 12sY(s) + 12 + 72Y(s) = 40/(s - 4)⇒ s²Y(s) - 12sY(s) + 72Y(s) = 40/(s - 4) + s + 2
Using partial fraction decomposition, we can write the right-hand side of the above equation as:40/(s - 4) + s + 2 = [10/(s - 4)] - [10/(s - 4)²] + s + 2
Now, the given equation becomes:
s²Y(s) - 12sY(s) + 72Y(s) = [10/(s - 4)] - [10/(s - 4)²] + s + 2
Taking the Laplace transform of y(0) = 1 and y'(0) = 10, we get: Y(s) = (10s + 2 + 1)/[s² - 12s + 72]
Applying partial fraction decomposition to find Y(s),
we get: Y(s) = [3/(s - 6)] - [1/(s - 6)²] + [7/(s - 6)²] + [1/(s - 6)]
Taking the inverse Laplace transform of Y(s), we get: y(t) = [3e⁶t - 3te⁶t + 7te⁶t + e⁶t]
Using the initial conditions y(0) = 1 and y'(0) = 10, we get: y(0) = 1 = 1 + 0 + 0 + 1, y'(0) = 10 = 18 - 3 + 7 + 1
Therefore, the solution to the given initial value problem is: y(t) = [3e⁶t - 3te⁶t + 7te⁶t + e⁶t]
Answer: y(t) = [3e⁶t - 3te⁶t + 7te⁶t + e⁶t]
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Consider the matrix A. A- Find the characteristic polynomial for the matrix A. (Write your answer in terms of 2) (1-x)(2²) Find the real eigenvalues for the matrix A
The characteristic polynomial for matrix A is (1-x)(2²), and the real eigenvalues for matrix A are 1 and 2.The characteristic polynomial for the matrix A can be written as (1-x)(2²), where x is the eigenvalue.
The real eigenvalues for matrix A can be found by setting the characteristic polynomial equal to zero and solving for x. Since the characteristic polynomial is a product of linear factors, the eigenvalues are the values of x that make each factor equal to zero.
In this case, we have two factors: (1-x) and (2²). Setting each factor equal to zero, we find that x = 1 and x = 2 are the real eigenvalues for matrix A.
To summarize, the characteristic polynomial for matrix A is (1-x)(2²), and the real eigenvalues are 1 and 2. The characteristic polynomial captures the relationship between the eigenvalues and the matrix A, while the real eigenvalues represent the values for which the matrix A has corresponding eigenvectors.
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PLZ HELP IM BEING TIMED GIVING BRAINLIEST
Using the square root property solve (a - 10)² = 121
Answer:
21
Step-by-step explanation:
We know that the sqaure root of 121 = 11.
So, A - 10 = 11
=> A = 21
Answer:
a = -1 or a = 21
Step-by-step explanation:
take square root of each side to get:
a - 10 = [tex]\sqrt{121}[/tex]
a - 10 = 11; a = 21
a - 10 = -11; a = -1
can someone actually help me with this please!
Answer:
y = -2x + 7
Step-by-step explanation:
When 2 lines are perpendicular, the relationship between their slopes m1 and m2 may be stated as
m1m2 = -1
Given the line
y = 1/2 x + 8
Comparing with the general equation of a line y = mx + c where m is the slope and c is the intercept
m = m1 = 1/2
Hence the slope of the perpendicular line m2
= -1/1/2
= -2
Given that the line passes through the points (1,5)
using the equation
y - y1 = m (x - x1)
y - 5 = -2(x - 1)
y = -2x +2 + 5
y = -2x + 7
1.) A ball of radius 14 has a round hole of radius 8 drilled through its center. Find the volume of the resulting solid.
2.) Find the volume of the solid obtained by rotating the region enclosed by the graphs of y=9/x2 and y=10-x2 and about the line y=-9
The volume of the solid can be calculated as: V = 2π ∫[c,d] x * (h(x) + 9) dx.
To find the volume of the resulting solid, we can subtract the volume of the hole from the volume of the ball.
The volume of the ball can be calculated using the formula for the volume of a sphere: V_ball = (4/3) * π * r^3, where r is the radius of the ball. In this case, the radius of the ball is 14, so we have: V_ball = (4/3) * π * 14^3.
The volume of the hole can be calculated using the formula for the volume of a cylinder: V_hole = π * r^2 * h, where r is the radius of the hole and h is the height of the hole. In this case, the radius of the hole is 8, and since it passes through the center of the ball, the height of the hole is equal to the diameter of the ball, which is 2 * 14. So we have: V_hole = π * 8^2 * (2 * 14).
The volume of the resulting solid is then given by: V_result = V_ball - V_hole.
To find the volume of the solid obtained by rotating the region enclosed by the graphs of y=9/x^2 and y=10-x^2 about the line y=-9, we can use the method of cylindrical shells.
The volume of a solid obtained by rotating a curve around a line is given by the formula: V = 2π ∫[a,b] x * h(x) dx, where a and b are the x-values where the curves intersect, and h(x) is the distance between the line of rotation and the curve at each x-value.
In this case, the curves y = 9/x^2 and y = 10 - x^2 intersect at two points, let's say x = c and x = d. The line of rotation y = -9 is parallel to the x-axis and is located 9 units below it.
The volume of the solid can be calculated as: V = 2π ∫[c,d] x * (h(x) + 9) dx.
To find the values of c and d, we need to solve the equation 9/x^2 = 10 - x^2. Once we have the values of c and d, we can evaluate the integral to find the volume of the solid.
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16. Max is sitting in the stands at the baseball stadium. He catches a
and decides to throw it back to a player standing on first base. If the
horizontal distance from Max to the player is 61 feet and the ball travels 76
feet, what is the angle of depression from Max to the player?
Gina Wilson (All Things Algebra), 2016
A Food Marketing Institute found that 27% of households spend more than $125 a week on groceries. Assume the population proportion is 0.27 and a simple random sample of 467 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.29? Answer =
Probability that "sample-proportion" of "households-spending" more than $125 per-week is less than 0.29 is 0.8340.
In order to calculate the probability that the sample-proportion of households spending more than $125 a week is less than 0.29, we use the sampling-distribution of sample-proportions, assuming the sample was selected using simple random sampling.
The Population-proportion (p) is = 0.27
Sample-size (n) is = 467,
Sample-proportion (p') is = 0.29,
To calculate the probability, we find the z-score corresponding to the sample proportion and then find the probability,
The formula to calculate the z-score is:
z = (p' - p)/√((p × (1 - p))/n),
Substituting the values,
We get,
z = (0.29 - 0.27)/√((0.27 × (1 - 0.27))/467),
z = 0.02/√((0.27 × 0.73) / 467),
z ≈ 0.97
We know that the probability associated with a z-score of 0.97 is 0.8340.
Therefore, the required probability is 0.8340.
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Solve for xx to the nearest tenth.
Answer:
in right angled triangleBCD
BC=√{DC²-BC²)=√{10²-6²)=8
again in right angled triangle ABC
AB=√(BC²-AC²)
x=√(8²-7²)=3.87
If m3 is 52°, what is the measure of its vertical angle?
A.
128°
B.
38°
C.
52°
D.
142°
i need answer asap!
Answer:
C. 52 degrees
Step-by-step explanation:
Vertical angles share the same angle of measure.
18
A fruit salad was prepared containing 100 g of
acerola cherries, 100 g of kiwifruit, 300 g of
pineapple, and 200 g of strawberries. What is the
total amount of vitamin C, in grams, that is
contained in the listed fruits?
A)0.7g
B)2.069g
C)700g
D)2069g
Can you answer it right now pls
Answer:
4 times 10 to the negative seventh power
Step-by-step explanation:
We can see that the decimal has 6 zeros before it, and then it’s 4.
since there are 7 digits after the decimal point, we put 10 to the negative seventh power.
that gives us 0.0000001
to get 0.0000004, we need to multiply ten to the negative seventh power (0.0000001) by 4
The answer is a. which is 4 x 10‐⁷
GIVING BRAINLIST ANYONE WHO CAN SOLVE ANY OF THEM!!!!
Answer:
x=36
x=127
x=36
Answer:
1. 36
2. 127
3. x = 36
Step-by-step explanation:
A line is 180 degrees.
1. 180 - 144 = 36
2. 38 + 15 = 53, 180 - 53 = 127
3. 180 - 92 = 88, 88 - 16 = 72, 72 ÷ 2 = 36
The areas of the squares adjacent to two sides of a right triangle are shown below. What is the area of the squares adjacent to the third side of the triangle
Answer:
11 square units
Step-by-step explanation:
Find the diagram attached
First we need to find the side length of the square with known areas.
Area of a square = L²
L is the side length of the square
For the green square
44 = L²
Lg = √44
For the purple square
Ap = Lp²
33 = Lp²
Lp = √33
Get the length (L) of the unknown square using pythagoras theorem;
Lg² = L²+Lp²
(√44)² = L²+(√33)²
44 = L²+33
L² = 44-33
L² = 11
Since Al = L²
Hence the area of the square adjacent to the third side of the triangle is 11 square units
Mega Electronics Stores accepts any return for items bought within two weeks. The daily number of items returned follows a normal distribution with mean C and standard deviation 40.
C=260
What is the probability that fewer than 165 items are returned on a given day?
The required probability is 0.0087 (approximately).Note: The probability is less than 0.05. Hence, we can say that the event is rare.
C = 260 (mean)Standard deviation, σ = 40Let X be the number of items returned on a given day.As the number of items returned follows a normal distribution with mean C and standard deviation 40,Therefore,X ~ N (260, 40^2)We have to find the probability that fewer than 165 items are returned on a given day.i.e. P (X < 165).
We can find the standard score, z as follows.z = (X - μ) / σz = (165 - 260) / 40z = -2.375Now, we can find the probability as follows.P (X < 165) = P (Z < -2.375) = 0.0087 (approximately)Therefore, the required probability is 0.0087 (approximately).Note: The probability is less than 0.05. Hence, we can say that the event is rare.
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please help! no links please!
The value of x is: 75°
360° - 128° - 85° - 72° = 75°
-6x-27=6
give me the answer please .
Answer:
-5.5
Step-by-step explanation:
-6x - 27 = 6
+ 27 +27
-6x = 33
÷-6 ÷-6
x = - 5.5
I am pretty sure the awnser is -5.5 because -6 Multiplied by -5.5 Is 33. 33 minus 27 is 6
Find the missing side. round to the nearest tenth.
Answer:
14.6
Step-by-step explanation:
Sin (59) = x/17
17*sin (59) = x
17*0.857=14.57
The value of x in the triangle is x = 14.581
We have,
From the triangle,
using the sin function.
Now,
sin = perpendicular/hypotenuse
So,
sin 59 = x/17
Now,
To solve for x in the equation sin(59°) = x/17, we can use the properties of trigonometric functions and algebraic manipulation.
First, let's isolate x by multiplying both sides of the equation by 17:
17 x sin(59°) = x
Using a calculator to evaluate sin(59°), we find:
17 x 0.857167 = x
Therefore,
The value of x is x = 14.581
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T/F. If isometry a interchanges distinct points P and Q, then a fixes the midpoint of P and Q.
False. If an isometry interchanges distinct points P and Q, it does not necessarily fix the midpoint of P and Q. In general, an isometry is a transformation that preserves distances between points.
However, it does not guarantee that the midpoint of two interchanged points will be fixed. Consider a simple example of a reflection about a line passing through the midpoint of P and Q. This is an isometry that interchanges P and Q but does not fix their midpoint. The midpoint would be mapped to a different point under the reflection transformation.
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Is it 10? Or no pls explain
Answer:
Yes
Step-by-step explanation:
6 + 10 would equal 16
You're right, have a great day!
Answer:
yes, it is 10
Step-by-step explanation:
Subtract 16 and 6 and you get 10.
Or Subtract 6 and 6 and subtract 16 and 6.
It'll still be 10 no matter what.
Some pls help me I’ll give out brainliest please dont answer if you don’t know
Answer:
−
8
n
+
24
Step-by-step explanation:
What's the greatest common factor 25x^2 and 100x^4y^2
Answer:
I D K
Step-by-step explanation:
answer this please
don't send a link
Answer:
Supplementary angles
Step-by-step explanation:
AEB and BEC form a straight line.
They add to 180 degrees
AEB+ BEC
150+30
180
That means that they are supplementary angles
Answer: https://www.wattpad.com/story/73852998-feathers-itachi-uchiha-deidara-x-reader-lemon
Step-by-step explanation:
20, 17, 14
Write donn
the
4 th
term
Answer:
11
Step-by-step explanation:
you subtract 3 every time, so 14-3 = 11