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TransE, RotatE, and QuatE are three popular models used in knowledge graph embeddings. Each model offers unique characteristics and approaches to representing entities and relations in a knowledge graph. In comparing these models, it is important to consider their capabilities in capturing different types of relationships, their expressiveness, and their computational efficiency.

TransE is a simple yet effective model that represents entities and relations as low-dimensional vectors. It assumes that the relation vector can be obtained by translating the entity vectors. This model performs well in capturing one-to-one and many-to-one relations but may struggle with modeling more complex relationships.

RotatE is a rotational model that represents relations as complex rotations in a low-dimensional space. It excels in capturing symmetric, antisymmetric, and asymmetric relations. The rotational nature of RotatE allows it to model diverse relationships accurately.

QuatE is a quaternion-based model that represents entities and relations using quaternions. It captures complex relations by leveraging quaternion algebra and has shown promising results in capturing hierarchical relationships and multi-relational patterns.

In conclusion, the choice between TransE, RotatE, and QuatE depends on the specific requirements of the knowledge graph and the types of relationships it contains. TransE is suitable for simple relationships, RotatE excels in capturing various types of relationships, and QuatE is advantageous for hierarchical relationships and multi-relational patterns. Understanding the strengths and limitations of each model is crucial in selecting the most appropriate one for a given knowledge graph application.

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Answer:

27 x 9^3x = 3^3 x 9^3x = 3^3 x (3^3)^3x = 3^3 x 3^9x = 3 ^3+9x

3^3+9x = 3k

ln(3^3+9x) = ln(3^k)

3+9x(ln3)=k(ln(3))

k= 3(1+3x)/ln(3)

Step-by-step explanation:

ln(x^n) = n(ln(x))

Given :

Two pyramid with same volume .

To Find :

If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B .

Solution :

\(V_a=V_b\)

Volume of pyramid is given by :

\(V=\dfrac{\text{Area of base}\times height}{3}\\\\V=\dfrac{Ah}{3}\)

Now , h'=3h

\(V'_b=\dfrac{Ah'}{3}\\\\V'_b=3\dfrac{Ah}{3}\\\\V'_b=3V_a\)

Therefore , new volume of pyramid B is 3 times the value of pyramid A .

Hence , this is the required solution .

The Radical Form (√x)  ,the solutions to the equation √x - 2 + 4 = x are x = 1 and x = 4.

The equation √x - 2 + 4 = x for x, we can follow these steps:

1. Begin by isolating the radical term (√x) on one side of the equation. Move the constant term (-2) and the linear term (+4) to the other side of the equation:

  √x = x - 4 + 2

2. Simplify the expression on the right side of the equation:

  √x = x - 2

3. Square both sides of the equation to eliminate the square root:

  (√x)^2 = (x - 2)^2

4. Simplify the equation further:

  x = (x - 2)^2

5. Expand the right side of the equation using the square of a binomial:

  x = (x - 2)(x - 2)

  x = x^2 - 2x - 2x + 4

  x = x^2 - 4x + 4

6. Move all terms to one side of the equation to set it equal to zero:

  x^2 - 4x + 4 - x = 0

  x^2 - 5x + 4 = 0

7. Factor the quadratic equation:

  (x - 1)(x - 4) = 0

8. Apply the zero product property and set each factor equal to zero:

  x - 1 = 0   or   x - 4 = 0

9. Solve for x in each equation:

  x = 1   or   x = 4

Therefore, the solutions to the equation √x - 2 + 4 = x are x = 1 and x = 4.

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1) Solving for z

Letting z on the left side, and the other terms on the right side. Lastly, dividing all by 2.

Answer:

0.390625 grams

Step-by-step explanation:

can i get a second opinion on this

Answer:

378

Step-by-step explanation:

To form a 5-letter word from the letters of the word FORMULATED, we need to select 4 letters out of the 9 non-vowel letters (F, R, M, L, T, D), and then append one of the 3 vowels (O, A, E) to the end of the word.

The number of ways to select 4 letters out of the 9 non-vowel letters is given by the combination formula:

C(9, 4) = 9! / (4! * 5!) = 126

For each of these combinations of 4 letters, we can append one of the 3 vowels to form a 5-letter word with a vowel at the end. So the total number of 5-letter words that can be formed is:

126 x 3 = 378

Therefore, there are 378 5-letter words that can be formed from the letters of the word FORMULATED if each word has to have a vowel at the end.

The probability that at least 16 of the 20 people who have a headache experience relief successfully is 0.976.

To find the probability that at least 16 of the 20 people who have a headache experience relief successfully, we can use the binomial probability formula: P(X) = (n choose X) * p^X * (1-p)^(n-X)

Where n is the number of trials, X is the number of successes, and p is the probability of success.
In this case, n = 20, p = 0.8 (since we are given that 80% of people experience relief successfully), and we want to find the probability that X is greater than or equal to 16.

We can calculate this by finding the probability that X is less than or equal to 15, and then subtracting that from 1:
P(X >= 16) = 1 - P(X <= 15)
= 1 - [(20 choose 0) * 0.8^0 * 0.2^20 + (20 choose 1) * 0.8^1 * 0.2^19 + ... + (20 choose 15) * 0.8^15 * 0.2^5]
= 1 - 0.0115
= 0.9885
Therefore, the probability that at least 16 of the 20 people who have a headache experience relief successfully is 0.9885, or 0.989 to three decimal places.

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The differences-of-means ​estimator, denoted by E(Y|X=1) -E(Y|X=0), is an estimator of the causal effect of X on Y because the differences-of-means estimator​ estimates that (A) the change in the expectation of Y as a result of an observation being in the treatment group as opposed to the control group.

So, in the given situation: The differences-of-means estimator estimates the change in the expectation of Y as a result of an observation being in the treatment group as opposed to the control group, and is denoted by E(Y|X=1) -E(Y|X=0).

Therefore, the differences-of-means ​estimator, denoted by E(Y|X=1) -E(Y|X=0), is an estimator of the causal effect of X on Y because the differences-of-means estimator​ estimates that (A) the change in the expectation of Y as a result of an observation being in the treatment group as opposed to the control group.

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The complete question is given below;
Suppose you have a binary randomized controlled experiment designed to measure the causal effect of X on Y. Let the control group be identified by X​ = 0 and the treatment group by X​ = 1.

The differences-of-means ​estimator, denoted by E(Y|X=1) -E(Y|X=0), is an estimator of the causal effect of X on Y because the differences-of-means estimator​ estimates:

A. the change in the expectation of Y as a result of an observation being in the treatment group as opposed to the control group.

B. the expectation of Y for observations within the control group.

C. the expectation of Y for observations within the treatment group.

D. All of the above.

To summarize, the functions f(x) are:

a) f(x) = -1/2 cos(2x) + C
b) f(x) = 2√x + C
c) f(x) = (1/68)(1 + 2x)³⁵ + C
d) f(x) = (1/201)(x² + 1)¹⁰¹ + C

To find a function f such that:

a) f′(x) = sin(2x), we need to integrate the derivative function with respect to x. The function f(x) is given by:

f(x) = ∫sin(2x) dx = -1/2 cos(2x) + C

b) f′(x) = 1/√x, we integrate the derivative function with respect to x:

f(x) = ∫(1/√x) dx = 2√x + C

c) f′(x) = (1 + 2x)³⁴, we integrate the derivative function with respect to x:

f(x) = ∫(1 + 2x)³⁴ dx = (1/68)(1 + 2x)³⁵ + C

d) f′(x) = x(x²+ 1)¹⁰⁰, we integrate the derivative function with respect to x:

f(x) = ∫x(x²+ 1)¹⁰⁰ dx = (1/201)(x² + 1)¹⁰¹ + C

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Answer:

what

Step-by-step explanation:

Given:

The equations of a system of equations are

\(y=-2x^2+3x-1\)

\(x+y=-1\)

To find:

The solution of the given system of equations.

Solution:

We have,

\(y=-2x^2+3x-1\)           ...(i)

\(x+y=-1\)                      ...(ii)

Using (i) and (ii), we get

\(x+(-2x^2+3x-1)=-1\)

\(x-2x^2+3x-1+1=0\)

\(-2x^2+4x=0\)

Taking out the common factors.

\(2x(-x+2)=0\)

Using zero product property,we get

\(2x=0\) and \(-x+2=0\)

\(x=0\) and \(2=x\)

For x=0, we have

\(0+y=-1\)

\(y=-1\)

For x=2, we have

\(2+y=-1\)

\(y=-1-2\)

\(y=-3\)

Therefore, the two solutions of the given system of equations are (0,-1) and (2,-3).

A box with a square base and a top is to be constructed from 10 square meters of material. 40 square meters will maximize the volume that the box can hold.

LSD use among secondary school understudies is a specific concern. More Volume is a proportion of consumed three-layered space. It is frequently evaluated mathematically utilizing SI inferred units or by different supreme units. Volume is characterized as the space involved inside the limits of an article in three-layered space. It is otherwise called the limit of article. Volume is a proportion of consumed three-layered space. It is frequently measured mathematically utilizing the SI determined unit, the cubic meter. The volume of a compartment is by and large comprehended to be the limit of the compartment, how much liquid (gas or fluid) that the holder could hold, instead of how much space the actual holder dislodges. Three layered numerical shapes are additionally relegated volumes.

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David, Jeff, and Paula have (7d)/3 books.

To find out how many books David, Jeff, and Paula have altogether in terms of d, we can use the given information as follows:

1. David has d books.
2. David has 3 times as many books as Jeff, so Jeff has d/3 books.
3. David has the same number of books as Paula, so Paula also has d books.

Now, to find the total number of books for all three of them, we simply add the number of books each person has:

Total books = David's books + Jeff's books + Paula's books
Total books = d + d/3 + d

To combine these terms, we can find a common denominator (in this case, 3):
Total books = (3d + d + 3d) / 3

Now, we can simplify the expression:
Total books = (7d) / 3

So, altogether, David, Jeff, and Paula have (7d)/3 books in terms of d.

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Answer:

x=1

Step-by-step explanation:

The simplified sum of the expression ∑+1=−1 (2 − 1) is 2.

The given expression is the sum of (2 - 1) from i = -1 to n, where n = 1. Therefore, the expression can be simplified as follows:

∑+1=−1 (2 − 1) = (2 - 1) + (2 - 1) = 1 + 1 = 2

In this case, the value of n is 1, which means that the summation will only be performed for i = -1. The expression inside the summation is (2 - 1), which equals 1. Thus, the summation is equal to 1.

Adding 1 to the result of the summation gives:

∑+1=−1 (2 − 1) + 1 = 1 + 1 = 2

Therefore, the simplified sum of the expression ∑+1=−1 (2 − 1) is 2.

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Answer:

100 meters per hour.

Step-by-step explanation:

7,200 seconds / 60 = 120 minutes

120 minutes / 60 = 2 hours

200 meters / 2 hours = 100 meters

Since the squirrel moved 200 meters in 2 hours, the squirrel moved 100 metres per hour.

Answer:

x = 12

Step-by-step explanation:

By answering the presented question, we may conclude that Pythagorean 13.15. Therefore, the measure of the hypotenuse is approximately 13.2 cm

The basic Euclidean geometry relationship between a right triangle's three sides is known as the Pythagorean Theorem. This rule states that the areas of squares with the other two sides added together equal the area of the square with the hypotenuse side. The Pythagorean Theorem states that a right triangle's hypotenuse, which is the side opposite the right angle, equals the sum of its sides. It is sometimes written in general algebraic notation as a² + b² = c.

We can use the Pythagorean theorem to find the length of the hypotenuse of a right triangle:

c² = a² + b²

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

Substituting the given values, we get:

c² = 13² + 2²

c² = 169 + 4

c² = 173

Taking the square root of both sides, we get:

c = √173

Using a calculator, we get

c ≈ 13.15

Rounding to the nearest tenth, we get:

c ≈ 13.2 cm

Therefore, the length of the hypotenuse is approximately 13.2 cm.

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The usefulness of the data include:

Some examples of limitations include:

It should be noted that data and statistics to help them make important policy decisions, to identify problems in an organization, and to predict outcomes.

The limitation include the fact that a limited sample size or lack of reliable data can impact it.

In conclusion, it should be noted that the concept here shows the limitation and the usefulness of the data.

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Forgive me if I got a few wrong in the inches system. From where I am, we use the metric system and different syllabus. There's some answers I'm quite unsure so make sure to check with someone else

Answer:

1. 24 in

2. 30 in.

3. 14/3/13 in

4. 7 in

5. 5in

Step-by-step explanation:

The scale of drawing to the scale of actual model:

1:6

so when the questions ask for actual, we need to x6.

1. actual width of painting = width of drawing x 6

4in x 6 = 24in

2. actual height of painting = height of drawing x 6

5in x 6 = 30in

3. This one you should take 5/6 and x2 since we have two edges so like

5 - 2(5/6) = 3/1/3

4 - 2(5/6) = 2/1/3

so the final equation should be:

3/1/3 + 2/1/3 x 6 (since we are looking for the actual height of H) = 14/3/13 in

4. actual width of H through center = 1inch + 2(1/2)in (because we have 2 vertical parallel) x 6 so:

2(1/2) + 1in x 6 = 7in

5. Look back on Q3,

drawing top edge to top edge of H = drawing left edge to left edge to H = 5/6

so, 5/6 x 6 = 5in

Hope I could help in someway

A machine purchased 8 years ago for $76000 is worth $36000 today, we can calculate the value of the machine 3 years from now.

The exponential decay formula is given by: V = V0 * e^(-kt), where V is the value at time t, V0 is the initial value, k is the decay constant, and t is the time.

To find the decay constant, we can use the given information. Let's denote the decay constant as k. We know that after 8 years, the value of the machine is $36000, so we can set up the equation as follows:

36000 = 76000 * e^(-8k)

To solve for k, we divide both sides of the equation by 76000 and take the natural logarithm of both sides:

ln(36000/76000) = -8k

Simplifying further:

k ≈ 0.1023

Now we can calculate the value of the machine 3 years from now using the formula:

V = 76000 * e^(-0.1023*3)

Calculating this expression, we find that the value of the machine 3 years from now is approximately $48,478.06.

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The system capacity or design life level (DDL) of the stormwater collection system is :

1.616 million gallons per day.

To compute the system capacity or design life level (DDL) for a stormwater collection system with a mean drainage loading of 1.2 million gallons per day (mgd), a standard deviation of 0.4 mgd, a design life of 15 years, and a maximum risk of failure of 0.15 over its design life, follow these steps:

1. Determine the z-score for the maximum risk of failure (0.15) using a standard normal distribution table or calculator. The z-score represents the number of standard deviations away from the mean for a given probability.

2. Since the risk of failure is 0.15, we want to find the z-score associated with the probability of 1 - 0.15 = 0.85. Using a standard normal distribution table or calculator, the z-score for 0.85 is approximately 1.04.

3. Calculate the drainage loading at the design life level (DDL) using the formula: DDL = mean + (z-score × standard deviation).

4. Substitute the given values into the formula: DDL = 1.2 + (1.04 × 0.4) = 1.2 + 0.416 = 1.616 mgd.

So, the system capacity of the stormwater collection system is 1.616 million gallons per day (mgd).

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Mr. Jones saved 1/5 of his wages, which is equivalent to (1/5) * $4800.00 = $960.00.

To calculate how much of his wages was spent, we subtract the amount saved from his total wages. Mr. Jones earned $4800.00 a week and saved $960.00, so the amount spent can be found by subtracting the savings from the total:

Amount spent = Total wages - Amount saved

= $4800.00 - $960.00

= $3840.00.

Therefore, Mr. Jones spent $3840.00 of his wages.

In this scenario, we are given Mr. Jones' weekly earnings of $4800.00. The question asks us to determine how much of his wages were spent, given that he saved 1/5 of his wages. To find the amount saved, we multiply his wages by 1/5, which results in $960.00. To find the amount spent, we subtract the amount saved from the total wages, resulting in $3840.00. This means that Mr. Jones spent $3840.00 of his wages, while the remaining $960.00 was saved.

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Answer:

1. D just find all the surface

2.F same here

Answer:

E and F: (-1.5,2)

F and G: (3,2)

G and E: (1.5,5)

Step-by-step explanation:

a) The midpoint formula is (x2+x1) / 2 , (y2 + y1) / 2. So let's say your two points were (3,1) and (7,4). x2 would be 7 and x1 would be 3. (7 + 3) / 2 = 5. Follow the same steps for (7,4) and you would get (4 + 1) / 2 = 2.5. The middle of your line from (3,1) to (7,4) would be at (5, 2.5)

Use this for all of your points:

E and F: (-1.5,2)

F and G: (3,2)

G and E: (1.5,5)

I didn't have time to do the others but go to GeoGebra for a free graph.

Answer:

44

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

hope this helps

The Gram-Schmidt process can be used to find an orthonormal basis for the subspace of R4 spanned by the given vectors x1, x2, and x3.

The Gram-Schmidt process is a method to orthogonalize a set of vectors. To find an orthonormal basis for the subspace of R4 spanned by x1, x2, and x3, we start by selecting the first vector, x1, as our initial basis vector. To make it orthonormal, we normalize it by dividing it by its magnitude, giving us the first orthonormal vector, u1.

Next, we consider the second vector, x2. We subtract the projection of x2 onto u1 from x2 itself, yielding a new vector, v2. Then, we normalize v2 to obtain the second orthonormal vector, u2.

Moving on to the third vector, x3, we subtract its projections onto both u1 and u2 from x3, resulting in a new vector, v3. Normalizing v3 gives us the third orthonormal vector, u3.

Finally, the orthonormal basis for the subspace of R4 spanned by x1, x2, and x3 is given by u1, u2, and u3.

Therefore, using the Gram-Schmidt process, we can find an orthonormal basis for the subspace of R4 spanned by x1 = (4, 2, 2, 1)T, x2 = (2, 0, 0, 2)T, and x3 = (1, 1, -1, 1)T.

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Greetings.

The answer is y = -2.

Explanation:

The equation is defined to solve for y-term. Our y is currently our subject at this point and needs to be solved.

We move -3 to another side and leave y as the subject of equation. Moving to another side will change the sign/operator to opposite.

Plus ---> Minus

Minus ---> Plus

Multiply ---> Divide

Divide ----> Multiply

\(y-3=-5\\y=-5+3\\y=-2\)

Hope this helps! :)