a. 135
b. 120
c. 144
d. 108

Answer:

4 < x < 14

Step-by-step explanation:

................

Answer:8

Step-by-step explanation:because let's put in x first before anything so thats 2 times 2 thats 4 then you can do 4+4 to equal 8

so the answer is 8=y

hope this helps :}

Develop similarity measures by applying the Jaccard index formula to the membership degrees of the fuzzy sets and use these measures for clustering objects based on their fuzzy characteristics.

The question is asking about new similarity measures of intuitionistic fuzzy sets based on the Jaccard index and their application to clustering.

To answer the question, first, let's understand what fuzzy sets and clustering are. Fuzzy sets are a generalization of classical sets where an element can have a degree of membership ranging between 0 and 1. Clustering, on the other hand, is a technique used to group similar objects together based on their characteristics.

Now, the question specifically mentions the Jaccard index as a basis for similarity measures. The Jaccard index is a measure of similarity between two sets, which is calculated as the ratio of the intersection of the sets to the union of the sets.

To develop new similarity measures for intuitionistic fuzzy sets based on the Jaccard index, you can apply the Jaccard index formula to compare the membership degrees of the elements in the fuzzy sets. The resulting similarity measure will provide a quantitative value indicating the degree of similarity between the sets.

These new similarity measures can then be applied to clustering. In clustering, the similarity measures between objects are used to determine the groupings. By utilizing the Jaccard index-based similarity measures for intuitionistic fuzzy sets, you can cluster objects based on their fuzzy characteristics and similarities.

In summary, the question asks about new similarity measures of intuitionistic fuzzy sets based on the Jaccard index and their application to clustering. To answer this, you can develop similarity measures by applying the Jaccard index formula to the membership degrees of the fuzzy sets and use these measures for clustering objects based on their fuzzy characteristics.

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Using integration by parts,

a) ∫x cosh²x dx = (1/2)(x sinh2x/2) - (1/4)(sinh2x/2) + (1/2)x + C.

b) ∫\(cosh(x)^{(-1)\) dx = x \(cosh(x)^{(-1)\) + ln|sinh(x)| + C.

c) ∫z \(tanh^{(-1)\)(x) dx = z \(tanh^{(-1)\)(x) - z arctan(x) + C.

a) ∫x cosh²x dx:

To solve this integral using integration by parts, we need to choose u and dv. Let's set u = x and dv = cosh²x dx.

Taking the derivatives, du = dx and integrating dv, we get:

v = ∫cosh²x dx.

To find v, we can rewrite cosh²x using the identity cosh²x = (cosh2x + 1)/2:

v = ∫(cosh2x + 1)/2 dx.

Splitting the integral, we have:

v = (1/2)∫cosh2x dx + (1/2)∫dx.

Now, we can evaluate the two integrals separately:

v = (1/2)∫cosh2x dx + (1/2)∫dx = (1/2)(sinh2x/2) + (1/2)x + C,

where C is the constant of integration.

Now, using the integration by parts formula:

∫u dv = uv - ∫v du,

we can substitute u, v, and dv back into the formula:

∫x cosh²x dx = (1/2)(x sinh2x/2) - (1/4)(sinh2x/2) + (1/2)x + C.

So, the solution to the integral is:

∫x cosh²x dx = (1/2)(x sinh2x/2) - (1/4)(sinh2x/2) + (1/2)x + C.

b) ∫\(cosh(x)^{(-1)\) dx:

To solve this integral using integration by parts, we need to choose u and dv. Let's set u = \(cosh(x)^{(-1)\) and dv = dx.

Taking the derivatives, du = -sinh(x)\(cosh(x)^{(-2)\) dx and integrating dv, we get:

v = ∫dx = x.

Using the integration by parts formula:

∫u dv = uv - ∫v du,

we can substitute u, v, and dv back into the formula:

∫\(cosh(x)^{(-1)\) dx = x \(cosh(x)^{(-1)\) - ∫(-sinh(x)\(cosh(x)^{(-2)\) dx).

Simplifying the integral on the right side, we have:

∫\(cosh(x)^{(-1)\) dx = x \(cosh(x)^{(-1)\) + ∫sinh(x)\(cosh(x)^{(-2)\) dx.

The integral on the right side can be rewritten as:

∫sinh(x)\(cosh(x)^{(-2)\) dx = ∫(1/cosh(x)) d(sinh(x)).

Using the substitution u = sinh(x), du = cosh(x) dx, the integral becomes:

∫(1/cosh(x)) d(sinh(x)) = ∫(1/u) du = ln|u| + C = ln|sinh(x)| + C.

Therefore, the solution to the integral is:

∫\(cosh(x)^{(-1)\) dx = x \(cosh(x)^{(-1)\) + ln|sinh(x)| + C.

c) ∫z \(tanh^{(-1)\)(x) dx:

To solve this integral using integration by parts, we need to choose u and dv. Let's set u = \(tanh^{(-1)\)(x) and dv = dz.

Taking the derivatives, du = (1/1+x²) dx and integrating dv, we get:

v = ∫dz = z.

Using the integration by parts formula:

∫u dv = uv - ∫v du,

we can substitute u, v, and dv back into the formula:

∫z \(tanh^{(-1)\)(x) dx = z \(tanh^{(-1)\)(x) - ∫(z/1+x²) dx.

The integral on the right side can be evaluated as:

∫(z/1+x²) dx = z arctan(x) + C.

Therefore, the solution to the integral is:

∫z \(tanh^{(-1)\)(x) dx = z \(tanh^{(-1)\)(x) - z arctan(x) + C.

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Answer:

9.28

Step-by-step explanation:

hope this help!!!

Answer:

Step-by-step explanation:

Half life means the period after which the material will have only 50% of it left, as if by magic.

Half life is given as 12 hours, so 24 hours is twice half-life.

If we start with 96 grams, after 12 hours, there will be 48 grams left.

After another 12 hours, (total of 24 hours), only half is left, namely 24 grams.

Answer:

(r-4)(r+5)

Step-by-step explanation:

r^2+r-20

(r-4)(r+5)

The solution to the expression given as 5x + 3y > 12 has the ordered pair of (3, 0)

From the question, we have the following inequality that can be used in our computation:

5x + 3y > 12

Solving further, we need to collect the like terms

So, the expression becomes

3y > 12 - 5x

Next, we divide through the inequality by 3

So, we have the following representation

y > 12/3 - 5/3x

Evaluate

The equation becomes

y > 4 - 5/3x

At this point, we assume any value for x and then solve for y

Assume that the value of x is 3

So, we have the following representation

y > 4 - 5/3 * 3

Evaluate the products

y > -1

A value greater than -1 is 0

So, we have

x = 3 and y = 0

Express as ordered pairs

(x, y) = (3, 0)

Hence, the ordered pair of the solution is (3, 0)

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Answer:

Let C be the position of the meteorological station, B the position of the balloon and CB be the cable.

Let the height of the balloon from the ground be AB=hmetres.

In a right angled triangle ACB

BC

AB

=sin60

∘

⇒

200

h

=

2

3

since

sin60

∘

=

2

3

⇒h=200×

2

3

⇒h=100

3

∴h=100×1.732=173.2 since

3

=1.732

Hence, the height of the balloon above the ground is 173.2m

By inscribing the given information in a right triangle, we will see that the ballon is 167.7 meters above the ground.

Think in the situation as in a right triangle, you have a hypotenuse that is equal to the length of the cable, you know one angle of 57°, and the opposite cathetus to this angle represents the height at which the ballon is, this is what we want to find.

Using the relation:

sin(θ) = (opposite cathetus)/hypotenuse.

Where:

Replacing that we get:

sin(57°) = height/200m

sin(57°)*200m = height = 167.7m

So the balloon is 167.7 meters above the ground.

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Answer: A (3, -4)

Step-by-step explanation:

A minimum is at the lowest point on the parabola. The minimum and maximum can be seen by looking at the vertex.

If you go right 3 spaces on the x-axis horizontally, then down 4 spaces vertically on the y-axis you get (3, -4).

4 is negative because you are going down below the x-axis.

The point that is three-sevenths of the distance from (4, -5) to (-4, -2) on the line joining them is (4/7, -26/7).

To find the point that is three-sevenths of the distance from the first point to the second point on the line joining (4, -5) and (-4, -2), we can use the concept of linear interpolation.

Let's calculate the distance between the two points first:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using the coordinates: (x1, y1) = (4, -5) and (x2, y2) = (-4, -2)

Distance = sqrt((-4 - 4)^2 + (-2 - (-5))^2)

= sqrt((-8)^2 + (3)^2)

= sqrt(64 + 9)

= sqrt(73)

Now, we can find the point that is three-sevenths of this distance from the first point.

Three-sevenths of the distance = (3/7) * sqrt(73)

To find the coordinates of this point, we need to determine the direction of the line. We can subtract the coordinates of the first point from the second point to get the direction vector:

Direction vector = (x2 - x1, y2 - y1)

= (-4 - 4, -2 - (-5))

= (-8, 3)

Now, we can calculate the coordinates of the desired point by multiplying the direction vector by the fraction and adding it to the coordinates of the first point:

Point = (x1, y1) + (3/7) * Direction vector

Point = (4, -5) + (3/7) * (-8, 3)

= (4, -5) + (-24/7, 9/7)

= (4 - 24/7, -5 + 9/7)

= (28/7 - 24/7, -35/7 + 9/7)

= (4/7, -26/7)

Therefore, the point that is three-sevenths of the distance from (4, -5) to (-4, -2) on the line joining them is (4/7, -26/7).

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Answer:

19.2 inches

Step-by-step explanation:

6.1 + 6.1 + 7 = 12.2 + 7 = 19.2

perimeter is the outside distance of the shape so you don't need to know the altitude (or height) equals 5.

Answer:

169.59

Step-by-step explanation:

Solution,

Radius(r)=3

Height (h)=6

Volume of cylinder= pi r^2 h

= 3.14*(3)^2*6

= 3.14*9*6

=169.56 units^3

Hope it helps

Good luck on your assignment

Answer: Y = -3x

Step-by-step explanation:not needed

Answer:

the answer is c

Step-by-step explanation:

2+2=4-1 that three quik mathsss

Answer:

Well think about it

12 rolls is alredy out science they are asking about 16 roles 320 divided by 16 is 20 . so , the server brought 20 cases of paper towel containing 16 rolls .

Answer:

x = 3.464

Step-by-step explanation:

7x^2 - 84 = 0

7x^2 = 84

x^2 = 12

x= 3.464

If a television network wants to find out what people think about its new Friday-night show and decides to survey 250 people who watch this program then this group represent sample of the population.

Given that it is decided to survey 250 people who watches the program.

We are required to tell what the group represent in this research.

If it is decided to survey 250 people who watches this program then the group represent a sample of the population.

Sample is nothing but a small or large part of population that represents the characteristics of the population in which the researcher wants to find new things.

Hence if a television network wants to find out what people think about its new Friday-night show and decides to survey 250 people who watch this program then this group represent sample of the population.

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I assume you meant h(t) = 160t - 16t^2, as h(t) = 160t - 16t2 has no maximum.

There's two ways of solving this:

(i) By completing the square and finding the maximum turning point.

(ii) By using Calculus methods to find derivative and equating it to 0 in order to find maximum turning point.

(i) h(t) = 160t - 16t^2

h(t) = -16t^2 +160t

h(t) = -16(t^2-10t) (by taking out a common factor of -16)

h(t) = -16[(t-5)^2 - 25] (by completing the square)

h(t) = -16(t-5)^2 + 400 (on multiplying out by -16)

From this we see that the turning point is at (5;400), therefore the maximum height is 400 feet and is reached after 5 seconds.

Or...

(ii) h(t) = 160t - 16t^2

h`(t) = 160 - 32t (where h`(t) = derivative of h(t))

Now to find maximum of h(t), we set h`(t) = 0 and solve for t:

0 = 160 - 32t (on substituting h`(t) = 0)

32t = 160 (on solving for t)

t = 160/32 (on dividing both sides by 5)

t= 5

Now we have found that at 5 seconds, we will reach our maximum height. So to find this maximum height, we'll have to substitute t=5 into h(t) = 160t - 16t^2.

h(5) = 160(5) -16(5)^2

h(5) = 800 - 400

h(5) = 400 feet

So, once again we have shown that maximum height is 400 feet and is reached after 5 seconds.

The minimal score for admission is 628 and the mean blood pressure of patients is 155.

b) The minimal score for admission is the score which is located in the top 10% of the distribution. The score will be located at the 90th percentile. Since the scores are normally distributed, we can use the z-score to calculate the corresponding score at the 90th percentile.

The z-score at the 90th percentile is 1.28. Therefore, the minimal score for admission would be 500+1.28×100 = 628.

c) Since only 8% of patients exceed 140, the mean blood pressure of patients will be located at the 92nd percentile. Therefore, we can use the z-score to calculate the corresponding score at the 92nd percentile.

The z-score at the 92nd percentile is 1.5. Therefore, the mean blood pressure of patients would be 140+1.5×10 = 155.

Therefore, the minimal score for admission is 628 and the mean blood pressure of patients is 155.

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Step-by-step explanation:

x² - 9

1. There is no common factor other than 1.

2. √x² = x; √9 = 3

3. a = x; b = 3

4. x² - 9 = (x - 3)(x + 3)

Answer:

27

Step-by-step explanation:

First, lets write this down, 36 x 75%, then lets convert the percent: 36 x .75, multiply! And we get 27.

Answer:

\(\huge\boxed{\sf 27\ teachers}\)

Step-by-step explanation:

Total Teachers in the meeting = 36

First-year teachers = 75 % of 36

We know that:

[ "of" means to "multiply" ]

[ % means out of 100 ]

So,

= \(\frac{75}{100} * 36\)

= \(\frac{3}{4} * 36\)

= 3 * 9

= 27 teachers

\(\rule[225]{225}{2}\)

Hope this helped!

Answer:

(0, 2.5)

Step-by-step explanation:

Well we substitute y-y into x in the following equation,

2x + 4y = 10

2(y-y) + 4y = 10

2y - 2y + 4y = 10

Combine like terms

2y - 2y = 0

4y = 10

10/4

y = 2.5

If y is 2.5 we can plug those into y.

2x + 4(2.5) =10

2x + 10 = 10

-10

2x = 0

0/2

x = 0

Answer:

$2800

Step-by-step explanation:

Since we know that a tank with a diameter of 6m costs $700 to fill, we just need to figure out the equivalent values for when the tank is 24m. To do so, since 24 is 4 times 6, we multiply the cost by 4 as well, to get $2800.

The bill for a person who uses 560 kWh in a month is (d) $74

The function is given as:

For a person who uses 560 kWh, it means that:

x > 360

So, we use the following function to determine the bill

b(x) = 0.10(x - 360) + 54

Substitute 560 for x

b(560) = 0.10(560 - 360) + 54

Evaluate

b(560) = 74

Hence, the bill for a person who uses 560 kWh in a month is (d) $74

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The correct inequality symbol that makes the statement true is:

1000 < (6²)³.

The inequality symbols, and their meaning, are presented as follows:

In the context of this problem, the numbers being compared are presented as follows:

1000 and (6²)³.

The power of power property of a number with multiple exponents means that the base is kept while the exponents are multiplied.

The number in which this property is applied in this problem is (6²)³, in which:

Hence the equivalent number is given as follows:

(6²)³ = 6^6 = 6 x 6 x 6 x 6 x 6 x 6 = 46,656

Which is a greater number than 1,000, meaning that 1,000 is less than the number, and the inequality is:

1000 < (6²)³.

The problem is given by the image at the end of the answer.

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Using the chain rule, Therefore, f'(0) = 2.

Using the chain rule, we can take the derivative of both sides of the equation f(x) = f(g(x)) to obtain :

f'(x) = f'(g(x)) * g'(x)

substitute x = 0, we get:

f'(0) = f'(g(0)) * g'(0)

We are given that g(0) = -2 and g'(0) = 3. Therefore, we need to find g(0) and g'(0) in order to determine f'(0).

To do this, we can use the fact that f(x) = f(g(x)). Substituting x = 0 into this equation, we get:

f(0) = f(g(0))

Since f(-2) = 2, we have:

f(g(0)) = f(-2)

Using the chain rule, we can take the derivative of both sides of the equation f(x) = f(g(x)) with respect to x to obtain:

f'(x) = f'(g(x)) * g'(x)

substitute x = -2, we get:

f'(-2) = f'(g(-2)) * g'(-2)

We are given that f'(-2) = 2 and g'(-2) = 3. Therefore, we can solve for f'(g(-2)):

f'(g(-2)) = f'(-2) / g'(-2) = 2/3

Since f'(x) = f'(g(x)) * g'(x), we can substitute g(0) = -2 and f'(g(-2)) = 2/3 into the equation f'(0) = f'(g(0)) * g'(0) to obtain:

f'(0) = f'(g(0)) * g'(0) = f'(g(-2)) * g'(0) = (2/3) * 3 = 2

Therefore, f'(0) = 2.

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