let abc be an acute-angled triangle with circumcenter o and circumradius r. line ao meets again the circumcircle of ∆boc at a0 , bo meets again the circumcircle of ∆coa at b0 , and co meets again the circumcircle of ∆aob at c

To find the inverse Laplace transform of ℒ{e^(-s) / [s(s + 1)]}, we can use partial fraction decomposition and known Laplace transforms.

First, let's express the given function in partial fraction form:

e^(-s) / [s(s + 1)] = A/s + B/(s + 1)

To find A and B, we multiply both sides by s(s + 1) and then substitute appropriate values of s to simplify and solve for the coefficients:

e^(-s) = A(s + 1) + Bs

Setting s = 0, we get:

1 = A(0 + 1)

A = 1

Setting s = -1, we get:

e = B(-1)

B = -e

Therefore, the partial fraction decomposition is:

e^(-s) / [s(s + 1)] = 1/s - e/(s + 1)

Now, we can use the known Laplace transforms to find the inverse transform:

ℒ^(-1){1/s} = 1

ℒ^(-1){-e/(s + 1)} = -e^(-t)

Finally, we combine the inverse transforms:

f(t) = ℒ^(-1){e^(-s) / [s(s + 1)]} = ℒ^(-1){1/s} - ℒ^(-1){e/(s + 1)} = 1 - e^(-t)

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Step-by-step explanation:

21:18=7:6

42:36=7:6

63:54=7:6

Answer:

(p/3)-3=114

114 plus 3 = 117 (one-third of the novel)

117 x 3 = p = 351 (entire novel)

Step-by-step explanation:

(p/3)-3=114

114 plus 3 = 117 (one-third of the novel)

117 x 3 = p = 351 (entire novel)

The prime factorization of the number 21 is:

21 = 3*7

We want to write the prime factorization of 21.

To do so, we just need to divide the number by prime numbers.

The first prime number we can try is 2, if we divide by 2 we get:

21/2 = 10.5

This is not an integer, so 2 is not a factor.

The next one is 3:

21/3 = 7

Now we can rewrite:

21 = 3*7

Where 3 and 7 are prime numbers, so that is the prime factorization.

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Answer:

Step-by-step explanation:

Linda sold 14

John sold 29 which is 14 two times plus one

29+14=43

The number of square units occupied by the space inside the circle is called area

The number of square units occupied by the space inside a circle is given by the formula A = πr^2, where A is the area of the circle and r is the radius. The letter A is commonly used to represent area in mathematical equations. The formula states that the area of a circle is proportional to the square of its radius, meaning that as the radius increases, so does the area. The constant π, which is approximately equal to 3.14, represents the ratio of the circumference of a circle to its diameter.

The area of a circle can be used in many real-world applications, such as calculating the amount of space inside a circular room or the amount of material needed to cover a circular surface.

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The probability that a randomly selected household in the area will be in violation of the local law prohibiting owning more than three pets the number of households that own more than three pets divided by the total number of households in the area.

To calculate the probability, we need to determine the number of households that own more than three pets and the total number of households in the area. Let's assume there are a total of N households in the area.

The number of households that own more than three pets can vary, so we'll denote it as X. Now, to find the probability, we divide X by N. The probability can be written as P(X > 3) = X/N.

However, we don't have specific information about the number of households or the distribution of pet ownership in the area. Without these details, it is not possible to provide an exact probability. To calculate the probability accurately, we would need more information about the population of households in the area, such as the total number of households and the distribution of pet ownership. With this information, we could determine the number of households violating the law and calculate the probability accordingly.

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Step-by-step explanation:

can you send a picture so we can see at least?

The h'(3) = h'(x)|x=3 = 22. We can see from the calculation that the value of h'(3) depends on the slopes of both f(x) and g(x) at x=3, as well as their values at x=3.

To evaluate h'(3) for h(x) = f(x) * g(x), we will use the product rule. The product rule states that if h(x) = f(x) * g(x), then h'(x) = f'(x) * g(x) + f(x) * g'(x).
Given the graphs of f(x) and g(x), we need to find the values of f(3), g(3), f'(3), and g'(3).
1. Locate the point x = 3 on the graph of f(x) and determine the value of f(3).
2. Locate the point x = 3 on the graph of g(x) and determine the value of g(3).
3. Determine the slope of the tangent line at x = 3 on the graph of f(x), which represents f'(3).
4. Determine the slope of the tangent line at x = 3 on the graph of g(x), which represents g'(3).
Once you have the values of f(3), g(3), f'(3), and g'(3), plug them into the product rule formula:
h'(3) = f'(3) * g(3) + f(3) * g'(3)
After calculating, you'll get the value of h'(3). Please refer to the graphs of f(x) and g(x) to obtain the necessary values and complete the evaluation.

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We can conclude that the difference engine rule for the given function f(n) = 6n^2 - 5n^4 is as follows:

First Difference Function: -20n^3 - 30n^2 - 8n + 1

Second Difference Function: -90n^2 - 122n - 51

To calculate the difference functions for the given function f(n) = 6n^2 - 5n^4, we need to find the differences between consecutive terms. Let's calculate the first few differences:

f(n) : 6n^2 - 5n^4

f(n + 1) : 6(n + 1)^2 - 5(n + 1)^4

Now, let's expand and simplify these expressions:

f(n) : 6n^2 - 5n^4

f(n + 1) : 6(n^2 + 2n + 1) - 5(n^4 + 4n^3 + 6n^2 + 4n + 1)

Expanding further:

f(n + 1) : 6n^2 + 12n + 6 - 5n^4 - 20n^3 - 30n^2 - 20n - 5

Next, we subtract f(n) from f(n + 1) to find the first difference:

f(n + 1) - f(n) : (6n^2 + 12n + 6 - 5n^4 - 20n^3 - 30n^2 - 20n - 5) - (6n^2 - 5n^4)

Simplifying:

f(n + 1) - f(n) : 6n^2 + 12n + 6 - 5n^4 - 20n^3 - 30n^2 - 20n - 5 - 6n^2 + 5n^4

Combining like terms:

f(n + 1) - f(n) : 12n + 6 - 20n^3 - 30n^2 - 20n - 5

Further simplifying:

f(n + 1) - f(n) : -20n^3 - 30n^2 - 8n + 1

Therefore, the first difference function is -20n^3 - 30n^2 - 8n + 1.

To find the second difference function, we need to calculate the differences between consecutive terms of the first difference function:

f(n + 1) - f(n) : -20(n + 1)^3 - 30(n + 1)^2 - 8(n + 1) + 1 - (-20n^3 - 30n^2 - 8n + 1)

Expanding and simplifying:

f(n + 1) - f(n) : -20(n^3 + 3n^2 + 3n + 1) - 30(n^2 + 2n + 1) - 8n - 8 + 20n^3 + 30n^2 + 8n - 1

Combining like terms:

f(n + 1) - f(n) : -20n^3 - 60n^2 - 60n - 20 - 30n^2 - 60n - 30 - 8n + 20n^3 + 30n^2 + 8n - 1

Simplifying further:

f(n + 1) - f(n) : -90n^2 - 122n - 51

Therefore, the second difference function is -90n^2 - 122n - 51.

From the calculations, we can conclude that the difference engine rule for the given function f(n) = 6n^2 - 5n^4 is as follows:

First Difference Function: -20n^3 - 30n^2 - 8n + 1

Second Difference Function: -90n^2 - 122n - 51

The difference engine rule shows how the values of the function change as n increases, and it provides a way to predict future values based on the differences between consecutive terms.

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Answer: The correct inequality that matches the graph is 6x + y < 3.

This inequality can be graphed by plotting the points (0,3) and (1,9) as the boundary of the solution set, and shading the area above the line. The graph will be a line with a negative slope that pass through the points (0,3) and (1,9) and the shaded area will be above the line, which match the graph you have described.

We can check this by plugging the points (0,3) and (1,9) into the inequality to see if they satisfy it:

6(0) + 3 < 3 => 3 < 3 which is true

6(1) + 9 < 3 => 6 + 9 < 3 which is false

This confirms that the inequality 6x + y < 3 matches the graph.

Step-by-step explanation:

To determine the elasticity, we need to differentiate both sides of the equation with respect to x and then multiply by (x/y):

Differentiating the equation with respect to x:

3.45 * d/dx(log(y)) = 87.6 * d/dx(log(x))

Using the property of logarithmic differentiation, we have:

3.45 * (1/y) * dy/dx = 87.6 * (1/x) * dx/dx

Simplifying and rearranging the equation:

(1/y) * dy/dx = (87.6/3.45) * (1/x)

(1/y) * dy/dx = 25.43/x

Multiplying both sides by (x/y):

dy/dx = (25.43/x) * (x/y)

dy/dx = 25.43/y

The elasticity is given by the ratio of the derivative of y with respect to x to the ratio of y to x. In this case, the elasticity is:

Elasticity = dy/dx * (x/y)

Substituting the value we obtained for dy/dx:

Elasticity = (25.43/y) * (x/y)

Elasticity = 25.43 * (x/y^2)

Therefore, the elasticity is given by 25.43 times the ratio of x to y squared.

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There are 5,040 different seating arrangements possible.

(a) To find the number of different juries possible, we can use the combination formula. We want to choose 6 men out of 14 and 6 women out of 13, so we have:

C(14, 6) x C(13, 6) = 1,352,697,600

Therefore, there are 1,352,697,600 different juries possible.

(b) To find the number of different seating arrangements possible, we can use the permutation formula. We know that we need to seat the jurors so that no two people of the same sex are seated next to each other. Let's start with the men - we have 6 men to seat, and they cannot be seated next to each other. We can think of this as creating "gaps" for the men to sit in. For example, if we have 6 men, we would need 7 gaps: _ M _ M _ M _ M _ M _ (where the underscores represent the gaps). Then we can choose which gaps the men will sit in, which we can do using the combination formula. We have 7 gaps to choose from, and we need to choose 6 of them for the men to sit in. Therefore, we have:

C(7, 6) = 7

Now we can seat the women in the gaps between the men. We have 6 women to seat, and we have 7 gaps for them to sit in (including the gaps at the ends). We can think of this as arranging the women and gaps in a line:

_ M _ M _ M _ M _ M _

We need to choose which 6 of the 7 gaps the women will sit in, and then arrange the women in those gaps. We can choose the gaps using the combination formula, and then arrange the women in those gaps using the permutation formula. Therefore, we have:

C(7, 6) x P(6, 6) = 7 x 720 = 5,040

Therefore, there are 5,040 different seating arrangements possible.

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Based on the information provided, 2 is not a solution of x>5 because a possible solution requires a number greater than 5.

Inequalities include symbols such as >, ≤, ≥, among others that should be interpreted correctly to solve the inequality. In this case, the symbol in the inequality is >, which means greater than. Based on this, the value of x should be greater than 5, for example, 7, 19, 2948, etc.

Therefore, 2 is not a solution to the inequality x>5 because a number greater than 5 rather than less than 5 is required to solve this expression.

Note: This question is incorrect and incomplete; here is the complete question:

Explain why 2 is NOT a solution of x>5

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Given:

Three line segments have measures of 4 units, 6 units, and 8 units.

To find:

Will the segments form a triangle?

Solution:

We know that three line segments can form a triangle if the sum of two smaller sides is greater than the largest side.

Three line segments have measures of 4 units, 6 units, and 8 units. Here, the measure of the largest sides is 8 units.

The sum of two smaller sides is

\(4+6=10\)

\(4+6>8\)

Since the sum of two smaller sides is greater than the largest side, therefore the segments will form a triangle.

Answer:

59

Step-by-step explanation:

So, lets look at our numbers in the sequence. So it goes 5 to 8, 8 to 11, 11 to 14, and 14 to 17. This seems like a change in three. So the every 1 term changes the orginal 5 value by 3.

So wouldnt this mean we can multiply the change in terms by the amount of terms? Which is 19*3? Well, sort of. This is the right way of doig this, but we must remember that we already know the first term, 5. So this means we will be doing 18*3.

This gets you 54. Now just add the amount of the 18 terms onto the first term:

54+5

=

59

So your answer is 59.

Hope this helps!

The equation in point-slope form is y - 5 = (5/3)(x + 5). The general form of the equation is 5x - 3y + 40 = 0.

To find the equation of a line parallel to the given line and passing through the point (-5,5), we can use the point-slope form of a linear equation. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope of the line. First, we need to find the slope of the given line, and then we can substitute the values into the point-slope form to obtain the equation. Additionally, we can convert the equation to the general form, which is Ax + By + C = 0, by rearranging the terms.

The given line has the equation 5x - 3y - 2 = 0. To find the slope of this line, we can rearrange the equation in slope-intercept form (y = mx + b), where m represents the slope. Rearranging the equation gives us:

-3y = -5x + 2

y = (5/3)x - 2/3

From the equation, we can see that the slope of the given line is 5/3. Since the line we want to find is parallel to this line, it will have the same slope.

Now, using the point-slope form with the point (-5,5) and the slope 5/3, we can write the equation:

y - 5 = (5/3)(x - (-5))

y - 5 = (5/3)(x + 5)

This is the equation of the line in point-slope form.

To convert it to general form, we can multiply through by 3 to eliminate the fraction:

3y - 15 = 5x + 25

5x - 3y + 40 = 0

This is the equation of the line in general form.

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Answer:

C. To make predictions about the values of y for a given​ x-value (I THINK)

Answer: 1. 64 | 2. 32

Step-by-step explanation:

Formula for a rectangle is Area = Length*Width

Therefore: 8*8 = 64

Formula for a triangle is Area = 1/2*Base*Height, which is also 1/2*length*width

Therefore: 1/2*8*8 = 32

Hope this helps :)

Carl has 2 5/36 yard cable, more than 1 yard, not specified left.

What is yard ?

A yard is a unit of length measurement in the U.S. customary system and the imperial system. It is equal to 3 feet or 36 inches. The symbol for yard is "yd". It is mostly used in the United States and the United Kingdom for measuring small lengths, such as in construction, textiles, and landscaping.

Carl has three lengths of cable, 5/6 yard long, 1/4 yard long and 2/3 yard long. The total length of the cable that Carl has is:

5/6 + 1/4 + 2/3 = (30 + 15 + 40) / 36 = 85 / 36 = 2 5/36 yard

To check whether he has at least one yard of cable or not, we need to compare the total length of the cable he has (2 5/36 yard) with 1 yard. Since 2 5/36 is greater than 1, it means he has more than 1 yard of cable. So, he will have at least 1 yard of cable left after using some of it.

Carl has 2 5/36 yard cable, more than 1 yard, not specified left.

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Carl has three lengths of wire, each measuring 5/6 yards, 1/4 yards, and 2/3 yards. The wire that Carl has measures a total of:

5/6 + 1/4 + 2/3 = (30 + 15 + 40) / 36 = 85 / 36 = 2 5/36 yard

We need to compare the entire length of the cable he has (2 5/36 yard) with 1 yard to see if he has at least one yard of cable or not. He has more than one yard of cable since 2 5/36 is larger than 1, which is greater than 1. After using some of the wire, he will still have at least 1 yard of it.

Answer:

Step-by-step explanation:

x+3*2=12-2*2

x+6=12-4

x+6=8

  -6 -6

x=2

Answer:

Step-by-step explanation:

A). In this case, the five-number summary of the data set would be:

   Minimum: 16

   Q1 (also known as the lower quartile): 22

   Median: 25

   Q3 (also known as the upper quartile): 43

   Maximum: 50

B.) are those the only two box plots listed?

Answer: 40

Step-by-step explanation:

A brown mouse has onequarter the number of

pieces of cheese as a grey mouse. After the brown

mouse took 12 pieces from the grey mouse, and the grey mouse

ate 6 of her remining pieces of cheese, they each have the same

number of pieces of cheese. How many pieces did the grey

mouse have initially?

x= grey mouse 1/4x = brown mouse

1/4x - 18 = x +12

3/4x = 30

(4/3)3/4x=30(4/3)

     x=40

Answer:

Nelson's average speed was 8 miles per hour.

Step-by-step explanation:

To find Nelson's average speed, you need to divide the distance he traveled by the time it took him to travel that distance. In this case, Nelson traveled 20 miles in 2 1/2 hours, so his average speed was 20 miles / 2.5 hours = <<20/2.5=8>>8 miles per hour.

Answer:

8 miles per hour

Step-by-step explanation:

In order to find Nelson's average speed, we can set up a proportion. To solve for x, x being miles traveled in one hour.

\(\frac{20 miles}{2.5hours} =\frac{x miles }{1 hour}\)

x= 8

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

The math property for 12=17-5 then 17-5=12 would be the symmetric property of equality.

Tip: The symmetric property of equality states that no matter what side the equations and answer are it will still be equal, but it only works for the equal sign.

The math property for 12=17-5 then 17-5=12 would be the symmetric property of equality.

A number system is defined as a system of writing to express numbers.

Given that 12 = 17 - 5, then 17 - 5 = 12

we need to check which property will be used.

The math property for 12=17-5 then 17-5=12 would be the symmetric property of equality.

The symmetric property of equality is really quite simple. This property states that if a = b, then b = a. That is, we can interchange the sides of an equation, and the equation is still a true statement.

Hence, the math property for 12=17-5 then 17-5=12 would be the symmetric property of equality.

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Answer:

24 feet cubed

Step-by-step explanation:

use the formula its quite simple

Answer:

24 ft cubed

Step-by-step explanation:

Thats the answer on edge

The space-mean speed of the four vehicles is approximately 64 mph.

The given information about the speeds of four vehicles measured at the midpoint of a roadway section are as follows:Vehicle Speed (mph)A 55B 50C 74D 78The space-mean speed of the four vehicles can be found out by the following formula:Space-mean speed = {Sum of the individual speeds of the vehicles}/{Number of vehicles}Space-mean speed = (55 + 50 + 74 + 78)/4Space-mean speed = 257/4Space-mean speed ≈ 64 mph (rounded to the nearest mph)

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Step-by-step explanation:

x+35+25=180

x+60 =180

x = 120.

y+x =18

The probability of of a random student having blue eyes and dark hair

 is 35% .

let consider the total students in the school be (U) = 100%

out of them ,

students having blue eyes (A) = 60%

students having  dark hair (B) = 55%

students with neither blue eyes nor dark hair (A∪B)' = 20%

let the students with blue eyes and dark hair be (A∩B) = x %

Then according to the set theorem

U = n(A∪B) + n(A∪B)'

U = n(A) + n(B) - n(A∩B) + n(A∪B)'

100 = 60 + 55 - x +20

∴ x = 60 + 55 +20 - 100

x = 35 %

So the probability of random student having blue eyes and dark hair is 35% .

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