find the area of the shaded region in the simplest form

Answer:

100 ft

Step-by-step explanation:

If you use a editor and see that the building doubles by 50 twice pls make me brainiest :D

Answer:

x = 36

Step-by-step explanation:

Tan (30) = opposite / adjacent

The opposite is known: it is 12 √3

Tan (30o) = 1 / √3

Tan(theta) = opposite/adjacent.

Opposite = 12\(\sqrt{3}\)

Adjacent = x

\(\frac{1}{\sqrt{3} } = \frac{12\sqrt{3} }{x}\)                            Cross multiply

1*x = 12*(\(\sqrt{3}\))^2

x = 12 * 3

x = 36

Answer:

Step-by-step explanation:

Given the expression 3 * 2 2/3

This can also be expressed as;

3 * 2 2/3

= 3 * 8/3

= (24/3)

= 8

hence the product of both numbers is 8

The equivalent value of the fraction is A = 8

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first fraction be represented as p

Let the second number be represented as q

Now , A = pq

when the value of p = 2 2/3

And , when the value of q = 3

On simplifying the equation , we get

A = ( 2 2/3 ) / ( 3 )

So , the left hand side of the equation is equated to the right hand side by the value of ( 2 2/3 ) / ( 3 )

A = ( 2 2/3 ) / ( 3 )

A = ( 8/3 ) / ( 3 )

On simplifying , we get

Multiply by 3 on the fraction , we get

A = ( 8 x 3 ) / 3

A = 8

Therefore , the value of A = 8

Hence , the fraction is A = 8

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p= 610/62, or 9.84 hope this hopes (5)

Answer:

the answer is 5.

Step-by-step explanation:

hope this helps..

The scale factor used to create the travel version of the piece is 1: 0.16

0.6 is the scale factor used to reduce the dimensions of the original piece having sides measuring 3 inches each.

Scale factor is calculated by dividing the new reduced scale by original scale. Hence:

0.5/3 = 0.166

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Scale Factor = New Shape Dimension / Original Shape Dimension

Enlarging a small form into a huge one is known as scaling up. Upscaling always uses a scale factor greater than 1. A scale factor 2 means the figure is enlarged twice the original figure's size.

A large number gets scaled down in order to become a smaller one. Scaling down always results in a scale factor less than 1.

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The inverse Laplace transform of F(s) is \(e^{-2t\) - 3t * \(e^{-2t\) + 10 * \(e^{-3t\).

To find the inverse Laplace transform of F(s) = (2s + 10) / (\((s + 2)^2\) (s + 3)), we can use partial fraction decomposition.

First, we decompose the rational function F(s) into simpler fractions:

F(s) = A / (s + 2) + B / \((s + 2)^2\) + C / (s + 3)

To find the values of A, B, and C, we can multiply both sides of the equation by the denominator (\((s + 2)^2\) (s + 3)) and simplify:

2s + 10 = A(s + 2)(s + 3) + B(s + 3) + C\((s + 2)^2\)

Expanding and collecting like terms:

2s + 10 = A\(s^2\) + (5A + B)s + (6A + 2B + C)

By comparing the coefficients of \(s^2\), s, and the constant term, we obtain a system of equations:

A = 1

5A + B = 2

6A + 2B + C = 10

From the first equation, we find A = 1. Substituting this into the second equation, we get:

5(1) + B = 2

B = -3

Finally, substituting the values of A = 1 and B = -3 into the third equation, we find:

6(1) + 2(-3) + C = 10

6 - 6 + C = 10

C = 10

Therefore, we have A = 1, B = -3, and C = 10.

Now, we can rewrite F(s) in partial fraction form:

F(s) = 1 / (s + 2) - 3 / \((s + 2)^2\) + 10 / (s + 3)

Taking the inverse Laplace transform of each term separately, we have:

\(L^{-1\) {1 / (s + 2)} = \(e^{-2t\)

\(L^{-1\) {-3 / \((s + 2)^2\)} = -3t * \(e^{-2t\)

\(L^{-1\) {10 / (s + 3)} = 10 * \(e^{-3t\)

Therefore, the inverse Laplace transform of F(s) is given by:

f(t) = \(e^{-2t\) - 3t * \(e^{-2t\) + 10 * \(e^{-3t\)

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Answer:

The number is 33

Step-by-step explanation:

23+10= 33

Hope this helps! :)

Answer:

B

Step-by-step explanation:

1. The perimeter of the shape is 9x²+ 7x +8

2. The third side of the triangle is 2x²+x+4

The perimeter of a shape is the total measurement of all the edges of a shape e.g. a triangle has three edges, so its perimeter is the total of those three edges added together.

1. The trapezium has 4 sides, and the perimeter is found by adding all the sides. Therefore,

5x²+7 + x²+2x + 2x²+3x -4+ x²+2x+5

= 9x²+7x + 8

2. A triangle has 3 sides, therefore the other side is found by;

5x²-6x+7 -( x²+2x+1+ 2x²-5x+2)

= 5x²-6x +7 - ( 3x²-7x+3)

= 2x²+x+4

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The Perimeter is 238! Have a good day:)

Answer:

The perimeter of the larger octagon is 238.

Step-by-step explanation:

Multiply the perimeter of the smaller octagon by 7.

34 x 7 = 238.

Answer:

x = 6.375

Step-by-step explanation:

Step 1:

4.2+0.8 = 5

(1.6x+1.8)÷2.4 = 5

Step 2:

5 · 2.4 = 12

1.6x + 1.8 = 12

Step 3:

12 - 1.8 = 10.2

1.6x = 10.2

Step 4:

10.2 ÷ 1.6 = 6.375

x = 6.375

Answer:10 squared plus 9 squared equals 15 squared

Step-by-step explanation:

take the square root of your answer

Answer:

$8,706

Step-by-step explanation:

Lionnel is considering doing some long term investments with the money she inherited

She would like to have $50,000 at the end of 30 years

The interest is 6%

Therefore the amount that Lionnel would need to put into the account can be calculated as follows

A= P(1+r)^t

50,000 = P(1+6/100)^30

50,000 = P (1+0.06)^30

50,000 = P(1.06)^30

50,000= 5.7434P

P = 50,000/5.7434

P= $8,706

Hence Lionnel will need to put $8,706 into an account earning 6% interest

Answer:

It's A-$8,706 :))

Step-by-step explanation:

Answer:

I have made it in above picture

Answer:

above sea level

Step-by-step explanation:

Answer:

10.8

Step-by-step explanation:

We need to use the cosine:

cos(26deg) * 12 ~= 0.89879404629 * 12 ~= 10.7855285556 ~= 10.8

Jacki's estimates are reasonable because they make the total of the five winning basketball scores equal to 500 points.

The correct answer is D. It is reasonable because all the scores equal 500.

First, we know that the five winning scores totaled 500 points.
Three of the scores (81, 112, and 97) are already recorded in the team log. We can add these three scores together to find out how many points we need to reach 500:

81 + 112 + 97 = 290 points.

To find the remaining points needed, we can subtract the sum of the known scores (290 points) from the total points (500 points):

500 - 290 = 210 points.
Jacki estimated that the other two scores were 100 and 110 points.

We can add these two scores together to check if they equal the remaining points needed (210 points):

100 + 110 = 210 points.

Since Jacki's estimates add up to the remaining points needed (210 points), we can conclude that her estimates are reasonable.

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The volume of the solid is approximately 807.08 cubic units.

To determine the volume of the solid, we can use the method of cylindrical shells.

Imagine taking a slice of the solid parallel to the base, with the cross-sectional area being a square of side length x (where x is a function of the height). The volume of this slice is the product of the square area and the height. The height of the slice is equal to the difference in the radii of two consecutive circular cross sections.

The radius of the larger circular cross-section can be found using the Pythagorean theorem, which states that the square of the hypotenuse (the radius) is equal to the sum of the squares of the other two sides (the height and half the side length of the square). Thus, we have:

r² = x² + (15-x)²

Solving for x, we get:

x = 15 * √(1 - (r/15)²)

The volume of the slice is then given by:

V = x² * (15 - x)

To find the total volume of the solid, we integrate this expression with respect to r from 0 to 15. The result is approximately 807.08 cubic units.

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Answer:

OK, dilations of a triangle are just making them smaller.

Step-by-step explanation:

A) Dilations increase the length of line segments is not true. If you dilate a triangle, it does not increase the length of the line segments.

B) Dilations of a triangle are congruent to the original triangle is not true. Congruent means the same in shape in size, and similar means the same in shape, not size.

C) Dilations of a triangle keep angle measures the same is true. Dilations do not change the angle measurements.

D) Dilations of a triangle are similar to the original triangle is true. Similar means same in shape, not size.

E) Dilations increase the measure of angles is not true. Like i said, dilations do not change the angle measurements, whether increasing or decreasing the size.

Hope this helps, i took this about a month ago so i hope my memory is sharp enough <3

To find the fraction of the square quilt block that is shaded, we need to count the number of shaded unit squares and divide it by the total number of unit squares in the quilt block. Let us begin by counting the number of shaded unit squares.

We notice that there are a total of 6 unit squares that are shaded. The unit squares that are shaded are the 2 squares that are completely shaded and the 4 squares that are half shaded due to the presence of triangles.

Next, we need to count the total number of unit squares in the quilt block. We notice that the quilt block is made up of 9 unit squares, each of which can be divided into 4 smaller unit squares. Thus, the total number of unit squares in the quilt block is 9 x 4 = 36.

Therefore, the fraction of the square quilt block that is shaded is 6/36 or 1/6.

To summarize, the shaded portion of the quilt block consists of 6 unit squares out of a total of 36 unit squares. Thus, the fraction of the square quilt block that is shaded is 1/6.

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The sum of the squares of the digits of the 1000th number in the sequence is 5.

To find the 1000th number in the sequence 2, 3, 5, 6, 7, 10, we can observe the pattern of the sequence. It consists of all positive integers that are not perfect powers.

The sequence starts with the prime numbers (2, 3, 5, 7), followed by numbers that are products of two primes (6 = 2 * 3, 10 = 2 * 5).

After that, the sequence includes numbers that are products of three primes (30 = 2 * 3 * 5, 42 = 2 * 3 * 7, 70 = 2 * 5 * 7), and so on.

We can see that each number in the sequence is built by multiplying distinct primes together.

To find the 1000th number in the sequence, we need to continue this pattern until we reach the desired position.

Let's calculate the 1000th number:

We start with the prime numbers: 2, 3, 5, 7.

Next, we multiply them together: 2 * 3 * 5 * 7 = 210.

So, the 1000th number in the sequence is 210.

To find the sum of the squares of the digits of 210, we calculate:

\((2^2) + (1^2) + (0^2) = 4 + 1 + 0 = 5.\)

Therefore, the sum of the squares of the digits of the 1000th number in the sequence is 5.

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Minimum cost in terms of material used:\(C = 4cπ(r^2 + rh) = 4c.\)

We can solve this problem using the method of optimization. Let's first identify the variables and constraints:

Variables:

r: the radius of the barrel

h: the height of the barrel

Constraints:

Volume constraint: \(πr^2h = 32π\)

Non-negative constraints: r ≥ 0, h ≥ 0

We want to minimize the cost of the material used, which consists of the cost for the side of the barrel and the cost for the top and bottom of the barrel. Let's denote these costs by Cs and Ctb, respectively.

To express Cs and Ctb in terms of r and h, we need to find the surface area of the side of the barrel and the surface area of the top and bottom of the barrel, respectively.

Surface area of the side of the barrel:

lateral area = 2πrh

Surface area of the top and bottom of the barrel:

top area = bottom area =\(πr^2\)

Therefore, the total surface area of the barrel is:

A = lateral area + 2(top area) =\(2πrh + 4πr^2\)

The cost of the material for the side of the barrel is half that of the cost for the top and bottom. Let's denote the cost per square foot of the top and bottom as Ct, then the cost per square foot of the side is Cs = 0.5Ct.

The total cost of the material used can now be expressed in terms of r and h as follows:

C = Cs(lateral area) + Ct(2 top area) = \(0.5Ct(2πrh) + Ct(4πr^2) = Ct(2πrh + 4πr^2)\)

Now, we need to express Ct in terms of Cs. Let's assume that the cost per square foot of the side is Cs = c, then the cost per square foot of the top and bottom is Ct = 2c.

Therefore, the total cost of the material used can be expressed as:

\(C(r, h) = 2c(2πrh + 4πr^2) = 4cπ(r^2 + rh)\)

Now, we can formulate the optimization problem as follows:

minimize \(C(r, h) = 4cπ(r^2 + rh)\)

subject to πr^2h = 32π

r ≥ 0, h ≥ 0

To solve this problem, we can use the method of Lagrange multipliers. The Lagrangian function is:

\(L(r, h, λ) = 4cπ(r^2 + rh) - λ(πr^2h - 32π)\)

Taking partial derivatives with respect to r, h, and λ, we get:

\(dL/dr = 8cπr + λπh = 0\)

\(dL/dh = 4cπr + λπr^2 = 0\)

\(dL/dλ = πr^2h - 32π = 0\)

Solving these equations simultaneously, we get:

\(r = (4/π)^(1/3)\)

h = 4r

\(λ = (2/π)^(2/3)/2\)

Therefore, the dimensions of the barrel that can be constructed at a minimum cost in terms of material used are:

\(r = (4/π)^(1/3)\)

\(h = 4r = 4(4/π)^(1/3)\)

To find the minimum cost, we need to substitute these values of r and h into the cost function:

\(C = 4cπ(r^2 + rh) = 4c\)

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Answer:

A and B are correct

Step-by-step explanation:

if x:y is 1:3 then x is 1 and y is 3

1/3 of 3 is 1 so A is correct

3/4(1+3) is 3 so B is correct

But

1/4 × 3 is not 1 so C is not correct

3/4 ×1 is not 3 so D isn't correct

Answer:

The fifth answer is correct! have a great day

Answer:

3 and 4

Step-by-step explanation:

23x5= 115

115+35=150

23x2=46

46+35= 81

which gives us numbers 3 and 4

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Based on the explanation below, the conclusion that Elan is tired because Elan stayed up late is invalid.

In the question, it is stated that if Elan stays up late, he will be tired the next day.

However, staying up late is not the only thing that could make Elan get tired.

This implies that there are so many other things than can make Elan get tired such as working for long hours.

It is possible that Elan was tired because Elans worked long hours.

By implication, the conclusion is invalid.

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Answer:

17,-15

Step-by-step explanation:

Answer:

Please Give Brainliest

Step-by-step explanation:

The smallest value within the class is the lower class limit, and the largest value within the class is the upper class limit.

A class limit is a set of boundary values in the form of a range that describes the lowest and highest data values that a class can contain. The lower class limit refers to the smallest data value in a class, whereas the upper class limit refers to the largest data value in a class. The width of a class is determined by the difference between the upper and lower class limits. Here are a few examples to give you a better understanding of how this works:

Class:              5-9 5 9

Lower Limit:    10-14 10 14

Upper Limit:    15-19 15 19

This shows class limits for three different classes.

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Answer:

what are the models

Step-by-step explanation:

but 4/16 and ¼ are both equivalent fractions for 2/8

The equation to calculate the experimentally determined magnitude of the Coulomb force as a function of l, xball, m, and the local gravitational constant g can be given as:

\(F=(k*q1*q2)/(l^2+xball^2)^(3/2)\)

Where:

F is the magnitude of the Coulomb force.

k is the electrostatic constant.

q1 and q2 are the charges involved.

l is a constant representing the separation distance in one dimension.

xball is the variable representing the distance in the other dimension (it can vary).

m is a constant representing the mass of the objects involved.

g is the local gravitational constant.

The equation takes into account the inverse square relationship between the separation distance and the magnitude of the Coulomb force. The distance in both dimensions (l and xball) contributes to the overall distance between the charges. The constant terms (k, q1, q2, m, and g) are used to factor in the specific values of the charges and masses involved.

Please note that this equation assumes a simplified scenario and may not account for other factors or complexities that could affect the Coulomb force in a specific experimental setup.

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When a fish is attached to a vertical spring and slowly lowered to its equilibrium position, the spring stretches by an amount d, as it balances the force exerted by the spring with the force due to the fish's weight.

Here, a fish attached to a vertical spring. When a fish is attached to a vertical spring and slowly lowered to its equilibrium position, the spring will stretch by an amount d.
The equilibrium position is the point where the force exerted by the spring equals the force due to the fish's weight (gravitational force). In this scenario, the spring stretches until it reaches a balance between these forces. The amount by which the spring stretches is denoted as d.
To summarize, when a fish is attached to a vertical spring and slowly lowered to its equilibrium position, the spring stretches by an amount d, as it balances the force exerted by the spring with the force due to the fish's weight.

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