If 36 sqrt2 - 24 sqrt2 = sqrtN, what is N?

Organ systems must interact with one another.

Answer:  The required sum is 504.

Step-by-step explanation:  We are given to find the sum of the following arithmetic series using the formula for the sum of an arithmetic series :

[tex]\sum_{i=1}^{18}(2i+9).[/tex]

The given arithmetic series can be written, in expanded form, as follows :

[tex]11+13+15+17+~.~.~.~+43+45.[/tex]

We know that

the sum of first n terms of an arithmetic series with first term a and common difference d is given by

[tex]S=\dfrac{n}{2}\{2a+(n-1)d\}.[/tex]

In the given series, a = 11 and d = 13 - 11 = 15 - 13 = . . . =2.

Therefore, the sum up to 18 terms will be

[tex]S_{18}=\dfrac{18}{2}\{2\times 11+(18-1)\times2\}=9(22+34)=9\times56=504.[/tex]

Thus, the required sum is 504.

The sum of the arithmetic series ∑₁¹⁸(2i + 9) using the arithmetic series formula is 504.

To find what is the sum of the arithmetic series ∑₁¹⁸(2i + 9) below using the formula for the sum of an arithmetic series, we proceed as follows

The formula for the sum of therms of an arithmetic series is given by

Sₙ = n/2(a + Tₙ) where

Now, since we have that arithmetic series, ∑₁¹⁸(2i + 9), the nth terms is U = 2i + 9

Now, the first term is when i = 1.

So, U₁ = a = 2(1) + 9

= 2 + 9

= 11

Also, the last term is when i = 18

So, U₁₈ = T₁₈ = 2(18) + 9

= 36 + 9

= 45

So, the sum of terms Sₙ is when n = 18

S₁₈ = 18/2(11 + 45)

= 9(56)

= 504

Answer: The house fly is 8 times the mass of the mosquitio

Answer:

Median = 31

Step-by-step explanation:

The median is the middle number which comes after arranging the set in ascending order.

Here, the given data is: 28, 45, 12, 34, 36, 45, 19, 20

The data arranged in the ascending order is as follows:

12, 19, 20, 28, 34, 36, 45, 45

Since the number of terms is even, we have two middle numbers, viz.,

28 and 34

The median would be the average of these two.

Therefore, Median = [tex]$ \frac{28 + 34}{2} $[/tex]

= 31

The answer is 31.

The median of the set 28, 45, 12, 34, 36, 45, 19, 20 is 31.

To find the median of a set of numbers, you should first arrange the numbers in ascending order and then locate the middle number.

If there is an even number of terms, the median is the average of the two middle numbers. Let's do that with the given set: 28, 45, 12, 34, 36, 45, 19, 20.

Therefore, the median of the given set is 31.

The new area of the park that will not be wooded after expansion is represented by the expression 41.25x³ - 24.75x² + 15x - 13.5.

The current area of the park is given by the polynomial 11x² + 4x + 6. If the city expands the park by a factor of 5x - 3, the total new area of the park becomes (11x² + 4x + 6) * (5x - 3), which represents the expansion of the park.

However, the question asks for the part of the park that will not be wooded, which we know is three-fourths of the total park. So, we multiply our expanded park equation by 3/4 (or 0.75) to find this area:

(3/4) * [(11x² + 4x + 6) * (5x - 3)]

Using distributive property, we can further expand the expression:

=(3/4) * [(55x³ - 33x² + 20x - 18)]

So the area that will not be wooded after expansion is expressed as 41.25x³ - 24.75x² + 15x - 13.5.

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Given that the current area of the park is represented by a second degree equation, the expansion of the park will proportionally increase its area. The new area after expansion will be the product of the current area and the expansion factor, so we will need to multiply our current area, which is given by 11x^2 + 4x + 6, by the expansion factor, which is 5x - 3.

This will yield: (5x - 3)*(11x^2 + 4x + 6) as the total new area of the park.

Now that we've calculate the total new area of the park, we need to find out the area of the park that will be wooded and the area that will not be. We know that the wooded area will be one-fourth of the total area, so we can find this by dividing our total area by 4.

This yields: (5x - 3)*(11x^2 + 4x + 6) / 4 as the wooded area of the park.

After discovering the area that will be wooded, we can find the non-wooded area by subtracting the wooded area from the total area of the park.

Therefore, the new area of the park that is not wooded is given by:

3*(5x - 3)*(11x^2 + 4x + 6) / 4

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Answer:

The answer is A.

Step-by-step explanation:

There are 7 1/12ths, so it is equal to 7/12

Answer: 90° which is a right angle

Step-by-step explanation:

The tangent to a circle is perpendicular to the radius at the point of tangency. The angle between a radius and tangent is 90°>

Taking into account the rule of three, the total distance that Ms. Wilson walked in 4 days is 3 miles.

In first place, the rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.

That is, what is intended with it is to find the fourth term of a proportion knowing the other three.  

If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied.

To solve a direct rule of three, the following formula must be followed, being a, b and c known data and x the variable to be calculated:

a ⇒ b

c ⇒ x

So: [tex]x=\frac{cxb}{a}[/tex]

You can applied the following rule of three: if each day last week, Ms. Wilson walked [tex]\frac{3}{4}[/tex] mile, in 4 days what is the total distance that Ms. Wilson walked?

[tex]total distance=\frac{4 daysx\frac{3}{4} miles }{1 day}[/tex]

total distance= 3 miles

Finally, the total distance that Ms. Wilson walked in 4 days is 3 miles.

Learn more about the rule of three with this example:

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Answer:

5.1

Step-by-step explanation:

I Has This Study Island Before

To divide 49 in the ratio of 4:2:1, find the total quotient of the ratio parts, divide 49 by this total, and then multiply each part of the ratio by the result.

The ratio of the coefficients is 4:2:1, which can be simplified to 2:1:1. To divide 49 in this ratio, follow these steps:

Solution:

we are given that

You have a large container of olive oil. You have used [tex]22 \frac{1}{2}[/tex] quarts of oil.

Twenty-five percent of the olive oil remains.

we have been asked to find how many quarts of olive oil remain?

Let there were x quarts of olive oil.

It mean , we can write

[tex]x-22 \frac{1}{2}=\frac{1}{4}*x[/tex]

[tex]x-\frac{1}{4}*x=22 \frac{1}{2}[/tex]

[tex] \frac{3x}{4}=22 \frac{1}{2}[/tex]

[tex] 3x=4*22 \frac{1}{2}[/tex]

[tex] x=\frac{4}{3}* \frac{45}{2}[/tex]

[tex] x=30[/tex]

Hence quarts of olive oil remain [tex] =30-\frac{45}{2}=\frac{15}{2}=7\frac{1}{2}[/tex]

On a map of Scotland, drawn to the scale of 1:325,000, 65 KM of real-world distance will be represented by 20 cm on the map.

The question pertains to the scale existing on a map. A map scale enables us to convert the measurements on the map into the corresponding real-world distances. Here, we have a map of Scotland that is drawn to the scale of 1:325,000. This signifies that 1 cm on the map equates to 325,000 cm in reality.

To ascertain how many cm on the map would represent 65 KM, we first need to convert 65 KM into cm. As we know, 1 KM is equal to 100,000 cm. Therefore, 65 KM will be equivalent to 65 * 100,000 = 6,500,000 cm.

Now, we divide the real-world cm (6,500,000 cm) by the scale (325,000), which gives us the cm on the map. Thus, 6,500,000 cm / 325,000 = 20 cm

So, on this map, 65 KM will be denoted by 20 cm.

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Answer:

(y+1)\div (a+2)

Step-by-step explanation:

y-aw=2w-1

y+1=2w+aw

y+1=w(2+a)

(y+1)/(a+2)=w

Answer: w= (y+1)\div (a+2)

Answer:

  d = 8

Step-by-step explanation:

Since the variable appears on only one side of the equation, all terms not containing the variable can be eliminated from that side by adding their opposite to both sides of the equation. That is, add -17 to both sides of the equation:

  9 -17 = -d + 17 - 17

  -8 = -d . . . . . simplify

Now, the equation can be multiplied by a number that will give "d" on one side of the equation. Here, that number is -1. Multiply both sides of the equation by -1:

  (-1)(-8) = (-1)(-d)

  8 = d . . . . . simplify

The solution is d = 8.

Answer:

8

Step-by-step explanation:

[tex]9= -d +17\\9-17= -d +17- 17 \\-8/-1 = -d/-1\\8 = d[/tex]

Contractor A estimated a job would cost $54,000 to complete in 90 days.

Per day charge of Contractor A = $54,000 / 90 = $ 600 / day

Contractor B estimated he could complete the same job for $49,500 in 120 days.

Per day charge of Contractor A = $49,500 / 90 = $ 412.50 / day

Therefore, Contractor A charges $ 600 per day and contractor B charges $412.50 per day.

Hope it helps..!!

Thank You :)

Answer:

A  IS CORRECT

Step-by-step explanation:

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