What is the area of this polygon? 28.5 units² 34.5 units² 37.5 units² 40.5 units² 6 sided polygon on a coordinate plane with vertices at (negative 6, negative 2), (negative 5, 1), (negative 1, 4), (1, 1), (5, 3), and (1, negative 2)

The answer is 15,

because F(X)'s minimum value is (-3, -3)

and G(X)'s maximum value is (12, 3)

So when you subtract -3 from 12, you get a number that is greater then both. (because of the negative 3)

12 - (-3) = 15

Answer:

A.  15

Step-by-step explanation:

I got it rigth on the test :)

Have a great day fam!

Answer:

10 hrs

Step-by-step explanation:

sally earns $5/hr while Adam earns $4/hr

let the number of Hour sally works be 'x'

From question Adam work 2 hrs more than sally,

therefore Adam works (x + 2)hrs also the both earn same amount per week

therefore;

4 x [tex](x + 2)[/tex] = 5 x [tex]x[/tex]

4x + 8 = 5x

5x - 4x = 8

x = 8hrs

Adam works for (8+2)hrs = 10hrs

Final answer:

By defining equations based on the relationships between Jen's, Carrie's, and Fran's numbers and solving them, we find that Carrie's number is 64, Jen's number is 73, and Fran's number is 70.

Explanation:

To solve for Fran's number, we need to use the information given: Jen's number is 9 more than Carrie's, and Fran's number is 3 less than Jen's number. Their total sum is 207. We can set up equations to solve this. Let Carrie's number be c, Jen's number be c + 9 (since it is 9 more than Carrie's), and Fran's number be c + 9 - 3 (since it is 3 less than Jen's).

The equation to express the sum of their numbers will be: c + (c + 9) + (c + 9 - 3) = 207.

Now let's solve the equation:

Now that we have Carrie's number, we can find Fran's number:

Therefore, Fran's number is 70.

Answer: 343 in³

Explanation: In this problem, we're asked to find the volume of a cube.

It's important to understand that a cube is a type of rectangular prism and the formula for the volume of a rectangular prism is shown below.

Volume = length × width × height

In a cube however, the length, width, and height are all the same. So we can use the formula side × side × side instead.

So the formula for the volume of a cube is side × side × side or s³.

So to find the volume of the given cube, since each side has a length of 7 inches, we can plug this information into the formula to get (7 in.)³ or (7 in.)(7 in.)(7 in).

7 x 7 is 49 and 49 x 7 is 343.

So we have 343 in³.

So the volume of the given cube is 343 in³.

Answer:

343 in³

Step-by-step explanation:

Answer:

  85 m

Step-by-step explanation:

The diagonal of a square is √2 times the length of the side. The park will have a side length of 120/√2 m ≈ 84.85 m, about 85 meters.

_____

The relations are ...

  diagonal = (√2)×(side length)

  side length = diagonal/√2 . . . . . . . . . divide the above equation by √2

Answer:

S = 128πx² + 64πx + 8π

Step-by-step explanation:

Suraface area of a cylinder is given by:

S = 2πrh + 2πr²

We know that the height is 3 times as big as the radius, hence:

h = 3r

so we can plug in the new h value and rewrite the S equation as:

S = 2πrh + 2πr²

S = 2πr(3r) + 2πr²

S = 6πr² + 2πr²

S = 8πr²

We're given in the question that the radius is ​(4x + 1​) inches, so plug that into r.

Given: r = 4x + 1​

Therefore,

S = 8πr²

S = 8π(4x + 1​)²

S = 8π(16x²+8x+1)

S = 128πx² + 64πx + 8π

Answer:

The answer to your question is 128πx² + 64πx + 8π

Step-by-step explanation:

Data

radius = (4x + 1)

height = 3(4x + 1)

Formula

Area = 2πrh + 2πr²

Substitution

Area = 2π(4x + 1)(3)(4x + 1) + 2π(4x + 1)

Simplification

Area = 6π(4x + 1)² + 2π(4x + 1)²

Area = 6π(16x² + 8x + 1) + 2π(16x² + 8x + 1)²

Area = 96πx² + 48πx + 6π + 32πx² + 16πx + 2π

Area = 128πx² + 64πx + 8π

Answer:

Step-by-step explanation:

Triangle ABC is a right angle triangle.

From the given right angle triangle

BC represents the hypotenuse of the right angle triangle.

With m∠B as the reference angle,

AB represents the adjacent side of the right angle triangle.

AC represents the opposite side of the right angle triangle.

To determine BC , we would apply the Sine trigonometric ratio which is expressed as

Tan θ = opposite side/hypotenuse. Therefore,

Sin 44 = 10/BC

0.695 = 10/BC

BC = 10/0.695

BC = 14.4 to 1 decimal place.

Answer:

321.24 ft²

Step-by-step explanation:

If 3in = 5ft

   1in = x

5/3 = 1.6

So 1in = 1.67 ft

Actual dimensions will be;

L = 19.2*1.67 = 32.06ft

W = 6*1.67 = 10.02ft

Area = 32.06 * 10.02 = 321.24 ft²

To find the length and width of the actual studio, set up a proportion to convert the given dimensions from the scale to the actual dimensions. Then, find the area of the actual studio by multiplying the length and width.

To find the length and width of the actual studio, we need to convert the given dimensions from the scale to the actual dimensions. Since the scale is 3 in.: 5 ft, we can set up the proportion:

3 in / 5 ft = 19.2 in / x ft

Cross multiplying and solving for x, we get:

x = 32 ft

The length of the actual studio is 32 ft. Similarly, we can find the width:

3 in / 5 ft = 6 in / y ft

Solving for y, we get:

y = 10 ft

The width of the actual studio is 10 ft.

To find the area of the actual studio, we multiply the length and width:

Area = length x width = 32 ft x 10 ft = 320 ft²

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Answer:

Insufficient information

Step-by-step explanation:

The information provided us isn't sufficient to determine the range for the measurements in list X. Because we need to be given the range for the measurements in Y at least. We also need the number of measurements in both X and Y.

Answer:

The equation of the normal line to the curve y = x² - 3x at the point (7, 28) is 11y + x - 315 = 0

Step-by-step explanation:

First, we need to find the slope of the line tangent to the curve at the point (7, 28).

To do this, we need to differentiate y with respect to x and evaluate at the point x0 = 7.

Given y = x² - 3x

dy/dx = 2x - 3

So, the slope, m of the tangent line is dy/dx at x = 7:

m = 2(7) - 3 = 11

Slope, m = 11

The slope, m2 of the line perpendicular to the tangent is given as m2 = -1/m

m2 = −1/11

Finally, given the slope m of a line, and a point (x0, y0) on the line, we can use the point-slope form of the equation of a line:

y - y0=m(x - x0)

The perpendicular line has slope m2 = -1/11, and (7, 28) is a point on that line, the desired equation is:

y - 28 = (-1/11)(x - 7)

Or multiplying by 11, we have

11y - 308 = -x + 7

11y + x - 315 = 0

The slope of the curve at point (7,28) is 11, found by differentiating the given function. The slope of the normal line is the negative reciprocal of that, -1/11. Inserting these into the line equation, we get y - 28 = -1/11 * (x - 7).

To find the equation of the line perpendicular to the tangent line, we first find the slope of the tangent line. The derivative of the given function y = x^2 - 3x tells us the slope of the curve at any point, so let's find the derivative:

y' = 2x - 3

Now, let's find the slope of the tangent line at the point (7,28) by plugging 7 into the derivative:

y'(7) = 2*7 - 3 = 11

The slope of the line perpendicular to this (the normal line) is the negative reciprocal of the tangent line's slope, so it's -1/11.  

The equation of the line with slope m that goes through the point (x1, y1) is:

y - y1 = m*(x - x1)

Substitute the slope of -1/11 and the point (7,28) into this equation to get the equation of the normal line:

y - 28 = -1/11 * (x - 7)

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Answer:

E) 13

Step-by-step explanation:

∫₀⁴ f'(t) dt = f(4) − f(0)

8 = f(4) − 5

f(4) = 13

Answer:

The answer is 12

Step-by-step explanation:

t5 = 24 = a × r⁴

t8 = 3 = a × r⁷

We divide one by the other

r³= 1 / 8

r = 1 / 2

t6 = a × r⁵ = t5 × r = 24 × (1/2) = 12.

Therefore the sixth term of the geometric sequence is 12

Answer:

The amount of acid in third container is =42%

Step-by-step explanation:

Given , one container is filled with a mixture that is 30% acid a second container filled with a mixture that is 50% acid and the second container 50% larger than the first .

Let, the volume of first container is = x

Then , the volume of second container = (x+ x of 50%)

                                                                 = x + 0.5 x

                                                                 = 1.5 x

Therefore the amount of acid in first container [tex]=x \times \frac{30}{100}[/tex] = 0.3 x

The amount of acid in second container [tex]=1.5x \times \frac{50}{100}[/tex]  = 0.75x

Total amount of acid= 0.3x + 0.75x = 1.05 x

Total amount  of solution = x+1.5x = 2.5x

The amount of acid in third container is = [tex]\frac{1.05x}{2.5x} \times 100%[/tex] %

                                                                     = 42%

Final answer:

By calculating the total acid content and total volume when two containers with different acid concentrations are mixed, we find that the third container has an acid concentration of 42%.

Explanation:

The question involves mixing two solutions of different acid concentrations and calculating the final concentration of acid. Let's assume the first container has 1 unit of volume. Since the second container is 50% larger, it has 1.5 units of volume. The first container has 30% acid, so it contains 0.3 units of acid. The second container has 50% acid, resulting in 0.75 units of acid. Together, the total volume of the solution is 2.5 units, and the total amount of acid is 1.05 units.

Therefore, the percentage of acid in the third container is calculated by dividing the total acid by the total volume: (1.05 units of acid / 2.5 units of volume) x 100% = 42%.

Answer:

Step-by-step explanation:

The diagonals of the parallelogram are A(-5, -1), C(-1, 5) and B(-9, 6), D(3, -2).

Slope of diagonal AC = (5 - (-1)) / (-1 - (-5)) = (5 + 1) / (-1 + 5) = 6 / 4 = 3/2

Slope of diagonal BD = (-2 - 6) / (3 - (-9)) = -8 / (3 + 9) = -8 / 12 = -2/3

For the parallelogram to be a rhombus, the intersection of the diagonals are perpendicular.

i.e. the product of the two slopes equals to -1.

Slope AC x slope BD = 3/2 x -2/3 = -1.

Therefore, the parallelogram is a rhombus.

The solutions to the equations:

(a) x/3 = 6 => x = 18 (Verified)

(b) (5x + 9)/2 = 12 => x = 3 (Verified)

(c) x/4 = 9/6 => x = 6 (Verified)

(d) 5/x = 20/8 => x = 2 (Verified)

To solve the equation, follow these steps: identify the equation with one unknown, isolate x, substitute known values and solve, and check the solution.

The equations are

(a) x/3 = 6

(b) (5x + 9)/2 = 12

(c) x/4 = 9/6

(d) 5/x = 20/8

The answers to the question are

(a) x = 18

(b) x = 3

(c) x = 6

(d) x = 2

Step-by-step explanation:

(a) x/3 = 6

Therefore x = 3×6 = 18

x =18

Substituting the value of x in the above equation, we have

18/6 = 3 verified

(b) (5x + 9)/2 = 12

Multiplying both sides by 2 gives

(5x + 9)/2 × 2 = 12×2 = 24

5x + 9 = 24 or x = (24-9)/5 = 3

Substituting the value of x in the above equation, we have

(5×3 + 9)/2 = 24/2 = 12 verified

x = 3

(c) x/4 = 9/6

Multiplying both sides by 4, we have

x/4×4 = 9/6×4 = 6

x = 6

Substituting the value of x in the above equation, we have

(6/4 = 9/6 = 3/2 verified

(d) 5/x = 20/8

Inverting both equations, we have

x/5 = 8/20

Multiplying both sides by 20 we have x/5 × 20 = 8/20 × 20 or 4x = 8 and x = 2

Substituting the value of x in the original equation, we have

2/5 = 2/5 = 8/20 verified

x = 2

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Answer:

55% and 24%

Step-by-step explanation:

Firstly, we need an arbitrary number to serve as the number of students.

Let the total number of students be 120.

Firstly we need college-educated percentage.

Men are two-thirds, women are one-third

Men = 2/3 * 120 = 80

Women = 1/3 * 120 = 40

5/8 of men are college educated = 5/8 * 80 = 50

2/5 of women are college educated = 2/5 * 40 = 16

Total college educated = 50+ 16 = 66

% college educated = 66/120 * 100 = 55%

Percentage of college educated that are women.

Total college educated = 66

The % is 16/66 * 100 = 24%

Option D: [tex]20 \div 6-4[/tex] is the correct solution to the equation [tex]6(x+4)=20[/tex]

Option E: [tex]\frac{1}{6} (20-24)[/tex] is the correct solution to the equation [tex]6(x+4)=20[/tex]

Option F: [tex](20-24) \div 6[/tex] is the correct solution to the equation [tex]6(x+4)=20[/tex]

Explanation:

The expression is [tex]6(x+4)=20[/tex]

Let us find the value of x.

[tex]\begin{aligned}6(x+4) &=20 \\6 x+24 &=20 \\6 x &=-4 \\x &=-\frac{2}{3}\end{aligned}[/tex]

Now, we shall find the expression that is equivalent to the value [tex]x=-\frac{2}{3}[/tex]

Option A: [tex](20-4) \div 6[/tex]

Simplifying the expression, we have,

[tex]\frac{16}{6}=\frac{8}{3}[/tex]

Since, [tex]\frac{8}{3}[/tex] is not equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex](20-4) \div 6[/tex] is not equivalent to the equation [tex]6(x+4)=20[/tex]

Hence, Option A is not the correct answer.

Option B: [tex]16(20-4)[/tex]

Simplifying the expression, we have,

[tex]16(16)=256[/tex]

Since, 256 is not equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex]16(20-4)[/tex] is not equivalent to the equation [tex]6(x+4)=20[/tex]

Hence, Option B is not the correct answer.

Option C: [tex]20-6-4[/tex]

Simplifying the expression, we have,

[tex]20-10=10[/tex]

Since, 10 is not equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex]20-6-4[/tex] is not equivalent to the equation [tex]6(x+4)=20[/tex]

Hence, Option C is not the correct answer.

Option D: [tex]20 \div 6-4[/tex]

Using PEMDAS and simplifying the expression, we have,

[tex]$\begin{aligned}(20 \div 6)-4 &=\frac{10}{3}-4 \\ &=\frac{10-12}{3} \\ &=-\frac{2}{3} \end{aligned}$[/tex]

Thus, [tex]-\frac{2}{3}[/tex] is equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex]20 \div 6-4[/tex] is equivalent to the equation [tex]6(x+4)=20[/tex]

Hence, Option D is the correct answer.

Option E: [tex]\frac{1}{6} (20-24)[/tex]

Simplifying the expression, we have,

[tex]$\begin{aligned} \frac{1}{6}(20-24) &=\frac{1}{6}(-4) \\ &=-\frac{4}{6} \\ &=-\frac{2}{3} \end{aligned}$[/tex]

Thus, [tex]-\frac{2}{3}[/tex] is equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex]\frac{1}{6} (20-24)[/tex] is equivalent to the equation [tex]6(x+4)=20[/tex]

Hence, Option E is the correct answer.

Option F: [tex](20-24) \div 6[/tex]

Simplifying the expression, we have,

[tex]$\begin{aligned}(20-24) \div 6 &=-\frac{4}{6} \\ &=-\frac{2}{3} \end{aligned}$[/tex]

Thus, [tex]-\frac{2}{3}[/tex] is equivalent to [tex]x=-\frac{2}{3}[/tex], the expression [tex](20-24) \div 6[/tex] is equivalent to the equation [tex]6(x+4)=20[/tex]

Hence, Option F is the correct answer.

To solve 6(x + 4) = 20, we isolate x to get x = -2/3. The correct expressions representing the solution are E. 1/6(20 - 24) and F. (20 - 24) / 6.

To solve the equation 6(x + 4) = 20, we need to isolate x.

First, distribute the 6 on the left-hand side:

6x + 24 = 20

Next, subtract 24 from both sides:

6x = -4

Finally, divide by 6:

x = -4/6 = -2/3

Now, let's analyze the given choices:

Therefore, the correct choices are E and F.

The function that represent cost is c(t) = 40 + 0.5(t -400).

For the first 400 minutes [tex](\(0 \leq t \leq 400\))[/tex], the cost is a flat rate of $40.

T represents the overall conversation time in minutes in the provided question.

Speed cell wireless offers a $40 package for the first 400 minutes.

Additional $0.50 per minute for remaining time

Time remaining = (t - 400) minutes

So, the cost for more beyond 400 minutes is 0.5(t -400). $

Thus, the entire cost, c(t), is 40 + 0.5(t -400).

Answer:

1. The vertical components decrease by 14 units while the horizontal component increase by 3 units

2.it therefore means that the vertical component decreases by 70units

Step-by-step explanation:

Slope of a graph is change in the vertical axis over the the change in the horizontal axis

in the above question, if the average rate of change is -14/7 it therefore means that the vertical components decrease by 14 units while the horizontal component inc rfease by 3 units

what does that mean if the waterslide from x=0, and x=15

it means that the vertical components decrease why there is an increment distance in the horizontal axis

mathematically, we say

-14/3=-y/[tex]s= \frac{dy}{dx} , slope=s\\-14/3=\frac{-y}{15-0}[/tex]

14/3=y/15

y=70

it therefore means that the vertical component decreases by 70units

Answer:

On average, the slide drops 14 feet for every 3 feet of horizontal distance.

On average, the slide drops about 4.7 feet for every 1 foot of horizontal distance.

Step-by-step explanation:

on edg... Good Luck!!!

t= 2.25 secs

Step-by-step explanation:

Step 1 :

Equation for motion with uniform acceleration is v = u+ at

where v is the final velocity

          u is the initial velocity

          a is the acceleration due to gravity

          and t is the time

Step 2 :

Here , v = 0 because at the highest point final velocity is 0.

u = 72 feet/sec

a = -32 ft/sec^2

We need to find the time t.

Substituting in the equation we have,

0 = 72 -32 * t

=> 32 t = 72

=> t = 72/32 = 2.25 secs

The measure of the first, second and third angles are 20°, 27° and 133°.

An exterior angle of a triangle is the sum of two opposite interior angles.

According to given question

The residents of a downtown neighbourhood designed a​ triangular-shaped park as part of a city beautification program.

Let us assume the first angle to be x°.

Therefore from the given data second angle is (x + 7)° and the third angle is (7x - 7)°.

We know that the sum of all the interior angles of a given triangle is 180°.

∴ x + (x + 7) + (7x - 7) = 180°

  9x = 180°

    x = 180°/9

    x = 20°.

So, The first angle of the triangular park is 20°, The second angle is 27° and the third angle is 133°.

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Answer:

Step-by-step explanation:

Let t = flying time in seconds for each plane

Descending rate = 40 ft/s

Ascending rate = 60 ft/s

Descending height, hd= 19200 - 40t

Ascending height, ha = 60t

Equating hd = ha, therefore:

60t = 19200-40t

60t + 40t = 19200

100t = 19200

t = 19200/100

t = 192 seconds

h = 19200 - 192(40)

h = 19200 - 7680

= 11,520 ft.

After 192 seconds, the two airplanes will be at the same height, which is 11,520 feet.

To find the time it takes for the two airplanes to be at the same height, we need to set up an equation based on their rates of ascent and descent. Let's assume the height of the descending airplane is given by h1 and the height of the ascending airplane is given by h2. The descending airplane is descending at a rate of 40 feet per second, so its height after t seconds can be represented by the equation h1 = 19,200 - 40t. The ascending airplane is ascending at a rate of 60 feet per second, so its height after t seconds can be represented by the equation h2 = 60t. To find the time at which the two airplanes are at the same height, we can set h1 equal to h2 and solve for t: 19,200 - 40t = 60t. Simplifying this equation, we get 100t = 19,200, so t = 192 seconds. Therefore, after 192 seconds, the two airplanes will be at the same height.

To find the height at which the two airplanes are at, we can substitute the value of t into either the equation for h1 or h2. Let's use the equation for h1: h1 = 19,200 - 40(192) = 19,200 - 7,680 = 11,520 feet. Therefore, after 192 seconds, the two airplanes will be at a height of 11,520 feet.

Answer:

Step-by-step explanation:

Let x represent the number of pounds of soap that she makes and eventually sells.

She intially spent $72 to purchase soap-making equipment, and the materials for each pound of soap cost $7. This means that the total cost of making x pounds of soap would be

7x + 72

Lisa sells the soap for $10 per pound. This means that her revenue for x pounds of soap would be

10 × x = 10x

If she eventually sells enough soap to cover the cost of the equipment, then

7x + 72 = 10x

10x - 7x = 72

3x = 72

x = 72/3 = 24

She would need to sell make and sell 24 soaps.

The cost would be

72 + 7 × 24 = $240

The total sales would be

10 × 24 = $240

Answer: the system of equations are

a + c = 150

7.75a + 10.25b = 1470

Step-by-step explanation:

Let a represent the number of adult tickets that were sold.

Let c represent the number of child tickets that were sold.

The celluloid cinema sold 150 tickets to a movie. Some of these were child tickets and the rest were adult tickets. This means that

a + c = 150 - - - - - - - - - - - - - -1

A child ticket cost $7.75 and an adult ticket cost $10.25. If the cinema sold $1470 worth of tickets, it means that

7.75a + 10.25b = 1470 - - - - - - - - -2

The question can be answered by creating two linear equations, one representing the total number of tickets (a + c = 150) and the other representing the total earnings from the ticket sales (10.25a + 7.75c = 1470). Solving this system of equations will yield the number of adult and child tickets sold.

This problem can be solved using a system of linear equations, where one equation represents the total number of tickets sold and the other equation represents the total dollar value of the tickets sold.

The first equation is formed from the total number of tickets, which is the sum of adult tickets and child tickets: a + c = 150

The second equation is formed from the total cost of the tickets, where $10.25, the cost of an adult ticket, is multiplied by the number of adult tickets, and $7.75, the cost of a child ticket, is multiplied by the number of child tickets. This sum should be the total earnings from the ticket sales: 10.25a + 7.75c = 1470

Therefore, the system of equations to solve this problem is a + c = 150 and 10.25a + 7.75c = 1470.

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Answer:

Step-by-step explanation:

Let x represent the distance that the truck was driven.

Buck rented a truck for $39.95 plus $0.32 per mile. This means that the total cost of driving x miles with the truck would be

39.95 + 0.32x

Before returning the truck, he Filled the tank with gasoline, which cost $9.85. This means that the total amount that he spent is

39.95 + 0.32x + 9.85

If the total cost was $70.23, it means that

39.95 + 0.32x + 9.85 = 70.23

49.8 + 0.32x = 70.23

0.32x = 70.23 - 49.8 = 20.43

x = 20.43/0.32 = 63.8

Approximately 64 miles

Answer:

Fran was incorrect.

Correct representation: [tex]c \geq 15[/tex], where c is the number of customer during any time of day.

Step-by-step explanation:

We are given the following in the question:

Fran used the given inequality to represent the number of customers in a shop at any time.

[tex]c > 15[/tex]

where c is the number of customer during any time of day.

The least number of customers in a shop at any time during the day was 15.

Thus there could be 15 or greater than 15 customers in shop during any ime of day.

Thus, Fran was incorrect.

The correct representation is given by the inequality

[tex]c \geq 15[/tex]

where c is the number of customer during any time of day.

Answer:

Fran is incorrect.

The inequality is c ≥ 15

Step-by-step explanation:

The area of circle is 379.94 cm².

Step-by-step explanation:

Given,

Radius of circle = 11 centimeters

We have to calculate the area of circle.

We know that;

Area of circle = [tex]\pi r^2[/tex]

Here;

π = 3.14 , r = 11

Area of circle = [tex]3.14*(11)^2[/tex]

Area of circle = 3.14*121

Area of circle = 379.94 squared centimeters

The area of circle is 379.94 squared centimeters.

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Answer:

564,480

Step-by-step explanation:

The appliocation of factorial n! = n(n-1)(n-2)(n-3).....

Arrangement when french and English delegates are to seat together ;

since we have 10 delegates, Freench and english will be treated as 1 delegates as such we have 9groups. The number of ways of arranging 9groups = 9! and if the french and English are to be treated as a group = 2!

Hence, number of ways of arrangement = 9! x 2! = 725,760

In this case, English and french are to be seated next to each other while russia and US delegates are not to seat nect to each other ; both groups will be treated as 2 as such we have 8groups, the number of ways of arranging 8groups = 8!

french and english together = 2!

Russia and US together = 2!

The number of ways of arrangement = 8! x 2! x 2! = 161,280

hence the number of ways of arranging 10 delegates if french and english are to be seated next to each other and Russia and US are not to be seated next to each other;

N = 725,760 - 161,280 = 564,480

There are 282,240 different seating arrangements possible if the French and English delegates are to be seated next to each other and the Russian and U.S. delegates are not to be next to each other.

To determine the number of different seating arrangements, we can treat the French and English delegates as a single entity. Therefore, we have 9 entities overall (Russia, (France and England), United States, and the 6 remaining countries).

The number of arrangements of these 9 entities is 9! (9 factorial) which is equal to 362,880. However, since the Russian and U.S. delegates cannot be seated next to each other, we need to subtract the number of arrangements where they are together.

Let's consider the Russian and U.S. delegates as a single entity as well. Now we have 8 entities to arrange (Russian and U.S., (France and England), and the 6 remaining countries). The number of arrangements of these 8 entities is 8! which is equal to 40,320.

Finally, we need to consider the arrangements of the Russian and U.S. delegates within their entity. The Russian and U.S. delegates can be arranged in 2! (2 factorial) ways, which is equal to 2.

Therefore, the total number of different seating arrangements is 362,880 - (40,320 * 2) = 362,880 - 80,640 = 282,240.

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Answer:

  -6

Step-by-step explanation:

Take a couple of differences and see:

  11 -17 = -6

  5 -11 = -6

The common difference is -6.