Four integers have a mean of 8, a median of 6, a mode of 6 and a range of 14
Find the four integers

Interior angle-

All interior angles of a regular polygon are equal. The formula for calculating the magnitude of the interior angle is:

Interior angle of polygon = sum of interior angles ÷ number of sides. The sum of the exterior angles of a polygon is 360°.

Exterior angle-

An exterior angle is an angle that is parallel to, but outside, the interior angle of a polygon. The exterior angle measurement is equal to the sum of the two opposite interior angles.

according to the question,

given data

interior angle=8 exterior angle

we know that,

interior angle+ exterior angle=180

let us consider ,

exterior angle=x

so we can say that,

8 exterior angle + exterior angle =180

8x+x=180

9x=180

x=20

we know that ,

the number of sides=360/x

=360/20

=36/2

=18

the number of sides of the polygon is 18

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The number of volunteers recruited for the first 5 weeks is; 486 people

A geometric sequence is defined as a sequence in which the result of the division of consecutive terms is always the same, called common ratio r.

The nth term of a geometric sequence is given by:

aₙ = a₁rⁿ⁻¹

where;

a₁ is the first term

r is the common ratio

In this question, on the first week there are 6 people, and since each new people involve three more, the common ratio is 3, hence the parameters for the geometric sequence are:

a₁ = 6

r = 3

Hence the number of people after n weeks is:

aₙ = 6(3)ⁿ⁻¹

Thus, the number of volunteers recruited for the first 5 weeks is;

a₅ = 6(3)⁵⁻¹

a₅ = 6 * 3⁴

a₅ = 486

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Answer:

x + x - x = x

explanation:

give us the actual formula lol

Answer: He bought three adult tickets and two child tickets

Step-by-step explanation:

The answer is 28$

2+2= 4

8+8= 16

16 + 4= 20

20 + 8 =28

He bought two child tickets and three adult tickets

The expression that is equivalent to the perimeter of the rectangle in the image shown is, 6x + 8.

To find the perimeter of a rectangle, add all the four sides of the rectangle. The following formula can be used:

Perimeter (P) = 2(length + width).

In the rectangle shown below, the dimensions are:

Length of rectangle = 2x + 3

Width of rectangle = x + 1

Substitute into the perimeter each expression of the dimensions:

Perimeter = 2[(2x + 3) + (x + 1)]

Open the parentheses by applying the distributive property of equality:

Perimeter = 2(2x + 3 + x + 1)

= 2(3x + 4)

= 2(3x) +2(4)

= 6x + 8

Therefore, the expression is, 6x + 8.

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Answer: <D, < E, <C

Step-by-step explanation:

The point of the compass located in order to make the arcs is points X and Y.

An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc. A circle contains an arc. For instance, a quarter-circle and a semicircle are both examples of arcs. A minor arc is one that is smaller than half of the circle it is a part of, or less than a semicircle, whereas a major arc is one that is more than half of its circle.

Given

The following figure was drawn using a straightedge and a compass.

The point of the compass located in order to make the arcs:

1. points X and Y

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Step-by-step explanation:

d is the answer as far as I can tell from a little experience

The required solution of the given inequality is given as x > 4, and the answer for the blanks is to Divide both sides by -8 and change the inequality sign.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Given inequality,
-8x < 32
Divide both sides by -8
x > 4

The sign of the inequality change because multiplication with the negative value changes the inequality sign and the higher negative value is the least value.

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After solving the equation the length of AB is [tex]2\sqrt{3}[/tex]

What do you mean by trigonometry?

Trigonometry  “triangle” and  “measure”) is a branch of mathematics that studies the relationship between the side lengths and angles of triangles.

A trigonometric ratio is the ratio between the edges of a right triangle.

The sine function (sin) defined as the ratio of the opposite side of the angle to the hypotenuse.

In the given triangle ABC , use sin ratio to find AB.

tan θ = P/B

tan 30 = AB/6

[tex]\frac{1}{\sqrt{3} } =AB/6[/tex]

AB = [tex]\frac{6}{\sqrt{3} }[/tex] = [tex]\frac{6}{\sqrt{3} }\times \frac{\sqrt{3}}{\sqrt{3}}= \frac{6\sqrt{3}}{3}=2\sqrt{3}[/tex]

Therefore, length of AB is [tex]2\sqrt{3}[/tex]

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Answer:

management accountant prepared a decision model which solve sell at split off or process

further decision problem. Which function did he provided?

A. Scorekeeping function C) Problem solving function

B. Attention directing function. D) Record keeping function E) None

Answer:

3(4) - 2 is 10 the value is 10

5(2) + 6 is 16 the value is 16

I hope this helps have a good day or night!

Answer:

x ≥ 72/5

8.6 ≤ x -5 4/5= 8.6 ≤ x -29/5

8.6 ≤ x -29/5= x ≥ 72/5

The needed 3rd-degree polynomial function with real coefficients matching the specified constraints will be y=-5x³+10x²-45x+90.

A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables. x2 4x + 7 is an example of a polynomial with a single indeterminate x. Polynomials are sums of k-x^n terms, where k can be any number and n can be any positive integer. 3x+2x-5, for example, is a polynomial. Polynomials are introduced. This video defines words such as degree, standard form, monomial, binomial, and trinomial.

Here,

y=-5(x-2)(x-3i)(x+3i)

y=-5(x-2)(x²+9)

y=-5(x³-2x²+9x-18)

y=-5x³+10x²-45x+90

The required 3rd-degree polynomial function with real coefficients satisfying the given conditions will be y=-5x³+10x²-45x+90.

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Hello,

I hope you and your family are doing well!

To solve this problem, we can use the formula:

total cost = set-up fee + (cost per copy * number of copies)

In this case, we know the total cost and the set-up fee, and we want to find the number of copies. We can substitute these values into the formula and solve for the number of copies:

$32.20 = $14.95 + ($0.03/copy * number of copies)

Subtracting the set-up fee from both sides of the equation gives:

$17.25 = $0.03/copy * number of copies

Dividing both sides of the equation by the cost per copy gives:

number of copies = $17.25 / $0.03/copy = 575 copies

So Emilio was charged $32.20 to print 575 copies of the brochures.

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Happy Holidays!

the area of the generic rectangle will be x²-2x-15.

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A quadrilateral with equal angles and parallel opposite sides is referred to as a rectangle. Around us, there are a lot of rectangle items. The length and width of any rectangle form serve as its two distinguishing attributes. The width and length of a rectangle, respectively, are its longer and shorter sides.

Area of rectangle is A = a*b

(x + 3)(x - 5) in a generic rectangle

The product will give the area

x²-2x-15

hence the area of the generic rectangle will be x²-2x-15.

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Answer:

D.  b + c = 68

    0.08b + 0.15c = 6.00

Step-by-step explanation:

The total cost is $6.00

The total amount of copies is 68

To find the total cost, we multiply the amount of copies by the individual price. So we get

0.08b + 0.15c = 6.00

We add the amount of copies bought to get a total of 68, so we get this equation:

b + 6 = 68

Answer:

there will be only 1 more slice to eat

Answer:

-2

Step-by-step explanation:

Given,

g(x) = f(4)

or, 2 - 4x = 3*4 - 2

or, 2 - 4x = 10

or, 2 - 10 = 4x

or, -8 = 4x

or, x = -2

Answer:

The possible coordinates of point A are (-3, 8) and (-3, -4).

Step-by-step explanation:

We can find the possible coordinates of point A by using the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is equal to the square root of (x2-x1)^2 + (y2-y1)^2. We know that the x-coordinate of point A is -3 and the distance between point A and point B is 10 units. We can use this information to solve for the y-coordinate of point A:

Copy code

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

d = sqrt((5-(-3))^2 + (2-y1)^2)

d = sqrt(8^2 + (2-y1)^2)

d = sqrt(64 + (2-y1)^2)

d = sqrt(64 + (y1-2)^2)

d = 10

sqrt(64 + (y1-2)^2) = 10

64 + (y1-2)^2 = 100

(y1-2)^2 = 36

y1-2 = +/- 6

y1 = 8 or -4

Therefore, the possible coordinates of point A are (-3, 8) and (-3, -4).

Answer: $71.53

Step-by-step explanation:

77.76 = 100%

Answer:

 (a) A  and B are similar but not congruent

Step-by-step explanation:

All of the rectangles have sides in the ratio of 2:1, so are all similar. Only the rectangles that are the same size are congruent: A and C.

Dimensions of the Rectangle are : 16 feet by 13 feet .

A rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal . A rectangle has two dimensions. we can measure its length and, perpendicular to that, its width.

Rectangle is 3 feet longer than it is wide and its area is 208 sq-feet .

Area of Rectangle = l×b  ( Where l = length , b = breadth )

Therefore , Let X be the the width of rectangle . then from given it's length is (X+3).

∴ X × (X+3) = 208

∴ [tex]x^{2}[/tex]+3X-208 = 0

(X+16)(X-13) = 0

X = -16 & X = 13

Distance can't be negative so Width = X = 13 feet.

∴ Length = X+3 = 16 feet.

Thus the Dimensions are 16 feet by 13 feet .

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For the given triangle the coordinate of circumcenter is obtained as (1/3, 7/3).

The circumcenter for a triangle is defined as the center of the circle that touches all the vertices of the triangle. It is also found as the point of intersection of all of the perpendicular bisectors of the sides of triangle. All the vertices of the triangle are equidistant from the circumcenter.

Suppose the coordinate of the circumcenter be (x, y).

Now, all the vertices of the triangle should be equidistant from the circumcenter.

The equation can be written using distance formula as follows,

(x - 0)² + (y - 0)² = (x - 2)² + (y - 4)²

⇒ 4x + 8y = 20

⇒ x + 2y = 5                  (1)

And, (x - 0)² + (y - 0)² = (x - 5)² + (y - 1)²

⇒ 10x + 2y = 26

⇒ 5x + y = 13                  (2)

Multiply equation (2) by 2 nd then subtract equation (1) to get,

2(5x + y) -  (x + 2y) = 13 × 2 - 5

⇒ 9y = 21

⇒ y = 7/3

Substitute y = 7/3 in equation (1) to get,

x + 2 × 7/3 = 5

⇒ x = 5 - 14/3

⇒ x = 1/3

Hence, the coordinate of the circumcenter is given as (1/3, 7/3).

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By evaluating a revenue equation, we will see that she earned $139 last week.

We know that Isha is a pet sitter, and she earns $5 for each cat and $12 for each dog.

So, if she pet sats for x cats and y dogs, the revenue will be:

R(x, y) = $5*x + $12*y

In this case we know that she pet sat for 11 cats and 7 dogs, then we have:

x = 11

y = 7

So we need to evaluate the above revenue function, we will get:

R(11, 7) = $5*11 + $12*7

R(11, 7) = $55 + $84

R(11, 7) = $139

Isha earned $139 last week.

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The square root of 15 is approximately 4.

To approximate the square root of 15, we can find the perfect squares that are closest to 15. The perfect squares that are closest to 15 are 9 and 16. Since 15 is closer to 16, we can say that the square root of 15 is slightly less than 4.

Another approach could be:

The square root of 15 is approximately 3.87. Rounding to the nearest integer gives us 4. To round a number, we look at the number following the place value we are rounding to. If it is greater than or equal to 5, we round up. If it is less than 5, we round down. In this case, the digit following the ones place is 8, which is greater than 5, so we round up to 4.

The sum of the two complex numbers will give:

(-4 + i) + (10 - 5i) = 6 - 4i

So the correct option is the third one.

Let's assume we have two complex numbers which are:

A = a + bi

B = c + di

The sum between these two complex numbers is:

A + B = (a + bi) + (c + di)

Taking i as a common factor we can rewrite:

(a + bi) + (c + di) = a + c + (b + d)i

And that is the general sum.

Here we want to solve:

(-4 + i) + (10 - 5i)

Again, if we take i as a common factor we can rewrite:

-4 + 10 + (1 - 5)*i

6 - 4i

So the correct option is the third one.

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The value of the x would be 9.

Option (A) is correct.

What is a complementary angle?

A complementary angle is an angle that, when added to another angle, forms a right angle (90 degrees). Complementary angles are pairs of angles that add up to 90 degrees.

Angle JKM and angle MKN are complementary angles

so

   (3x + 2) + (6x + 7) = 90

  9x + 9 = 90

  9(x + 1) = 90

     x + 1 = 10

    x = 9

Hence, the value of the x would be 9.

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After solving the equation the value of the x would be 9. Therefore, the correct option is A.

What is a complementary angle?

A complementary angle is a pair of angles that add up to 90 degrees. Complementary angles can be adjacent angles, or angles that share a common vertex and side, or they can be nonadjacent angles that have no common points or sides. Complementary angles are usually referred to by their sum, such as "90-degree angles" or "angles that add up to 90 degrees." Complementary angles can also be called supplementary angles when they add up to 180 degrees.

Angle JKM and angle MKN are complementary angles

so   (3x + 2) + (6x + 7) = 90

 9x + 9 = 90

 9(x + 1) = 90

    x + 1 = 10

   x = 9

Hence, the value of the x would be 9.

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The solution to the equation f(x)=g(x) are x=-2 and x=1.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The given functions are f(x)=-x+6 and g(x)=-x²-2x+8.

Now, f(x)=g(x)

-x+6=-x²-2x+8

⇒ x²+x-2=0

⇒ x²+2x-x-2=0 (Splitting middle term method)

⇒ x(x+2)-1(x+2)=0

⇒ (x+2)(x-1)=0

⇒ x+2=0 and x-1=0

⇒ x=-2 and x=1

Therefore, the solution for the obtained equation are x=-2 and x=1.

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