PLEASE HELP 30 pts for this

The measure of each interior angle of the regular polygon is equal to 150°.

In Euclidean geometry, a regular polygon simply refers to a form of polygon which has all of its sides and interior angles being equal.

In Geometry, the sum of the interior angles of both a regular and irregular polygon is given by this formula:

Sum of interior angles = 180 × (n - 2)

Where:

n represents the number of sides of a regular polygon.

Similarly, the measure of each interior angle of a regular polygon can be calculated by using this mathematical expression:

Interior angles = [180 × (n - 2)]/n

Interior angles = [180 × (12 - 2)]/12

Interior angles = 180 × (10)/12

Interior angles = 1800/12

Interior angles = 150°

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The probability of odd or less than 6 is 0.75 which is 75%

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

From the question, there are 4 numbers

These include: 5,6,7,8

Pr(odd) 2/4

Pr(x<6) 1/4

Adding the fractions we have

1/2  + 1/4  = 3/4  = 0.75

Converted to percentage = 75%

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Answer: Acute Triangles

The shortest distance between planet Q and planet R is  1.64 × 10⁷ .

RP = 1.6 * 10⁷

most compact distance

The Pythagoras theorem x₂ = R * P² + Q * P² is then used to determine the shortest distance (x).

This results in x = (3.6 * 10⁶) + (1.6 * 10⁷) = 2.

x² = 12.96 * 10¹²  + 2.56 * 10¹⁴ should be evaluated.

Write the equation as: x²= 12.96 * 10¹² + 256 * 10¹²

Sums x² = 268.96*10¹² should be evaluated.

multiply both sides' square roots.

x = 16.4 * 10⁶

Replace with: x = 1.64 * 10⁷

In light of this, the distance between planet Q and planet R is 1.64 * 10⁷ km.

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The complete  question is

The distances between some planets are given below.

Planet Q is 3.6 x 10⁷ to the power of 6 km from planet P.

Planet R is 1.6 x 10⁷ to the power of 7 km from planet P.

Work out the shortest distance between planet Q and planet R. Give your answer in standard form.

The expression is factorized to give x(x+ 12) + 8( y + 12)

From the information given, we have that the expression as;

(x+y)²+8(x+y)+12

Now, expand the bracket, we get;

(x + 2) (x+2) + 8x + 8y + 12

expand the squared bracket, we get;

x² + 2x + 2x + 4 + 8x + 8y + 12

Now, collect like terms

x² 2x + 2x + 8x + 8y + 4 + 12

Add the collected like terms, we get;

x² + 12x + 8y + 16

Now, let's factorize in airs by grouping, we get;

(x² + 12x) + (8y + 16)

Factor the common terms

x(x+ 12) + 8( y + 12)

Hence, the expression is x(x+ 12) + 8( y + 12)

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The solution to the system of linear equations is: x = 5, y = (6x + 7 - 10/4)/(-5) = -4/5, z = -5/4.

To solve the system of linear equations using elimination, we can manipulate the coefficients of the variables to make one of the variables zero in one of the equations. Then, we can use this equation to eliminate that variable from the other equations.

Starting with the first two equations:

6x - 5y - 4z = -7

5x - 4y - 4z = -5

We can multiply the first equation by 5 and the second equation by 6 to get rid of the coefficients of x in both equations:

30x - 25y - 20z = -35

30x - 24y - 24z = -30

Now, we can subtract the first equation from the second equation to eliminate x:

0y - 4z = 5

So, z = -5/4

Next, we can use this value of z to solve for y in either of the first two equations:

6x - 5y - 4(-5/4) = -7

Expanding the right side:

6x - 5y + 10/4 = -7

And solving for y:

y = (6x + 7 - 10/4)/(-5)

Finally, we can use the value of y and z to solve for x in any of the first two equations:

6x - 5((6x + 7 - 10/4)/(-5)) - 4(-5/4) = -7

Expanding and solving for x:

6x - (6x + 7 - 10/4)/5 - 10/4 = -7

Multiplying both sides by 5:

30x - 6x - 7 + 2 = -35

And solving for x:

x = 5

Finally, we can use the values of x, y, and z to check the third equation:

3y + 6z = 6

Substituting the values we found:

3((6x + 7 - 10/4)/(-5)) + 6(-5/4) = 6

Expanding and solving:

The left side is equal to 6 and the right side is equal to 6, so the solution is consistent.

Therefore, the solution to the system of linear equations is:

x = 5, y = (6x + 7 - 10/4)/(-5) = -4/5, z = -5/4

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(a) Circumference of Earth in kilometers: 40,075.017 km

(b) Surface area of Earth in square kilometers: 510.1 million km^2

(c) Volume of Earth in cubic kilometers: 1.08 trillion km^3

To calculate these values, we use mathematical formulas that relate to the sphere shape of the Earth.

For (a), we use the formula for the circumference of a circle, C = 2 * pi * r, where r is the radius of the Earth in meters (6.37 x 10^6 m). We then convert this result to kilometers by dividing by 1000.

For (b), we use the formula for the surface area of a sphere, A = 4 * pi * r^2, where r is the radius of the Earth. Again, we convert this result to square kilometers.

For (c), we use the formula for the volume of a sphere, V = (4/3) * pi * r^3, where r is the radius of the Earth. We then convert this result to cubic kilometers by dividing by 10^9.

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Answer: 12 11/26 laps

Step-by-step explanation:

9 3/13= 9 6/26

9 6/26+ 3 5/26=12 11/26.

When rotated about its center, a regular heptagon has 7 rotational symmetries. In addition to rotational symmetry, a regular heptagon has 1 line of reflectional symmetry.

Rotation symmetry, also known as radial symmetry or circular symmetry, is a fundamental concept in geometry that refers to the property of a shape to remain unchanged after rotating it about a fixed point. This point is typically the center of the shape, although it can be any point within the shape.

The amount of rotation required for the shape to become congruent to its original form is called the "angle of rotation." If a shape can be rotated multiple times and still remain unchanged, it is said to have multiple rotational symmetries.

For example, a circle has an infinite order of rotational symmetry, as it can be rotated 360 degrees and still look exactly the same. On the other hand, a square has 4 rotational symmetries, as it can be rotated 90 degrees and still look the same 4 times.

Rotational symmetry is a useful concept in mathematics and science as it provides a way to describe the symmetry of objects and shapes in the real world. It also helps us understand how objects and shapes change when they are rotated, and it provides a way to classify objects based on their symmetrical properties.

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If line m and n are parallel, the value of x is determined as 10.

The value of x is determined by applying the following rules of parallel lines as shown below.

The corresponding angles of the parallel lines are equal,

the corresponding angles are given as;

8x + 50 = 130

now solve for x, by making x the subject of the formula.

8x = 130 - 50

8x = 80

divide through by 8

8x / 8 = 80 / 8

x = 10

Thus, the value of x is function of the corresponding angles.

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Therefore, in order for Joey to earn the same hourly wage as Blake, she will have to labor for 8 six-month periods or 4 years.

We'll refer to the quantity of six-month intervals as x. Blake's hourly wage can be represented as 16 + 0.50x, and Joey's hourly wage may be represented as 12 + 1.50x after x intervals. We may set the two expressions equal to one another and solve for x to determine when Joey's salary will match Blake's salary:

12 + 1.50x = 16 + 0.50x \s0.50x = 4 \sx = 8

Joey will therefore need to work for 8 six-month periods, or 4 years, in order to make the same hourly rate as Blake.

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The complete coordinates are (8, 0), (0, -8), (-8, 0) and (0, 8)

From the question, we have the following parameters that can be used in our computation:

x^2 + y^2 = 64

The above is the equation of a circle

Express 64 as 8^2

So, we have

x^2 + y^2 = 8^2

When y = 0, the possible values of x are

x = -8 and x = 8

When x = 0, the possible values of y are

y = -8 and y = 8

This means that the complete coordinates are (8, 0), (0, -8), (-8, 0) and (0, 8)

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The number which satisfies the given condition is 28.

According to the question

The number 28 is less than 50 and has a multiple of 7. It becomes 82, which is also a multiple of 8 when its digits are inverted. As a result, the criteria can only be satisfied by the number 28. This may be verified by quickly determining whether any other number less than 50 that is a multiple of 7 has its digits switched around to become a multiple of 8. However, it is clear that none of the other figures satisfy both requirements.

In light of this, the answer to this issue is 28.

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The number which satisfies the given condition is 28.

According to the question

The number 28 is less than 50 and has a multiple of 7. It becomes 82, which is also a multiple of 8 when its digits are inverted. As a result, the criteria can only be satisfied by the number 28. This may be verified by quickly determining whether any other number less than 50 that is a multiple of 7 has its digits switched around to become a multiple of 8. However, it is clear that none of the other figures satisfy both requirements.

In light of this, the answer to this issue is 28.

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The sample space for choosing one card is, S={I, L, L, M, P, T, U, Y}

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results.

Given that,

A set of eight cards were labeled with M, U, L, T, I, P, L, Y.

Here, the sample space is;

{ S, U, B, T, R, A, C, T}

Now, Elements in order is,

⇒ S = {I, L, L, M, P, T, U, Y}

Therefore, the sample space for the given cards is,

S = {I, L, L, M, P, T, U, Y}

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Answer: I think the answer would be C

The number of ways you can select n elements from N elements by using factorial (!) when n=2 and N=10 is 45.

Factorial is a crucial mathematical operation that is used to determine the number of possible arrangements or the ordered set of numbers. Daniel Bernoulli is credited with discovering the factorial function's well-known interpolating feature. Numerous mathematical ideas, including probability, permutations and combinations, sequences and series, etc., use the factorial concept. A factorial function, in essence, multiplies a number by each number below it until it equals 1. For instance, the factorial of 3 is equal to 6 and reflects the multiplication of the integers 3, 2, and 1.

Now,

The number of ways you can select n elements from N elements when n=2 and N=10 is [tex]\frac{N!}{n!(N-n)!}[/tex]

=[tex]\frac{10!}{2!(8)!}[/tex]

=[tex]\frac{10 \times 9 \times \times 8!}{8! \times 2 !}[/tex]

=45

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The area of the shaded portion is area of the outer circle - area of the inner circle = 1017.36 - 379.94 = 637.42 yards²

All points on a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

The following are some of the circle's crucial characteristics:

The radius of the inner circle = 22 /2 = 11 yard = r1

The distance between the inner cirle and outer circle = 7 yards

The radius of the outer circle = 18 yards = r2

The Area of the outer circle = π*r2² = 3.14 * 18² = 1017.36 yards²

The Area of the inner circle = π*r1² = 3.14 * 11² = 379.94 yards²

The area of the shaded portion is area of the outer circle - area of the inner circle = 1017.36 - 379.94 = 637.42 yards²

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The equation we will use is Equation 1: 2x − 3y = 11. The values of x and y are 1 and -3.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given;

Equation 1: 2x − 3y = 11

Equation 2: x + 2y = −5

Now,

Equation 2: x + 2y = −5

x=-5-2y

Substituting the value of x in equation 1

2(-5-2y)-3y=11

-10-4y-3y=11

-10-7y=11

-7y=11+10

-7y=21

y=-3

Substituting the value of y in equation 2

x+2*-3=-5

x=-5+6

x=1

Therefore, the solution of the system of equations will be x=1,y=-3

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2/5th of a number is 40% of that number.

In order to calculate the percentage of a given number that is equal to 2/5 of that number, we must first convert the fraction to percentage form, which is as follows:

= 2/3 * 100

= 0.4 * 100

= 40%

We will use the following example to validate the aforementioned process:

Assume that it is 50.

First, 2/5 of 50 equals 2/5 * 50, or 20.

Second, 40% of 50 equals 40/100 * 50 = 0.4 * 50 = 20.

The equality of the two results is evident.

2/5 of a number is therefore 40% of that number.

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The question is incomplete;

\dfrac25 start fraction, 2, divided by, 5, end fraction of a number is what percentage of that number?

The length d for the angle of depression 3° and altitude 1m is equal to 19 m to the nearest metre using the trigonometric ratio of cosine for the angle 87°

The angle of depression is an angle formed between the horizontal line and the line of sight when an observer looks downwards.

Considering the right triangle formed by the length d and the altitude of 1 m, we shall derive a complementary angle as:

90° - 3° = 87°

such that;

cos 87° = 1/d {adjacent/hypotenuse}

d = 1/cos 87°

d = 19.1073.

Therefore, the length d for the angle of depression 3° and altitude 1m is equal to 19 m to the nearest metre using the trigonometric ratio of cosine for the angle 87°.

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The area enclosed between the graph of Æ and the x-axis for 1 ≤ x ≤ 3 is estimated to be 4/3.

Ram's Rule is a numerical integration method used to estimate the area under a curve by dividing it into trapezoids. The formula for calculating the area under the curve is given by A = (1/2) x (b - a) x (f(a) + f(b)), where A is the area, b and a are the limits of the integration and f(a) and f(b) are the values of the function at the limits a and b respectively.

In this case, the area enclosed between the graph of Æ and the x-axis for 1 ≤ x ≤ 3 can be estimated using Ram's Rule as follows:

A = (1/2) x (3 - 1) x (1/1 + 1/3)

 = (1/2) x (2) x (4/3)

 = 4/3.

Therefore, the area enclosed between the graph of Æ and the x-axis for 1 ≤ x ≤ 3 is estimated to be 4/3.

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The volume of the solid is 0 cubic units.

Integration is a fundamental concept in calculus that deals with finding the area under a curve and calculating the accumulation of values over an interval. Integration can be thought of as the reverse of differentiation, which is the process of finding the rate of change of a function at a given point.

There are two main types of integration: definite and indefinite integration. Definite integration involves finding the exact area between a curve and the x-axis over a specified interval. Indefinite integration involves finding the general antiderivative of a function, which is a function that, when differentiated, will yield the original function.

The process of integration can be represented symbolically as ∫ (the integral symbol) and the result of an integration is typically represented as an antiderivative. The fundamental theorem of calculus states that differentiation and integration are inverse operations, so the derivative of an antiderivative is the original function.

The volume of the solid is given by the definite integral:

V = ∫_[tex]{y=2}^{1} A(y) dy[/tex]

Where A(y) is the area of the cross-section at y. Since the cross-sections are squares, we know that A(y) = [tex]y^{2}[/tex].

So, the volume is given by:

V = ∫_[tex]{y=2}^{1} y^{2} dy = [\frac{y^{3} }{3} ]_{y=2}^{y=1} = (\frac{8}{3} - (\frac{2^{3} }{3}= (\frac{8}{3}-\frac{8}{3} ) =0[/tex]

The volume of the solid is 0 cubic units.

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Answer:To calculate the length and width of the original figure with a scale factor of 50%, you need to reverse the scaling by multiplying the new dimensions by 100% / 50% = 2.

So if the new length is L, the original length would be L * 2 = 2L. Similarly, if the new width is W, the original width would be W * 2 = 2W.

Step-by-step explanation:here's a step-by-step explanation:

Identify the new length (L) and new width (W) of the figure.

Multiply the new length by a factor of 2 to find the original length: 2L = L * 2

Multiply the new width by a factor of 2 to find the original width: 2W = W * 2

The original length is 2L and the original width is 2W.

Note: This process works for any scale factor, not just 50%. To find the original dimensions, simply multiply the new dimensions by 100% / the scale factor.

Answer: The answer is 1/4.

Step-by-step explanation:

It is not possible to describe the standard deviations of salary, hourly rate, years worked, education, and age without having the data.

Standard deviation is a measure of the spread or dispersion of a set of data. It is calculated as the square root of the variance and is used to give an idea of how far the individual values in a data set are from the mean or average.

In order to describe the standard deviations of salary, hourly rate, years worked, education, and age, we would need to have the actual data for those variables. Without the data, it is not possible to calculate the standard deviations and describe what they tell us about the variables.

It is important to note that the standard deviation can give us information about the distribution of the data and the variability of the values. For example, if the standard deviation is small, this means that the majority of the values are close to the mean, while a larger standard deviation indicates that the values are more spread out. This information can be useful in making inferences about the variables and in making predictions about future values.

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The area of the logo is 6 square feet.

We start wit a logo of 4 inches by 6 inches, and we want to make it 6 times larger, so the new dimensions are:

6*(4 inches) = 24 inches.

6*(6 inches) = 36 inches.

Remember that:

1ft = 12 in

Writting that in feet, we will get:

24 inches = (24/12) ft = 2ft

36 inches = (36/12) ft = 3ft

Then the area of the logo is:

A = 2ft*3ft = 6 ft²

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The value of the integral expression is -1/2ln(9)

From the question, we have the following parameters that can be used in our computation:

Integral of 4/(9 - 8x) from 2 to 9

Using a graphing calculator as a guide, we have the following:

Integrand = -ln(|8x - 9|)/2 from 2 to 9

Substitute the known values in the above equation, so, we have the following representation

Integrand = -ln(|8 * 9 - 9|)/2 + ln(|8 * 2 - 9|)/2

Evaluate

Integrand = -1/2(ln(63/7)

Evaluate the quotient

Integrand = -1/2ln(9)

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The value of in x° is sin x = 3/z

The ratio of an angle's opposing side to its adjacent side, or its tan

tan x = 3/y

cos x = y/z

We choose 3 and y to represent the opposite and adjacent sides, respectively, because this ratio is 3:y.

Technically, we ought to write 3t and yt, but we'll take a chance since y appears in the second ratio as well!

Since y is already used to represent the adjacent side, z is used to represent the length of the hypotenuse.

The right triangle's sides are now finished.

Because tan x = sin(x)/cos(x), therefore

sin x = tan(x)*cos(x)

        = (3/y)*(y/z)

        = 3/z

Answer: a) sin x = 3/z

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The distributive property to factor out the greatest factor 24+18t is 6(4+3t).

The distributive property to factor out the greatest common factor 24+18t.

The Distributive Property is an algebraic property that is used to multiply a single value and two or more values within a set of parenthesis. The distributive Property States that when a factor is multiplied by the sum/addition of two terms, it is essential to multiply each of the two numbers by the factor, and finally perform the addition operation. This property can be stated symbolically as:

Well, some of the common factors that 24 and 18 shares are 2, 3, and 6.

The greatest factor is 6.

⇒ [tex]\frac{24}{6}[/tex]=4

⇒ [tex]\frac{18t}{6}[/tex]=3

Because 6x4=24 and 6 x 3t= 18t

Therefore, the distributive property to factor out the greatest factor 24+18t is 6(4+3t).

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The inequality and number line that shows the solution is x>-7.

Given,

-4x <28

(-4x) (-1) > 28 (-1)

Simplify

4 x>-28

Divide both sides by 4

[tex]\frac{4 x}{4} > \frac{-28}{4}[/tex]

Simplify

x>-7

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Answer:

X=5 Cars

Y=6 Vans

Step-by-step explanation:

Let's assume the number of cars used is x and the number of vans used is y.

We can set up two equations based on the information given:

x + y = 11 (the total number of vehicles used)

5x + 8y = 73 (the total number of students that went on the trip)

We can use substitution to solve for one of the variables in terms of the other:

y = 11 - x

5x + 8(11 - x) = 73

5x + 88 - 8x = 73

-3x = -15

x = 5

So the class used 5 cars and 11 - 5 = 6 vans.