The measure of one interior angle of a regular icosagon, or 20-sided figure, is (12x - 6)°.
Part A: What is the sum, in degrees, of the interior angles of a regular icosagon?
O 1800
O 3204
O 3240
O 3600
Part B: Which equation could be used to find the value of x?
O 162 = 12x6
O 180 = 12x - 6
O 3240 = 18(12x-6)
O 3600 = 20(12x - 6)

[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"z" varies directly with }x^2}{z = k(x^2)}\hspace{5em}\textit{we also know that} \begin{cases} z=96\\ x=4 \end{cases} \\\\\\ 96=k(4^2)\implies \cfrac{96}{4^2}=k\implies 6=k\hspace{8em}\boxed{z=6x^2} \\\\\\ \textit{when x = 3, what's "z"?}\qquad z=6(3^2)\implies z=54[/tex]

There are 7.8 pounds per bag of apples

Since unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that ;

Petra has 126 pounds of apples to sell. She has 39 bags in all.

126 total pounds = 39pounds of apples . since there are 5 bags of apples ,

We would divide 5 by 39.

39/5= 7.8 pounds per bag of apples .

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Based on the survey, we can say that between 12,776 and 14,000 citizens in the town would support a new coffee shop.

The margin of error is a measure of the uncertainty in the survey results. It is based on the sample size and the level of confidence desired. In this case, the margin of error is 1.7%.

This means that the actual percentage of citizens in the town who would support a new coffee shop could be as much as 1.7% higher or lower than the survey result of 37%.

To calculate the range of possible values for the percentage of citizens who would support a new coffee shop, we add and subtract the margin of error from the survey result:

37% + 1.7% = 38.7%

37% - 1.7% = 35.3%

Therefore, based on the survey, we can say that between 35.3% and 38.7% of the citizens in the town would support a new coffee shop.

To determine the number of people who would support a new coffee shop, we need to multiply the percentage by the population of the town:

35.3% of 36,170 = 12,776

38.7% of 36,170 = 14,000

Therefore, based on the survey, we can say that between 12,776 and 14,000 citizens in the town would support a new coffee shop.

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The area of the composite figure is equal to 89.5 square yards

The composite figure can be observed to be made up of a large rectangle at the center with a smaller rectangle and a triangle by the sides, so we shall calculate for the area of the three shape and sum the results to get the total area of the composite figure as follows:

area of the larger rectangle = 14 yd × 5 yd = 70yd²

area of the smaller rectangle = 5 yd × 3 yd = 15 yd²

area of the triangle = 1/2 × 3 yd × 3 yd= 4.5 yd²

total area of the composite figure = 70yd² + 15 yd² + 4.5 yd²

total area of the composite figure = 89.5 yd²

Therefore, the area of the composite figure is equal to 89.5 square yards

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The unknown measures and angle measures are:

A. LH ≈ 45.68; m∠K ≈ 55°; m∠L ≈ 35°

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

The  unknown measures of the triangle can be founding as follow:

LH² = 56² - 32.4²  (Pythagoras Theorem)

LH = √(56²- 32.4²)

LH = 45.68 units

sin K = 45.68/56

K = sin⁻¹(45.68/56)

K ≈ 55°

Thus, m∠K ≈ 55°

sin L =  32.4/56

L = sin⁻¹( 32.4/56)

L ≈ 35°

Thus, m∠L ≈ 35°

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It is false that the vector u is formed according to the given linear combination.

If the statement regarding the linear combination is true, we have that the following equality is true:

u = 2v1 - 2v2 - v3.

The vectors are given as follows:

Hence we verify the equation as follows:

(6,8) = 2(1,2) - 2(3, 4) - (-1, 0)

(6,8) = (2, 4) - (6, 8) + (1,0)

(6,8) = (2 - 6 + 1, 4 - 8 + 0)

(6, 8) = (-3, -4).

The statement is false, as the sides of the equality are different.

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Answer:

When two parallel lines are intersected by a transversal, the alternate interior angles are the pairs of non-adjacent angles that are located between the two parallel lines and on opposite sides of the transversal. These angles are congruent, which means they have the same measure. The other type of angles mentioned in the statement, which are supplementary, are the pairs of adjacent angles that are located on the same side of the transversal and outside the parallel lines. These angles add up to 180 degrees.

The correct choice is "consecutive interior angles are supplementary."

The height and width of the prism are x and 3x - 2

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

V(x) = 3x^3 + x^2 - 2x + 3

Length = x + 1

This means that

Side area = Volume/Length

So, we have

Side area = (3x^3 + x^2 - 2x + 3)/(x + 1)

When evaluated, we have

Side area = 3x^2 - 2x + 3/(x + 1)

Ignoring the remainder, we have

Side area = 3x^2 - 2x

Factorize

Side area = x(3x - 2)

This means that

height = x and width = 3x - 2

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The probability of passing the test by random guessing is 0.003%.

To estimate the probability of passing a true/false test of 70 questions, we can use the normal approximation to the binomial distribution. Since each question has only two possible outcomes (true or false), the binomial distribution can be used to calculate the probability of getting a certain number of correct answers out of 70.

The mean of the binomial distribution can be calculated as np, where n is the number of trials (70) and p is the probability of success (0.5, since the responses are random guesses). The standard deviation of the binomial distribution can be calculated as the square root of np*(1-p).

To find the probability of passing the test, we need to find the number of correct answers required to achieve a score of 80% or higher. Since 80% of 70 is 56, we need to get at least 56 questions correct.

Using the normal approximation, we can approximate the binomial distribution with a normal distribution with mean 35 and standard deviation 4.79. To find the probability of getting at least 56 questions correct, we can standardize the value (56-35)/4.79 = 4.02 and look up the probability in a standard normal table. The probability of getting at least 56 questions correct is approximately 0.00003.

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The percentage of the new mixture of peanuts will be 13%. Then the correct option is C.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Jenny mixed 4 kg of mixed nuts containing 16% peanuts with 12 kg of mixed nuts containing 40% peanuts.

The percentage of the new mixture of peanuts will be given as,

P = [(4 x 0.16) / (12 x 0.40)] x 100

P = [0.64 / 4.80] x 100

P = 0.1333 x 100

P = 13.33%

P ≈ 13%

Thus, the correct option is C.

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According to the information, the ball returns to the ground about 13.6 feet away.

To calculate how many feet away the ball returns to the ground we have to consider that the ball starts 0 feet above the ground (assuming the ground level is the reference point, where h(x) = 0).

To find the maximum height, we need to find the vertex of the parabola, which occurs at

x = -b/2a

where,

a = -0.25

b = 3.4.

x = -3.4 / (2 * (-0.25)) = 6.8

So, the ball reaches a max height of h(6.8) = -0.25(6.8)^2 + 3.4(6.8) = 8.2 feet at a horizontal distance of 6.8 feet away from the club it was hit with.

To find when the ball returns to the ground, we set h(x) = 0 and solve for x:

0 = -0.25x^2 + 3.4x

0.25x(13.6 - x) = 0

x = 0 or x = 13.6

Since x = 0 is the starting point, the ball returns to the ground at x = 13.6 feet away from the club it was hit with.

Therefore, the ball returns to the ground about 13.6 feet away.

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The composite function f(f(x)) has a solution of - (1 - x)/x

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

f(x) = 1/1 - x

To calculate f(f(x)), we replace the occurence of x in the function f(x) = 1/1 - x with f(x)

Using the above as a guide, we have the following:

f(f(x)) = 1/1 - f(x)

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

f(f(x)) = 1/(1 - 1/(1 - x))

Evaluate

f(f(x)) = - (1 - x)/x

Hence, the solution is f(f(x)) = - (1 - x)/x

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The sides of the figure is solved to obtain

1. 3x - 8 = 2x - 3

2. x = 5

3. 5y = 3y + 2

4. y = 1

5. BE = 12

6. GH = 5

7. HF = 5

The equation to solve for x is written knowing that the tangents CH and BH are equal

1. CH = BH

3x - 8 = 2x - 3

2. solving for x

3x - 2x = -3 + 8

x = 5

3. HG = HF

5y = 3y + 2

4. solving for y

5y - 3y = 2

2y = 2

y = 1

5. BE = BH + HF

BE = 2x - 3 + 3y + 2

BF = 2 * 5  - 3 + 3 * 1 + 2

BE = 10 - 3 + 3 + 2

BE = 12

6. GH = 5y = 5 * 1 = 5

7. HF = 3y + 2

HF = 3 * 1 + 2

HF = 5

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Reflecting a point across the x-axis changes the sign of its y-coordinate while keeping the x-coordinate intact. As such, Z' can be rewritten in terms of (x, -y).

If a rectangle shifts downward by five units and rightward by three units, the transformation rule can be expressed as: (x, y) → (x + 3, y - 5).

Conversely, the given equation for this specified action is: (x, y) → (x - 3, y - 4).

Similar but reversed in reflection across the y-axis, where instead it is the x-coordinate that sees its sign changed, given the conditions that the y-coordinate stays constant. Hence, the transformation can be stated as: (x, y) → (-x, y).

The same applies for a mathematical exchange when it comes to reflecting about the x-axis; here the y-coordinate has its signs reversed with no transition in the x-coordinate – simply put, we have as follows: (x, y) → (x, -y).

Finally, observing what occurs when rototating clockwise 270° around the origin reveals each point experiencing an equal shift from said anchor point; permitting us to formalize the related rule accurately as: (x, y) → (y, -x).

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The angle in the rectangular coordinate system is 0 degrees, the compass bearing of the airplane is N (north).

The slope of the line can be found using the formula:

slope = (change in y-coordinate) / (change in x-coordinate)

In this case, the change in the y-coordinate is 0, and the change in the x-coordinate is 10. Therefore, the slope of the line is:

slope = (0 - 0) / (10 - 0) = 0

Since the slope of the line is 0, the line is horizontal, and the angle it makes with the x-axis is 0 degrees or 180 degrees. However, we need to determine which of these angles is the correct bearing of the airplane relative to the observer.

Since the airplane is in the positive x-axis, it lies in Quadrant I. In this quadrant, the angle that a line makes with the positive x-axis is measured counterclockwise from the positive x-axis.

Therefore, the angle that the line connecting the observer to the airplane makes with the positive x-axis is 0 degrees. This is the bearing of the airplane relative to the observer.

To express the bearing using the compass bearing method, we need to convert the angle from the rectangular coordinate system to the angle measured in degrees clockwise from the north direction.

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Answer:

Cannot be drawn directly.

Step-by-step explanation:

The graph of every function w = f (x, y, z) will be a surface in R 4, though it can't be drawn directly; however, slicing horizontally by w = c produces relations c = f (x, y, z) in x, y, and z whose graphs will be surfaces in 3-space which can be drawn. Therefore, the graph of the function shown above cannot be drawn directly.

U.S. or federal income taxes became public policy in 1913 with the ratification of the 16th Amendment of the U.S. Constitution that gave the Congress the right to charge and collect taxes. Over 41 U.S. states also levy and collect state income taxes. Even local governments may collect local taxes.

The 16th Amendment to the much-vaulted United States Constitution was officially ratified in the year 1913. This momentous action has allowed Congress to successfully levy and accumulate income taxes from both individuals and businesses nationwide.

Not only does the federal government take part in the process of collecting taxation by means of earnings, but its 41 associated states have also implemented their own income taxes against citizens living within. Rates remain distinctive between each region; with additional brackets for those with higher incomes who must pay accordingly.

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7 + 4 = 11 kites

So you add the kites together because they ask you how much Khalid and Annie got together.

Step-by-step explanation:

it says here "college".

well ...

X + X + X + Y = 4.2

3X + Y = 4.2

X + X + Y = 3.0

2X + Y = 3.0

what is the difference ?

one X (from 3X to 2X) on the left, and 1.2 (from 4.2 to 3.0) on the right.

so, X = 1.2

therefore,

X + Y = 1.8

why ?

because another X (= 1.2) was removed.

and 3.0 - 1.2 = 1.8

1.  A limit imposed by the government on the quantity of a good or product that can be brought into the country is called a quota. The Option B.

2. An option that is not be an effective argument for the U.S. to enact trade restrictions is hey make foreign products cheaper to U.S. shoppers. The Option D is correct.

3. If a country is on the gold standard, this means that it sets the value of its currency in relation to a specific amount of gold. The Option A is correct.

4. An economists tend to classify a country as less developed if the country's average level of Income is less than $3.040 per person. The Option C is correct.

5. The option that would not be considered a barrier to economic development is low population growth. The Option B is correct.

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Answer:

Y=1

Step-by-step explanation:

The probability that the point that is selected randomly would be in the semicircular region would be = 0.28.

To calculate the probability of a selected point, the formula for probability should be chosen. That is;

Probably = possible outcome/sample space

Possible outcome is the area of the semicircle = πr²/2

where r = 5 in

Area of semicircle = 3.14×5×5/2

=78.5/2 = 39.25 in²

The sample space = area of semicircle+area of square.

But Area of the square;

= length×width

= 10×10 = 100in²

sample space = 100+39.25 =139.25

Probability = 39.25/139.25 = 0.28

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As per the Pythagorean theorem, the length of the missing side, c, is approximately 8.06 units.

Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Now, let's use the Pythagorean Theorem to find the length of the missing side in your problem. You have a right-angled triangle with side a = 4 and side b = 7. To find the length of the missing side, let's call it c, we need to use the Pythagorean Theorem, which is:

c² = a² + b²

In this case, we know the values of a and b, so we can substitute them into the equation:

c² = 4² + 7²

Simplifying the right-hand side, we get:

c² = 16 + 49

c² = 65

To solve for c, we need to take the square root of both sides of the equation:

c = √65

c ≈ 8.06

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The rates that would fill Paige's boxes per minute is

15 boxes in 75 minutes

12 boxes in 75 minutes

1 box in 6 minutes

Given data ,

The rate at which Paige worked can be calculated by comparing the number of boxes filled by Paige with the time Paige worked.

Now , Andrew filled 5 boxes in 35 minutes,

So , The rate of Andrew = Number of boxes filled / Time taken = 5 boxes / 35 minutes = 1/7 boxes per minute

And , Paige worked for 75 minutes at a faster rate than Andrew, so Paige's rate must be greater than 1/7 boxes per minute

A. 15 boxes in 75 minutes:

Rate of Paige = Number of boxes filled / Time taken = 15 boxes / 75 minutes = 1/5 boxes per minute

B. 10 boxes in 75 minutes

Rate of Paige = Number of boxes filled / Time taken = 10 boxes / 75 minutes = 2/15 boxes per minute

C. 12 boxes in 75 minutes

Rate of Paige = Number of boxes filled / Time taken = 12 boxes / 75 minutes = 4/25 boxes per minute

D. 1 box in 6 minutes

Rate of Paige = Number of boxes filled / Time taken = 1 box / 6 minutes = 1/6 boxes per minute

E. 1 box in 9 minutes

Rate of Paige = Number of boxes filled / Time taken = 1 box / 9 minutes = 1/9 boxes per minute

Based on the calculations, options A, C, and D could be Paige's rates, as they are greater than 1/7 boxes per minute

Hence , the equations are solved

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Answer:

Please give brainliest

Step-by-step explanation:

c

The coordinates of a vertex of the image of D are (3, 1)

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

The coordinates of point D is

D = (1, 3)

The transformation rule is given as

y = x

Mathematically, this is represented as

(x, y) = (y, x)

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

D' = (3, 1)

Hence, the image of point D is D' = (3, 1)

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The parallel lines are

a) y = ( 4/7 )x + 6/7

b) 7y = 4x - 18

The perpendicular lines are

a) y = - ( 7/4 )x - 7/4

b) y = - ( 7/4 )x + 2

Given data ,

Let the equation of line be represented as A

Now , the value of A is

y = ( 4/7 )x - 3

where the slope of the line is m = 4/7 and y-intercept is b = -3

The parallel lines have the same slope and the perpendicular lines have the negative reciprocal slope

So , the equation of lines are

The parallel lines are

a) y = ( 4/7 )x + 6/7

b) 7y = 4x - 18

And , the perpendicular lines are

a) y = - ( 7/4 )x - 7/4

b) y = - ( 7/4 )x + 2

The lines which are neither parallel not perpendicular are y = 2/3x - 3 and y = -4/7x + 7

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Answer: Depends On the Numbers

Step-by-step explanation: State The Numbers

The requreid present value needed now to get $700 after 4 years at 11% compounded monthly is $451.73.

To find the present value of $700 after 4 years at 11% compounded monthly, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^{nt}[/tex]

Substituting the given values, we get:

[tex]700 = P(1 + 0.11/12)^{12*4}[/tex]

Simplifying this equation, we get:

[tex]P = 700 / (1 + 0.11/12)^{12*4}\\P = 700 / (1.00917)^{48}[/tex]

P = 700 / 1.487

P = 451.73

Therefore, the present value needed now to get $700 after 4 years at 11% compounded monthly is $451.73.

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