What is the sum of the interior angle of a regular nonagon

Answer:

2.13

Step-by-step explanation:

Step-by-step explanation:

\(| 2.35 – 4.89 | + | 8.39 – 3.72 |\\\\|-2.54|+|4.67|\\\\2.54+4.67\\\\\boxed{\underline{7.21}}\)

Angle BCF = 38 degrees

Angle BED = 79 degrees

Angle BDE = 63 degrees

Angle B = 79 degrees

Angle C = 79 degrees

Angle ACF = 38 degrees

Angle F = 104 degrees.

We have,

As ED//BC,

We can say that angle EDB = angle BCF = 38 degrees.

Also, in rhombus ABCF, angles BCF and CAF are equal,

So CAF = 38 degrees.

In triangle BED,

We have angle BED = 79 degrees and angle EDB = 38 degrees.

Angle BDE = 180 - (79 + 38) = 63 degrees.

In triangle BDE,

We also has angle B = angle EBD = 180 - (63 + 38) = 79 degrees.

In trapezium BCDE,

Angles B and C are equal, so angle C = 79 degrees.

Finally, in rhombus ABCF, angles CAF and ACF are equal,

So ACF = 38 degrees.

Therefore,

Angles A and C of triangle ACF equal 38 degrees each, and angle F is:

= 180 - (38 + 38)

= 104 degrees.

Thus,

angle BCF = 38 degrees

angle BED = 79 degrees

angle BDE = 63 degrees

angle B = 79 degrees

angle C = 79 degrees

angle ACF = 38 degrees

angle F = 104 degrees.

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The complete question.

In the figure, ABCF is a rhombus and BCDE is a trapezium. ED//BC, BCF=38 degrees, and BED= 79 degrees.

Find the following:

Angle BCF

Angle BED

Angle BDE

Angle B

Angle C

Angle ACF

Angle F

Answer:

The largest number =5 3/4

​The smallest number =1 2/5

​Required difference = 5 3/4 − 1 2/5 = 4 7/2

I could be very off. hope it helps somehow

The range or the given data is calculated as 10.2 . Range is the difference between minimum value and maximum value.

To find the range in the following data 1.0, 7.0, 4.8, 1.0, 11.2, 2.2, 9.4, we can make use of the formula for range in statistics which is given as follows:[\large Range = Maximum\ Value - Minimum\ Value\]

To find the range in the following data 1.0, 7.0, 4.8, 1.0, 11.2, 2.2, 9.4, we need to arrange the data in either ascending or descending order, but since we only need to find the range, it is not necessary to arrange the data.

From the data given above, we can easily identify the minimum value and maximum value and then find the difference to get the range.

So, Minimum Value = 1.0

Maximum Value = 11.2

Range = Maximum Value - Minimum Value

                  = 11.2 - 1.0

                     = 10.2

Therefore, the range of the given data is 10.2.

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Two questions about systems aaa and bbb, the given system is:

System aaa: x = -1/3 and y = -7/3
System bbb: x = -1/3 and y = -7/3

To answer two questions about systems aaa and bbb, let's first clarify the given system:

System aaa:
x - 4y = 9

System bbb:
2x + y = -3

Question 1: Solve system aaa.
To solve system aaa, we'll use the method of substitution:

Step 1: Solve one equation for one variable.
From the first equation in system aaa, we can isolate x:
x = 4y + 9

Step 2: Substitute the expression from Step 1 into the other equation.
Substitute the expression for x in the second equation of system aaa:
2(4y + 9) + y = -3

Step 3: Simplify and solve for y.
8y + 18 + y = -3
9y + 18 = -3
9y = -3 - 18
9y = -21
y = -21/9
y = -7/3

Step 4: Substitute the value of y into the expression for x.
Using the first equation in system aaa:
x - 4(-7/3) = 9
x + 28/3 = 9
x = 9 - 28/3
x = (27 - 28)/3
x = -1/3

Therefore, the solution to system aaa is x = -1/3 and y = -7/3.

Question 2: Solve system bbb.
To solve system bbb, we'll use the method of substitution:

Step 1: Solve one equation for one variable.
From the second equation in system bbb, we can isolate y:
y = -2x - 3

Step 2: Substitute the expression from Step 1 into the other equation.
Substitute the expression for y in the first equation of system bbb:
x - 4(-2x - 3) = 9

Step 3: Simplify and solve for x.
x + 8x + 12 = 9
9x + 12 = 9
9x = 9 - 12
9x = -3
x = -3/9
x = -1/3

Step 4: Substitute the value of x into the expression for y.
Using the second equation in system bbb:
y = -2(-1/3) - 3
y = 2/3 - 3
y = 2/3 - 9/3
y = -7/3

Therefore, the solution to system bbb is x = -1/3 and y = -7/3.

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Answer:

40%

Step-by-step explanation:

the answer is up head

Answer:

C)

hope this helped

Step-by-step explanation:

The rounded potential volume of the tank is approximately 348,700.9 cubic feet, making the approximate volume of the tank 348,700.9 cubic feet.

To calculate the potential volume of the tank (cylinder), we need to know the radius of the base. However, the given information only provides the circumference of the tank and the height. We can use the circumference to find the radius, and then use the radius and height to calculate the volume of the cylinder.

Let's proceed with the calculations step by step:

Step 1: Find the radius of the tank's base

The formula for the circumference of a cylinder is given by:

C = 2πr, where C is the circumference and r is the radius.

Given that the circumference is approximately 295.3 feet, we can solve for the radius:

295.3 = 2πr

Divide both sides by 2π:

r = 295.3 / (2π)

Calculate the value of r using a calculator:

r ≈ 46.9 feet

Step 2: Calculate the volume of the cylinder

The formula for the volume of a cylinder is given by:

V = π\(r^2h\), where V is the volume, r is the radius, and h is the height.

Substitute the values we have:

V = π(\(46.9^2)(40)\)

V = π(2202.61)(40)

Calculate the value using a calculator:

V ≈ 348,700.96 cubic feet

Step 3: Round the volume to the nearest tenth

The potential volume of the tank, rounded to the nearest tenth, is approximately 348,700.9 cubic feet.

Therefore, the potential volume of the tank is approximately 348,700.9 cubic feet.

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Answer:11x+4y+13

Step-by-step explanation:you have to combine like terms for example: 2x+3x+8=5x+8

Answer:

$0.13 to produce each box.

Step-by-step explanation:

S= ph+2b

p= 12.5+2.5+12.5+2.5=30

h=25

b= 12.5x2.5=31.25

S= (30)(25) +2 (31.25)

S= \(812.5cm^{2}\)

812.5 x 0.00016= 0.13

Answer:B

Step-by-step explanation:

Transformation involves changing the position of a shape.

To map ΔHJK to ΔLMN, we (b) Translate K to N and reflect across the line containing JK.

ΔHJK and ΔLMN are similar triangles; this means that the following sides are corresponding:

The first translation would be to translate corresponding sides K to N.

Then triangle HJK must be translated across a line that contains point K (i.e. either line JK or line HK)

By comparing the options, the true statement is:

(b) Translate K to N and reflect across the line containing JK.

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Answer:

The Total Number of dogs would be 5 I believe

I hope this helped! Let me know if there is anything else i can help with!

Step-by-step explanation:

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

our baseline here is

5 + 9 = 14 ft.

the height is 12 ft.

so, the area is

14×12 / 2 = 14×6 = 84 ft²

Answer:

-17/24

Step-by-step explanation:

Because they are negative numbers, the smaller fraction (when disregarding the negative sign) is always a larger number. -11/12 could be changed to -22/24, and therefore since it is a larger number when disregarding the negative (22/24), it is a smaller number altogether.

-17/24 > -22/24

1) The leading coefficient = -1

2) Real Zero

A real zero makes the function to be equal to zero

Hence

The zeroes are three in number

3) there

Answer:

y = (1/2)x + 12

Step-by-step explanation:

(-2, 11), (4, 14)

(x₁, y₁)  (x₂, y₂)

        y₂ - y₁        14 - 11             3             3            1

m = ------------ = ------------- = ----------- = --------- = -------

        x₂ - x₁          4 - (-2)       4 + 2          6           2

y - y₁ = m(x - x₁)

y - 11 = (1/2)(x - (-2))

y - 11 = (1/2)(x + 2)

y - 11 = (1/2)x + 1

  +11               +11

-------------------------------

y = (1/2)x + 12

I hope this helps!

If the best fit line is nearly horizontal, it suggests no significant relationship between height and head circumference.

In this scenario, the explanatory variable is the child's height, as it is being used to predict the head circumference.

The response variable is the head circumference itself, as it is the variable being predicted or explained by the height.

To draw a scatter diagram of the data, you would plot the child's height on the x-axis and the corresponding head circumference on the y-axis. Each data point would represent a child's measurement pair.

Once all the data points are plotted, you can then draw the best fit line, also known as the regression line, that represents the overall trend or relationship between height and head circumference.

By observing the scatter diagram and the best fit line, you can determine the relationship between a child's height and head circumference.

If the best fit line has a positive slope, it indicates a positive relationship, meaning that as height increases, head circumference tends to increase as well.

If the best fit line has a negative slope, it indicates a negative relationship, meaning that as height increases, head circumference tends to decrease.

By assessing the slope of the best fit line in the scatter diagram, you can determine whether the relationship between height and head circumference is positive, negative, or nonexistent.

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By using mathematical induction, we have proven that

P(n): 2n > n^2 for all n ≥ m,

where m is the minimal possible value.

Base case: P(m) is true.

For n = m, we have:

2m > m^2

Since m is the minimal possible value, we assume m ≥ 1. Therefore, 2m > m^2 holds true for the base case.

Inductive step: Assume P(k) is true for some arbitrary value k ≥ m.

We assume that 2k > k^2 is true.

Now, we need to prove P(k+1) using the assumption above:

We have:

2(k+1) > (k+1)^2

Simplifying the right side:

2k + 2 > k^2 + 2k + 1

Rearranging:

1 > k^2 - 1

Since k ≥ m, we know k^2 ≥ m^2. Therefore:

k^2 - 1 ≥ m^2 - 1

Now, since m is the minimal possible value, we can assume m ≥ 1, which implies m^2 - 1 ≥ 0.

Therefore, we have: 1 > k^2 - 1 ≥ 0

This inequality holds true for all values of k ≥ m.

By completing the base case and the inductive step, we have shown that P(n): 2n > n^2 is true for all n ≥ m using mathematical induction.

To prove P(n): 2n > n^2 for all n ≥ m using mathematical induction, we need to show two things:

Base case: P(m) is true.

Inductive step: Assume P(k) is true for some arbitrary value k ≥ m, and prove that P(k+1) is true.

Let's proceed with the proof:

Base case: P(m) is true.

For n = m, we have:

2m > m^2

Since m is the minimal possible value, we can assume m ≥ 1. Therefore, 2m > m^2 holds true for the base case.

Inductive step: Assume P(k) is true for some arbitrary value k ≥ m.

We assume that 2k > k^2 is true.

Now, we need to prove P(k+1) using the assumption above:

We have:

2(k+1) > (k+1)^2

Simplifying the right side:

2k + 2 > k^2 + 2k + 1

Rearranging:

1 > k^2 - 1

Since k ≥ m, we know k^2 ≥ m^2. Therefore:

k^2 - 1 ≥ m^2 - 1

Now, since m is the minimal possible value, we can assume m ≥ 1, which implies m^2 - 1 ≥ 0.

Therefore, we have: 1 > k^2 - 1 ≥ 0

This inequality holds true for all values of k ≥ m.

By completing the base case and the inductive step, we have shown that P(n): 2n > n^2 is true for all n ≥ m using mathematical induction.

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Answer:

\(-12x^2 +19x -4\)

Step-by-step explanation:

\(-12x^2 + 16x + 3x-4 = -12x^2 +19x -4\)

I'm assuming you don't need to solve for x.

Answer:

\( \sf \: - 12x {}^{2} + 19x - 4\)

Step-by-step explanation:

Simplify the expression

\( \sf \: - 12x {}^{2} + 16x + 3x - 4\)

\( \: \: \: \sf \: • Add \: similar \: elements \: to \: get \: the \: answer\)

\( \sf \: = 16x + 3x = 19x\)

\( \: \: { \underline { \boxed{ \orange{ \sf{ = - 12x {}^{2} + 19x - 4}}}}}\)

The bar that represents the bar that would be the largest in a histogram would be 2/15.

To identify the bar that would be the largest in a histogram we must take each of the options and perform the division to obtain a decimal number. Once we have all the decimal numbers, we must identify which is the largest of them and thus we will know which one would represent a larger bar in a histogram. Here is the procedure:

According to the above, the one that represents a larger bar would be 2 / 15 = 0.13

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Answer:

Step-by-step explanation:

To find the explicit formula for the given sequence, we can use the recursive formula and keep substituting until we get a general formula.

a₁ = 4

a₂ = a₁ - 4 = 4 - 4 = 0

a₃ = a₂ - 4 = 0 - 4 = -4

a₄ = a₃ - 4 = -4 - 4 = -8

a₅ = a₄ - 4 = -8 - 4 = -12

a₆ = a₅ - 4 = -12 - 4 = -16

We can see that the sequence is decreasing by 4 each time, and we can write the general formula as:

aₙ = 4 - 4(n - 1)

Simplifying the formula, we get:

aₙ = -4n + 8

Therefore, the explicit formula for the given sequence is aₙ = -4n + 8.

Answer:

they are the exact oposite of eachother

Step-by-step explanation:

for example : (8,-4) and (-8,4)

Answer:

\(a_n=48*1.5^{n-1}\)

Step-by-step explanation:

Geometric Sequence

In geometric sequences, each term is found by multiplying (or dividing) the previous term by a fixed number, called the common ratio.

We are given the sequence:

48, 72, 108, ...

The common ratio is found by dividing the second term by the first term:

\(r=\frac{72}{48}=1.5\)

To ensure this is a geometric sequence, we use the ratio just calculated to find the third term a3=72*1.5=108.

Now we are sure this is a geometric sequence, we use the general term formula:

\(a_n=a_1*r^{n-1}\)

Where a1=48 and r=1.5

\(\boxed{a_n=48*1.5^{n-1}}\)

For example, to find the 5th term:

\(a_5=48*1.5^{5-1}=48*1.5^{4}=243\)

Answer:

y = - 2x + 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (1, - 1) and (x₂, y₂ ) = (2, - 3) ← 2 ordered pairs from the table

m = \(\frac{-3-(-1)}{2-1}\) = \(\frac{-3+1}{1}\) = - 2 , then

y = - 2x + c ← is the partial equation

To find c substitute any ordered pair from the table into the partial equation

Using (3, - 5 ) , then

- 5 = - 6 + c ⇒ c = - 5 + 6 = 1

y = - 2x + 1 ← equation of line

Answer:

Step-by-step explanation:

We will need to find the equation and put it in the form y = mx + b where m is the slope and b is the y intercept.

Step 1 - Calculate the slope via the slope formula:

\(\frac{(y2 - y1)}{(x2 - x1}\)

We will use the first two x and y variables in the table, so simply plug the values in.

\(\frac{(-3) - (-1)}{2 - 1}\\\)

= \(\frac{-2}{1} = -2\)

This means the slope is 2 (y = -2x + b).

Step 2 - Plug the variables in:

To calculate the b, we can use one of the pairs of coordinates i.e. (1, -1) to calculate b by putting the variables into the above equation:

y = -2x + b

-1 = -2(1) + b

-1 = -2 + b

-1 + 2 = b

b = 1

This means the equation is:

y = -2x + 1

Hope this helps!

Answer:

2790×5=13950. ans=13950+93000=106950

Step-by-step explanation:

population increase rate per year =2790

then after 5 year population is 2790×5+93000=106950

The solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

As per data the system of linear equations,

\(\[ \left\{\begin{array}{c} x+2 y+3 z=9 \\ 2 x-y+z=8 \\ 3 x-z=3 \end{array}\right. \] 1)\)

Write the system in the matrix form \(\( A . X=B \)\)

We know that the matrix form of the system of linear equations is as follows.

\(\[A. X = B\]\)

Where

\(\[A=\begin{pmatrix} 1 & 2 & 3 \\ 2 & -1 & 1 \\ 3 & 0 & -1 \end{pmatrix}\[X=\begin{pmatrix} x \\ y \\ z \end{pmatrix}\]\)

and

\(\[B=\begin{pmatrix} 9 \\ 8 \\ 3 \end{pmatrix}\]2)\)

To solve the system, we can use row reduction method.

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 2 & -1 & 1 & 8 \\ 3 & 0 & -1 & 3 \end{pmatrix}\]\)

Applying the elementary row operations

\(\[R_{2}\to R_{2}-2R_{1}\]\)

and

\(\[R_{3}\to R_{3}-3R_{1}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & -6 & -10 & -24 \end{pmatrix}\]\)

Now applying the elementary row operations

\(\[R_{3}\to R_{3}-(6/5)R_{2}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & 0 & -1 & -2 \end{pmatrix}\]\)

Now, we need to apply back substitution method. Using the third row, we can get the value of z as z = 2.

Now, using the second row,

\(\[-5y - 5z = -10\]\\\-5y - 5(2) = -10\]\)

Solving this equation, we get y = 0.

Finally, using the first row, we can get the value of x as

\(\[x + 2y + 3z = 9\]\\x = 3\]\)

Hence, the solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

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In each scenario, the choice between mean and median as a representative measure of central tendency depends on the nature of the data and the specific context..

1. Scenario: Income distribution of a population

- If the income distribution is skewed or contains extreme values (outliers), the median would be a better representation of the central tendency. This is because the median is not influenced by outliers and provides a more robust estimate of the "typical" income level. However, if the income distribution is approximately symmetric without outliers, the mean can also be an appropriate measure.

2. Scenario: Exam scores in a class

- If the exam scores are normally distributed without significant outliers, the mean would be a suitable measure as it takes into account the value of each score. However, if there are extreme scores that deviate from the majority of the data, the median may be a better representation. This is especially true if the outliers are indicative of errors or exceptional circumstances.

3. Scenario: Housing prices in a city

- In this case, the median would be a more appropriate measure to represent the central tendency of housing prices. This is because the housing market often exhibits a skewed distribution with a few high-priced properties (outliers). The median, being the middle value when the data is sorted, is not influenced by these extreme values and provides a better understanding of the typical housing price in the city.

Ultimately, the choice between mean and median depends on the specific characteristics of the data and the objective of the analysis. It is important to consider the distribution, presence of outliers, and the context in which the data is being interpreted.

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