Assume that each circle shown below represents one unit. Express the shaded amount as a single fraction and as a mixed number.

We get the length of the arc that subtends a central angle of 1 radians as 6 miles with radius as 6 miles also.

We are being asked to solve for the length of the arc of a circle.

For this, we are given that:

A radius of around 6 miles.

And a central angle that is subtended by the arc which is equal to 1 radians.

In order to solve for this, we need to use the length of the arc formula.

The formula is:

s = r θ

Where r =  is the radius

and

θ = is the subtended central angle given in radians

Now, by substituting the values in the formula, we get that:

s = 6 mi (1 rad) = 6 miles

Therefore, we get the length of the arc that subtends a central angle of 1 radians as 6 miles with radius as 6 miles also.

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Answer:

See explanation

Step-by-step explanation:

Selected theme park admission prices has the lower standard deviation.

Specific home stereo system's distribution is more spread out since the ratio between the standard deviation and the mean is greater compared to that of selected theme park admission prices.

specific home stereo system: 3.99/59=0.0676.

selected theme park admission prices: 4/1499=0.002668

0.0676>0.002668

Answer:

The theme park ahs the lower standard deviation

Answer:

3

Step-by-step explanation:

i think its 3 because 28 divided by 9 is 3

The perimeter of the equilateral triangle will be 27x - 48.

It should be noted that the perimeter of an equilateral triangle is the addition of all its sides or multiplying by three since they're equal.

Therefore, the perimeter of the equilateral triangle will be:

= 3(9x - 16)

= 27x - 48

Therefore, the perimeter of the equilateral triangle will be 27x - 48.

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Find the perimeter of the equilateral triangle.

9x - 16

Step-by-step explanation:

SUPPLEMENTARY because they are on a staright line and add up to 180°

[tex]76 + (2x + 4) = 180 \\ 2x + 76 + 4 = 180 \\ 2x = 180 - 76 - 4 \\ 2x = 100 \\ \frac{2x}{2} = \frac{100}{2} \\ x = 50[/tex]

x=50°

The perimeter of the regular polygon is 232

The side lengths of the regular polygon are given as

4/3x - 1/3 and x + 7

The sides of regular polygon are equal

So, we have:

4/3x - 1/3 = x + 7

Multiply both sides by 3

4x - 1 = 3x + 21

Collect like terms

4x - 3x = 1 + 21

Evaluate the like terms

x = 22

Substitute x = 22 in x + 7

Side = 22 + 7

Side = 29

The perimeter of the regular polygon is calculated as:

Perimeter = Number of sides x Side length

So, we have

Perimeter = 8 * 29

Evaluate

Perimeter = 232

Hence, the perimeter of the regular polygon is 232

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A sun in a distant galaxy has an estimated Mass of 1.55272 x [tex]10^{31}[/tex] kg and the earth has a mass of 5.972 x [tex]10^{24}[/tex] kg,26x[tex]10^{5}[/tex] earths would it take to equal the mass of the sun.

A sun in a distant galaxy has an estimated Mass of 1.55272 x [tex]10^{31}[/tex]kg

earth has a mass of 5.972 x [tex]10^{24}[/tex]kg

Let x number of earths equal the mass of the sun

x (5.972 x [tex]10^{24}[/tex]) =  1.55272 x [tex]10^{31}[/tex]

x=  1.55272 x [tex]10^{31}[/tex] / 5.972 x [tex]10^{24}[/tex]

x= 26x[tex]10^{5}[/tex]

The wavelength of light emitted by a far-off galaxy extends and is "redshifted" toward the infrared region of the electromagnetic spectrum as it moves away from us. This means that by the time the light from a very distant galaxy that emits mostly visible or ultraviolet light reaches Earth, it will appear as infrared light.

Webb's ability to detect infrared light and the cosmos' expansion, which extends light to redder wavelengths, make it a good tool for identifying galaxies that originated at the beginning of the Universe's existence.

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The number of columns is in the title floor before the change in layout is 10

Given that A rectangular tiled floor is composed of 70 square tiles. The rectangular floor is rearranged so that 2 tiles are removed from each columns and 4 tiles are added to each row. After the change in layout, the floor will still have 70 tiles, and still be rectangular asked to find the number of columns in  the tile floor before the change in layout.

Let's assume the number of rows is x

The number of columns will be [tex]\frac{70}{x}[/tex]

After the changing, the rows can be x+4

The number of columns will be  [tex]\frac{70}{x}[/tex]-2

The equation will be (x+4)([tex]\frac{70}{x}[/tex]-2)=70

⇒[tex]x^{2} +4x-140=0[/tex]

⇒x=10

Therefore,The number of columns is in the title floor before the change in layout is 10

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Check the picture below.

Answer:

below

Step-by-step explanation:

25)-ab

=-(-1/2)(3/4)

=3/8

26)b÷c

=(3/4)×1/-6

=3/-24

=-1/8

27)c÷a

=-6÷-1/2

=6×2/1

=12

Answer: z=8

Step-by-step explanation:

5.3=z-2.7

5.3+2.7=z-2.7+2.7    ==> remove the 2.7 in 'z-2.7' to single out the variable z.

z=5.3+2.7

z=8

z = 8 ✅

Step 1:

Add 2.7 to both sides

5.3 = z - 2.7

5.3 + 2.7 = z - 2.7 + 2.7

      ⬆️                   ⬆️

Step 2:

Simplify

5.3 + 2.7 = z - 2.7 + 2.7

  ( = 8 )   ⬇️     ( = 0 )

    ⬇️     ⬇️

      8      = z

Answer:

28

Step-by-step explanation:

4 x 7 = 28

Answer:

This point would affect the mean more because the median is less sensitive to outliers.

Step-by-step explanation:

Hope this helps!

If the percentage increase between 2017 and 2018 continued for 2018 and 2019, there would be 10332908 millionaire households in 2019

The given parameters are:

Year Millionaire Households

2015 9,200,000

2016 9,350,000

2017 9,620,000

2018 9,970,000

From the question, we have

The percentage increase between 2017 and 2018 continued for 2018 and 2019

The percentage increase between 2017 and 2018 is calculated as

Percentage = (2018 - 2017)/2017 * 100%

So, we have

Percentage = (9,970,000 - 9,620,000)/9,620,000 * 100%

Evaluate

Percentage = 3.64%

The number of millionaire households in 2019 is calculated as

2019 = 2018 * (1 + percentage)

So, we have

Households = 9,970,000 * (1 + 3.64%)

Evaluate

Households = 10332908

Hence, if the percentage increase between 2017 and 2018 continued for 2018 and 2019, there would be 10332908 millionaire households in 2019

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The class boundaries are:

1 58000 but less than 88,000

2 88,000 but less than 118,000

3 118,000 but less than 148,000

4 148,000 but less than 178,000

5 178,000 but less than 208,000

6 208,000 but less than 238,000

The class interval width for the distribution that we have here is given as $30000.

The six midpoints and the class boundaries are:

238,000 - 58,000= 180000

180000 / 6 = 30000

1 58000 but less than 88,000

2 88,000 but less than 118,000

3 118,000 but less than 148,000

4 148,000 but less than 178,000

5 178,000 but less than 208,000

6 208,000 but less than 238,000

238,000 - 58,000= 180000

180000 / 6 = 30000

width = 30000

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Answer:

4

Step-by-step explanation:

the coefficient is usually a constant factor for a variable.

so, the answer here is 4.

The circle has an area of 28.26 ft².

It is assumed that the circle's radius is 3 feet.

The circle's area must be determined.

What is radius of a circle ?

A line segment from a circle's center to its perimeter is known as the radius.

As per the question ;

Radius of circle , r = 3 ft

Area of the circle is given by ;

A = πr²

A = π × 3²

A = 9π

or

A = 9 × 3.14

or

A = 28.26 ft²

Thus , the area of the circle will be 28.26 ft².

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Answer:

Option B. is correct.

Step-by-step explanation:

arctan(y) = tan - 1(y) = x+ kπ

for k = {...,-2,-1,0,1,2,...}

➫ e.g tan(45°) = 1

➫ and that would mean the arctangent of 1 is 45 degrees(We represent this in π/? form)

arctan(1) = tan-1(1) = 45° = -π/4

Hope this helps!

Answer:

  {-2}

Step-by-step explanation:

You want the solution set for the inequality 4(x +2)² ≤ 0.

The expression on the left cannot be negative, but it can be zero when ...

  x +2 = 0   ⇒   x = -2

The only solution to this inequality is x = -2.

Expressed as a set of solutions, we have ...

  x ∈ {-2}

Answer:

B. SAS

Step-by-step explanation:

Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.

4 × 10 then put a 6 by the 10 as an exponent.

Answer:

Step-by-step explanation:

97

Answer:

$97 per/tire

Step-by-step explanation:

         [tex]Borrow\:8\\4 \cdot 9 = 36\\= 38 - 36\\= 2\\4 \cdot 7 = 28\\28 - 28 = 0\\\\= 97\:\mathrm{R0}[/tex]

Answer: 2.1606

Step-by-step explanation:

36.01 x 0.06 =

3601/100 x 6/100=

3601 x 6/(100 x 100)=

21606/10000=2.1606

8A = [tex]2^{n + 3} * 3 * 5^{m}[/tex] is  a product of powers of its prime factors of Polynomials.

What is Polynomials ?

Given -  [tex]2^{n} * 3 * 5^{m}[/tex]

The numbers 2, 3 and 5 are already prime numbers.

Multiplying 8 on both sides

8 × A = [tex]2^{n} * 3 * 5^{m} * 8[/tex]

Expressing 8 as the product of prime numbers

8A = [tex]2^{n} * 3 * 5^{m} * 2 * 2 * 2[/tex]

8A = [tex]8A = 2^{n} * 3 * 5^{m} * 2^{3}[/tex]         (When the base is same, the power is added)

Adding the power of base 2, we add n and 3

8A = [tex]2^{n + 3} * 3 * 5^{m}[/tex]

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1. No, the set of data does not represent a function.

A function relates an input to an output. It is like a machine that has an input and an output. And the output is related somehow to the input.

We are given with (1,4), (2, 4), (3, 5), (2, 2)

This is because every output of this data does not have unique input.

4 and 2 have the same input i.e. 2.

2. Yes, the set of the data represents a function.

We are given with (10, 5), (12, 5), (7, 12), (12, 2)

It is a function as every input has a single output.

So, (10, 12, 07) are the elements of the domain and (2, 5, 7, 12) is the range of the function.

3. Yes, it is a function as every input of this data represents the single and unique output.

We are given with  (0, 0), (5, 4), (4, 5), (1, 0)

It has its unique elements and domain (0,1,4,5) and range is from (0, 1, 2, 3, 4, 5).

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The correct scientific notation of [0.789×(10⁵)] is 78900.

As per the question statement, we are provided with a multiplication of a decimal number and an exponential number.

We are required to determine its correct scientific notation.

A decimal number, say 0.059, can be expressed as a multiplication of a decimal number and an exponential number, such as [5.9×(10)⁻²].
But in our case, after performing the multiplication of the given values, we get, [tex][0.789*10^{5}]=(\frac{789}{1000}*100000)=(789*100)=78900[/tex]

And 78900 is not a decimal value. Hence, the correct scientific notation of [0.789×(10⁵)] is 78900.

[Note: Here, we need to know the procedure to convert a decimal into a fraction, using which we converted 0.789 into [tex]\frac{789}{1000}[/tex]. First, we will need to eliminate the decimal point and consider the digits in the same order as a complete number which will be our numerator. Secondly, we will use (10ⁿ) as the denominator, where "n" is the number of digits to the right side of the decimal point in the original decimal number. Thus, 0.789 can be written as [tex]\frac{789}{1000}[/tex], as there are three digits to the right of the decimal point in 0.789]

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The coordinates of C' after a reflection across the line y = -2 are (3, -2).

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.

Given that the verticles of ABC are A(-4,5,)B(-2,4), and C(-3,2). If ABC is reflected across the line y = - 2 to produce the image ABC, then we need to find the coordinates of the vertex C.

Let (x, y) represent the coordinate of the point C

x-coordinate value:

The line y = -2 is parallel to the x-axis, therefore the x-value will remain the same following a reflection across the x-axis.

Taking the point C' as the image of the corresponding point C(-3,2), we need that the x-coordinate of the point C' is also 3

x = 3

y-coordinate value:

The difference between the coordinate of the pre-image and the reflecting line is same as difference between the reflecting line and the coordinates of the image.

Therefore, the coordinates of the point C' is (x, y) = (3, -2)

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Answer:

  1000

Step-by-step explanation:

You want the next number after 222 in base 3.

In any useful number base, the counting at any given integer position is ...

  0, 1, 2, 3, ..., (base -1), 0 and add 1 to the next number position

For base 3, this is ...

  0, 1, 2, 10

When the digit in the next higher position is also (base -1), then it gets incremented to 0 and the carry is propagated to the left.

In base 10, the equivalent is ...

  999 +1 = 99(9+1) = 99(10) = 9(9+1)0 = 9(10)0 = (9+1)00 = 1000

In base 3, your incremented value is ...

  222 +1 = 22(2+1) = 22(10) = 2(2+1)0 = 2(10)0 = (2+1)00 = 1000

The next whole base 3 number after 222 is 1000.