Which equation could be used to calculate the sum of the geometric series? one-third two-ninths startfraction 4 over 27 endfraction startfraction 8 over 81 endfraction startfraction 16 over 243 endfraction

Answer:

[tex] {x}^{2} - 3x - 10 = 0 \\ (x - 5)(x + 2) = 0 \\ \\ x - 5 = 0 \: - > x = 5 \\ \\ x + 2 = 0 \: - > x = - 2[/tex]

Answer:

The empirical rule, also known as the 68 - 95 - 99.7 rule, is a statistical rule that states that in regular distribution, virutally every piece of data will fall within three standard deviations. More specifically, 68% of the data will be within one standard deviation of the mean, 95% will lie in two standard deviations, and 99.7% will be within three standard deviations.

Step-by-step explanation:

Explanation above.

hope this helps :)

Answer:

The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all observed data will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).

Step-by-step explanation:

Answer:

1/5

Step-by-step explanation:

Total Frequency is 14+21+70 = 105

Sewing has frequency of 21

21/105 = 0.2 = 1/5

Answer:

Each person will recieve between 3 and 4 liters

Step-by-step explanation:

Carrie makes 27 liters of lemonade and 8 people share the lemonade equally. If we divide the amount of liters of lemonade by the number of people we will get the amount of lemonade each people will get.

27/8 = 3.375

3.375 is in between 3 and 4 so each person will get between 3 and 4 liters of lemonade

Answer: A:2 R8

This image should help, but first, you should find the biggest number that 27 can be multiplied by, but stay under 62, which in this case is 2, because 27*3=81 and 2 is the maximum it can be while staying below 62. which makes the equation turn into 62-54=8, making the remainder 8.

Step-by-step explanation: hope this helps

The distance between the two points  (1,1) and (3,-4) , using the distance formula in the radical symbol, is √(29).

To measure the distance between two points of a coordinate system, the formula can be given as,

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Here, (x₁, y₁) are the coordinates of point 1 and  (x₂, y₂) are the coordinates of point 2.

The distance between the two points. (1,1), (3,-4)​ has to be find out. Use the distance formula to find the distance between them,

[tex]D=\sqrt{(1-3)^2+(1-(-4))^2}\\D=\sqrt{(-2)^2+(5)^2}\\D=\sqrt{4+25}\\D=\sqrt{29}[/tex]

Thus, the distance between the two points  (1,1) and (3,-4) , using the distance formula in the radical symbol, is √(29).

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If the area and width of the rectangle are 45x² − 42x − 48 and (5x − 8) then the length of the rectangle will be (3x + 2).

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a rectangle, opposite sides are parallel and equal and each angle is 90 degrees. And its diagonals are also equal and intersect at the mid-point.

A rectangle has an area of 45x² − 42x − 48 and a width of 5x − 8.

Then the length of the rectangle will be

area = length × width

Then we have

Area = 45x² − 42x − 48

Then the factor of the polynomial will be

Area = (5x − 8)(3x + 2)

Then the length of the rectangle will be (3x + 2).

More about the rectangle link is given below.

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Answer:

First blank is Dividend.
Second blank is Divisor
INCLUDED WHOLE PAGE!!
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Step-by-step explanation:

13(16.5)+12(16.5)+5(16.5)

16.5(13+12+5) = 30(16.5) = 495 ft²

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The required 95% credible interval for the number of people alive in the year 3000 CE is the true approximate value of different iterations.

Given that,
95% credible interval for the number of people who will be alive in the year 3000 CE (including digital people) is to be explained.

Statistic is the study of mathematics that deal with relations between comprehensive data.

Here,
95% credible interval for the number of people who will be alive in the year 3000 CE (including digital people), by going through certain iterations for the 95% credible interval for the number of people alive in the year 3000 CE will give the required interval.

Thus, the required 95% credible interval for the number of people alive in the year 3000 CE is the true approximate value of different iterations.

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Answer: A

Step-by-step explanation:

kil this monkey its gonna touch me

Answer:

Area of Triangle A = 4 cm²

Area of Rectangle = 24 cm²

Area of Triangle B = 4 cm²

Area of Trapezoid = 32 cm²  

Step-by-step explanation:

The formula to find the area of a triangle is: [tex]\frac{h_bb}{2}[/tex]

The base (b) is 2 and the height (h) is 4.

Now multiply,

2 times 4 = 8

Then divide,

[tex]\frac{8}{2}[/tex] which equals 4.

So the area of Triangle A and B is 4 cm² because they are the same triangles.

The formula to find the area of a rectangle is: a times b.

a=6 and b=4

Multiply,

6 times 4 = 24

So the area of the rectangle is 24 cm²

The formula to find the area of a trapezoid is: [tex]\frac{a+b}{2}h[/tex]

A=6

B=10

H=4

So now,

[tex]\frac{6+10}{2}4[/tex]

6+10=16

16 divided by 2 is 8.

Last multiply,

8 times 4 is 32.

The area of the trapezoid is 32 cm²

Hope this helped! And have a great day!

Answer:

B. 15

Step-by-step explanation:

The 5 is in the millions place. The 1 at left is in the 10 millions place.

That means 15 million.

Answer: B. 15

Answer:

Option B. 15

Step-by-step explanation:

To write it in words we have.

write in words: fifteen million, seven hundred and sixty-five thousand, one hundred and thirty-two

In Expanded Form:

     15,765,132 =

 10,000,000  

+ 5,000,000  

+ 700,000  

+ 60,000  

+ 5,000  

+ 100  

+ 30  

+ 2  

= 15,765,132

There you go the answer is Option B. 15

Hope this Helps! :3

Have a great day! :3

Work Shown:

A = area of the base

A = length*width

A = 9*10.1

A = 90.9

V = volume of the pyramid

V = (1/3)*(Area of the base)*(height)

V = (1/3)*(90.9)*(6)

V = 181.8

The units for the volume are in cubic inches. The result is exact.

Answer:

The ratio of the perimeters is 3

The ratio of the areas is 9

Step-by-step explanation:

Given:

Dilate a triangle with vertices (0, 0), (0, 2), and (2,0) using the scale factor k = 3.

To Find:

What is the value of the ratio (new to original) of the perimeters? the areas?

Solution:

What is the value of the ratio (new to original) of the perimeters?

Since, two figures are similar, then the ratio of its perimeters is equal to the scale factor

Let the following be:

k        ⇒          the scale factor

x        ⇒          the perimeter of the new triangle

y        ⇒          the perimeter of the original triangle

Knowing that:

k = x/y

Thus:

k = 3

Now Substitute:

x/y = 3

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What is the value of the ratio (new to original) of the areas?

Since, two figures are similar, then the ratio of its areas is equal to the scale factor squared.

k       ⇒          the scale factor

x        ⇒          the area of the new triangle

y        ⇒          the area of the original triangle

k ² = x/y

Since,

z = 3

Then,

x/y = 3 ²

3 ² means to 3 × 3

x/y = 9

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Kavinsky

To build a scale model we must take into account the original measurements of the original house.

A scale model is a tool that allows us to build a structure with a smaller or larger size than the original that we take as a reference.

To build a scale model we must take into account all the measurements of the original object, in this case a house to be able to reduce it adequately to a smaller scale.

For example, if its sides are 30 meters long by 2 meters high and we want to make a scale of half the size, we must make its sides 15 meters long by 1 meter high.

Learn more about scale model in: https://brainly.com/question/19512201

Answer:

y=4z-3

Step-by-step explanation:

Answer:

Step-by-step explanation:

I did two of them for you

Use distributive on the right side and you will find the correct answer

The screen shot should help you.

Add f and g together by combing like terms

answer: x^2 + 4x -13

Answer:

[tex](f+g)(x)=x^2+4x-13[/tex]

Step-by-step explanation:

Given functions:

[tex]f(x)=4x-8[/tex]

[tex]g(x)=x^2-5[/tex]

Composite function:

[tex]\begin{aligned}(f+g)(x) & =f(x)+g(x)\\ & = (4x-8)+(x^2-5)\\ & =4x-8+x^2-5\\ & =x^2+4x-8-5\\ & = x^2+4x-13 \end{aligned}[/tex]

Answer:

3/4 = x

Step-by-step explanation:

2/2x + 1 = 1/2

2/2x + 1 * 1/2x = 1/2 * 1/2x

2 + 1 = 1/4x

3 = 4x

3/4 = 4x/4

3/4 = x

Answer:

546

Step-by-step explanation:

Each square inch is equal to 6.5 square centimeters so you can multiply

84 × 6.5 = 546So, the area is 546 square centimeters.

Hope this helps =>

Answer:

[tex]541.93\ cm^2[/tex]

Step-by-step explanation:

Step 1:  Determine the area in square centimeters

[tex]84\ in^2 * \frac{(2.54\ cm)^2}{in^2}[/tex]

[tex]84\ in^2 * \frac{(2.54)^2 * (cm)^2}{in^2}[/tex]

[tex]84\ in^2 * \frac{6.4516\ cm^2}{in^2}[/tex]

[tex]541.9344\ cm^2[/tex]

Answer: [tex]541.93\ cm^2[/tex]

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 128 and 144 is 16Divide both the numerator and denominator by the GCD

128 ÷ 16144 ÷ 16Reduced fraction: 89

Therefore, 128/144 simplified to lowest terms is 8/9.

Circular equations are organized like this:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

We're given:

To find the equation of this circle, we must determine two things:

To determine the radius of the circle, find the distance between the given endpoints and divide by 2:

(6, 0) and (-6, 0)

⇒ There are 6 units between (0,0) and (6,0).

⇒ There are 6 units between (0,0) and (-6,0).

⇒ 6 + 6 = 12; the diameter of the circle is 12 units

⇒ 12 / 2 = 6

Therefore, the radius of the circle is 6 units.

To determine the center of the circle, find the midpoint of the given endpoints:

(6, 0) and (-6, 0)

⇒ The midpoint occurs at the very middle of these two points. The distance between the midpoint and (6,0) is equal to the distance between the midpoint and (-6,0).

⇒ We identified earlier that there are 6 units between (0,0) and (6,0), and that there are 6 units between (0,0) and (-6,0).

Therefore, the center of the circle is (0,0).

Plug the center and the radius into the equation:

[tex](x-h)^2+(y-k)^2=r^2\\x^2+y^2=6^2\\x^2+y^2=36[/tex]

[tex]x^2+y^2=36[/tex]

Answer:

16.5 m

Step-by-step explanation:

The triangle shown in the figure is a right triangle, so we can use the Pythagoreas Theorem.

a² + b² = c²

a² + 32² = 36²

a² + 1024 = 1296

a² = 272

a = √272

a = 16.5

Answer: 16.5 m

Answer:

See below ~

Step-by-step explanation:

Option A

Option B

Option C

Option C has the lowest rate, hence it is the best deal.

Answer:

Then the two numbers are -11 and -6.

Answer:

11   and   6

Step-by-step explanation:

x+ y = 17     or    y = 17-x

and

xy = 66       sub in   y = 17-x

x ( 17-x) = 66

-x^2 + 17x - 66 = 0     either factor this, or use quadratic formula to find

                                         x =  6     y = 11