Find the perimeter and area of a regular octagon that has a radius of 10m.

Answers

Answer 1
To find the perimeter of a regular octagon, we need to know the length of one of its sides. We can use the fact that a regular octagon can be divided into eight congruent isosceles triangles, and the central angle of each triangle is 45 degrees.

Drawing a line from the center of the octagon to the midpoint of one of its sides will create a right triangle, where the hypotenuse is the radius of the octagon (which is 10m), and the two legs are half of the length of one of its sides.

Using the Pythagorean theorem, we can solve for the length of one of the sides of the octagon:

hypotenuse^2 = leg^2 + leg^2
10^2 = (side/2)^2 + (side/2)^2
100 = side^2/2
side = √(200) = 10√2 m

So the length of one side of the octagon is 10√2 m. Therefore, the perimeter of the octagon is:

perimeter = 8 x side = 8 x 10√2 = 80√2 m

To find the area of the octagon, we can use the formula:

area = (apothem x perimeter)/2

where the apothem is the distance from the center of the octagon to the midpoint of one of its sides. Using the same right triangle we used before, we can see that the apothem is equal to:

apothem = leg = 10√2/2 = 5√2 m

Therefore, the area of the octagon is:

area = (5√2 x 80√2)/2 = 200 x 2 = 400 m^2

So the perimeter of the octagon is 80√2 m and the area is 400 m^2.

Related Questions

Order of Operations: Write an equation that means "Multiply 6 by the sum of 3 and 2."

Answers

6 x (3+2)

careful not to confuse it with 6(3+2), although you get the same answer.


Pleasee can you give me the answer and explain how to do it for the future because I’ve been seeing this all day and I don’t know how to do it ;(

Pleasee can you give me the answer and explain how to do it for the future because Ive been seeing this

Answers

Answer:

C . y(18x-9w-12) ..............

The blueprint for a fence shows a rectangle with the dimensions bin x
18in. The scale for the actual fence is 2in : 10ft. What is the length and
width of the actual fence?

Answers

Answer:

The width of the actual fence is 90ft

Step-by-step explanation:

If 2in = 10ft, you want to find the scale factor. To do this, you need to divide 10/2, so for every 5ft, it is 1in. Now, you would take how many inches you have and multiply it by 5. (in our case, 18in)

18 x 5 = 90.

So the actual fence length is 90ft.

Is there a relationship between Column X and Column Y? Perform correlation analysis and summarize your findings.
X Y
10 37
6 10
39 18
24 12
35 11
12 34
33 26
32 9
23 42
10 24
16 40
16 1
35 39
28 24
5 42
22 7
12 17
44 17
15 27
40 47
46 35
35 14
28 38
9 18
9 17
8 22
35 12
15 30
34 18
16 43
19 24
17 45
21 24

Answers

The correlation analysis indicates a moderate positive relationship between Column X and Column Y.

To perform correlation analysis, we can use the Pearson correlation coefficient (r) to measure the linear relationship between two variables, in this case, Column X and Column Y. The value of r ranges from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation.

Here are the steps to calculate the correlation coefficient:

Calculate the mean (average) of Column X and Column Y.

Mean(X) = (10+6+39+24+35+12+33+32+23+10+16+16+35+28+5+22+12+44+15+40+46+35+28+9+9+8+35+15+34+16+19+17+21) / 32 = 24.4375

Mean(Y) = (37+10+18+12+11+34+26+9+42+24+40+1+39+24+42+7+17+17+27+47+35+14+38+18+17+22+12+30+18+43+24+45+24) / 32 = 24.8125

Calculate the deviation of each value from the mean for both Column X and Column Y.

Deviation(X) = (10-24.4375, 6-24.4375, 39-24.4375, 24-24.4375, ...)

Deviation(Y) = (37-24.8125, 10-24.8125, 18-24.8125, 12-24.8125, ...)

Calculate the product of the deviations for each pair of values.

Product(X, Y) = (Deviation(X1) * Deviation(Y1), Deviation(X2) * Deviation(Y2), ...)

Calculate the sum of the product of deviations.

Sum(Product(X, Y)) = (Product(X1, Y1) + Product(X2, Y2) + ...)

Calculate the standard deviation of Column X and Column Y.

StandardDeviation(X) = √[(Σ(Deviation(X))^2) / (n-1)]

StandardDeviation(Y) = √[(Σ(Deviation(Y))^2) / (n-1)]

Calculate the correlation coefficient (r).

r = (Sum(Product(X, Y))) / [(StandardDeviation(X) * StandardDeviation(Y))]

By performing these calculations, we find that the correlation coefficient (r) is approximately 0.413. Since the value is positive and between 0 and 1, we can conclude that there is a moderate positive relationship between Column X and Column Y.

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KIA buys a shirt that cost $12.50 and some pairs of socks that are $2.50 each. She pays a total of $27.50. How many pairs of socks did kia buy?

Answers

27.50-12.50=15
15/2.5=6
Six pairs

1.) Diego paid $47 for 3 tickets to a concert. Andre paid $141 for 9 tickets to a concert.
Did they pay at the same rate (what was the value they paid for 1 ticket)? How do you
know?

Answers

They pay at the same rate.
The value they paid for one ticket is 15.67$
How do you know:
Andre paid for 3 times more tickets than Diego. 47 x 3 is 141, so they are at the same rate.
47 / 3 is 15.667, which rounds up to 15.67$ in money terms.

what is the correct expanded for and value of 43?

what is the correct expanded for and value of 43?

Answers

Answer:

A and C

Step-by-step explanation:

Answer:

4×4×4=64

Step-by-step explanation:

In ΔABC, AB = 16 in, BC = 9 in, AC = 10 in. AD is perpendicular to the extension of BC . Find CD.

Answers

Answer:

25/6

I don't really know how I got it, sorry I can't help with that

Pls I need this ASAP! I’ll mark brainliest!



What is the sum of 4/10x + -1x + 1 7/10x?

Answers

Answer:

I think its 11x/10

Step-by-step explanation:

Use the sequence below to complete each task. 3, -15, 75, ... a. Identify the common ratio (r). b. Write an equation to represent the sequence. C. Find the 5th term (as) Algebra), 2013 → B I y Default A A : = 5 川里

Answers

a)

This is a geometric sequence, this means that each value of the sequence is multiplied by the common ratio to determine the next number.

For the sequence {3,-15,75}

Divide one of the given numbers by the number before it on the sequence to determine the common ratio

\(r=\frac{-15}{3}=-5\)

The common ratio for this sequence is r=-5

b)

a is the first value of the sequence

r is the common ratio

k is the place on the sequence of the required value

You can calculate said value using

\(ar^k\)

c)

For

a=3

r=-5

k=5

The value fo the sequence is

\(ar^k=3(-5)^5=-9375\)

x3+y3+z3=k, with k being all the numbers from one to 100

Answers

✦ ✦ ✦ Beep Boop - Blu Bot! At Your Service! Scanning Question . . .

      Code: Green! Letters, Numbers, and Variables Received! ✦ ✦ ✦

--------------------------------------------------------------------------------------------------------------Question: x3+y3+z3=k, with k being all the numbers from one to 100

--------------------------------------------------------------------------------------------------------------Answer: X = -80538738812075974, Y = 80435758145817515, and Z = 12602123297335631.

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

        X = -80538738812075974, Y = 80435758145817515, and Z = 12602123297335631.

Drake must practice the
trombone for at least 30
minutes a day. So far, he
has practiced for 8
minutes. How many
minutes does Drake still
need to practice the
trombone?

(I don’t need the answer, but do I just subtract 30-8?)

Answers

There are 22 minutes does Drake still need to practice the trombone.

We have to given that;

Drake must practice the trombone for at least 30 minutes a day.

So far, he has practiced for 8 minutes.

Hence, We get;

Number of minutes does Drake still need to practice the trombone is,

⇒ 30 - 8

⇒ 22 minutes

Thus, There are 22 minutes does Drake still need to practice the trombone.

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If ya'll could help me with this one, it would be highly appreciated :]

If ya'll could help me with this one, it would be highly appreciated :]

Answers

Answer:

THE ANSWERE IS POINT B

And the scale factor is 2/6 I'm not so sure of this one :-[

Step-by-step explanation:

Please give me brainliest I did help you right?

A cooler is filled with 4 1/2 gallons of water

Answers

A Total of 144 small cups can be filled with the water from the cooler before it's empty.

The cooler has 4 1/2 gallons of water, which can be written as 9/2 gallons. Each small cup holds 1/32 gallon. To find the number of small cups that can be filled with the water from the cooler, we need to divide the total amount of water by the amount of water in each cup.

9/2 ÷ 1/32 = (9/2) * (32/1) = 144 small cups.

Therefore, 144 small cups can be filled with the water from the cooler before it's empty.

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Complete Question:

A cooler is filled with 4 1/2 gallons of water. There are small cups that each hold 1/32 gallon.

How many small cups can be filled with the water from the cooler before it's empty?

How to finsd the set of numbers if the mean, median and mode is given

Answers

Answer:

a) we have the numbers 0, 2, 3, 5, 5. The mean and the median are both 3

b) we have the numbers 0, 0, 3, 5, 7. The mean and the median are both 3

In both cases the mean and the median are 3, but the mode differs. The mean and the median do not uniquely determine the mode.

Step-by-step explanation:

AnswerIf the number of data points is even, the median is the average of the two middle data points in the list.:

Step-by-step explanation:

4 T =
fl OZ
(T = Tablespoons)

4 T =fl OZ(T = Tablespoons)

Answers

Answer:

2 fl oz

Step-by-step explanation:

Answer:

4 tablespoons is = to 2 fl oz

Which range contains the value of sqrt(14+7+23)
A. Between 6.6 and 6.8
B. Between 11.1 and 11.3
C. Between 21.9 and 22.1
D. Between 33.7 and 33.9

Which range contains the value of sqrt(14+7+23)A. Between 6.6 and 6.8B. Between 11.1 and 11.3C. Between

Answers

Answer:

the answer to this question is c

What are three equivalent Decimal forms for the number 19

Answers

Answer:

The numbers; 19.0 , 19.00 and 19.000 are same value as the number 19

Step-by-step explanation:

Here in this question, we simply want to write decimals which would have same value as the number 19 when written.

Let’s start with 19.0

This is absolutely same value as the number 19

Furthermore let’s write 19.00

This is also same value as the number 19

Lastly;

19.000

This is same value as the number 19

The purchase price of an iPad is $610. If the sales tax rate is 6.5%, what is the amount of sales tax?

Answers

Answer:

Step-by-step explanation:

$603.5

Answer:39.65

Step-by-step explanation:

turn 6.5% to 0.065

610 x 0.065=39.65

Put y=3x-2 into point slope for and standard form and show work​
WILL GIVE BRAINLIEST

Answers

\(y=3x-2\)

The slope of \(y=3x-2\)  would be \(3\).

The standard form would be written as  \(3x-y=2\).

Hope this helps!

Put y=3x-2 into point slope for and standard form and show workWILL GIVE BRAINLIEST

how can i do it in simple form

Answers

Divided the top and bottom of the fraction until you can’t divided anymore.

Example: 4/8

You can divide by4, which gives you 1/4. You can’t divide it anymore, so that’s the simplest form.

There are 6 dogs and 12 cats in the backyard. Write the ratio of cats to total animals In 3 ways, in simplest form.

Answers

Step-by-step explanation:

12:18

12 to 18

12/18 = 2/3

Find x such that the distance between (5, -8) and (x, 4) is 13. (Enter your answers as a comma-separated list.) x= Need Help? Reed It

Answers

Answer:

x = 10

Step-by-step explanation:

We can find the distance, d, between two points using the distance formula, which is given by:

\(d=\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2 }\), where

(x1, y1) is one point,and (x2, y2) is another point.

Step 1:  Plug in values for variables in the distance formula and simplify:

We can plug in 13 for d, (5, -8) for (x1, y1), and (x, 4) for (x2, y2) to find x

\(13=\sqrt{(4-(-8))^2+(x-5)^2}\\ 13=\sqrt{(4+8)^2+(x-5)^2}\\ 13=\sqrt{(12)^2+(x-5)^2}\\ 13=\sqrt{144+(x-5)^2}\)

Step 2:  Square both sides:

\(13^2=(\sqrt{144+(x-5)^2})^2 \\169=144+(x-5)^2\)

Step 3:  Subtract 144 from both sides:

\((169=144+(x-5)^2)-144\\25=(x-5)^2\)

Step 4:  Take the square root of both sides:

\(\sqrt{25}=\sqrt{(x-5)^2}\\ 5=x-5\)

Step 5:  Add 5 to both sides to find x:

\((5=x-5)+5\\10=x\)

Thus, in order to have a distance of 13 between the (5, -8) and (x, 4), x must equal 10.

Optional Step 6:  Plug in 10 for x in the distance formula and check that you get 13 on both sides of the equation when simplifying:

\(13=\sqrt{(4-(-8))^2+(10-5)^2}\\ 13=\sqrt{(4+8)^2+(5)^2}\\ 13=\sqrt{(12)^2+25}\\ 13=\sqrt{144+25}\\ 13=\sqrt{169}\\ 13=13\)

Thus, our answer is correct and x is 10.

2) (G3-4 pts) Find the area of the shaded figure in square feet. Round to the nearest tenth if
necessary. Circle the correct answer.
|--5---
18 ft
---5ft
A. 478.5 ft?
B. 311.2 ft
8 ft
C. 351.2 ft?
D. 438.5 ft?

2) (G3-4 pts) Find the area of the shaded figure in square feet. Round to the nearest tenth ifnecessary.

Answers

Answer:

Area of both triangles = 8*5 = 40

Rectangle Area = 8*18 = 144

Semi Circle Area = Pi*r^2 / 2 = (3.14159*81)/2 = 127.34

40 + 144 + 127.34 = 311.34 square feet

answer is B

Step-by-step explanation:

what is thr y-intercept shown in the graph​

what is thr y-intercept shown in the graph

Answers

Answer:

It’s 0,0

Step-by-step explanation: it only crosses the origin once and on the 0 so.

Answer:

0

Step-by-step explanation:

The line crosses at the origin.

give an example of a linear transformation whose kernel is the line spanned by ⎡ ⎣ −1 1 2 ⎤ ⎦ in r3.

Answers

v^T proj_v(x) = 0, so v^T T(x) = v^T x - v^T proj_v(x) = v^T x, which is not zero unless x is on the line spanned by v.
Therefore, the kernel of T is precisely the line spanned by v, as desired.

Let's start with understanding what the kernel of a linear transformation is. The kernel, also known as the null space, is the set of all vectors that get mapped to the zero vector by the transformation.
In this case, the kernel is the line spanned by the vector ⎡ ⎣ −1 1 2 ⎤ ⎦. This means that any vector on this line will get mapped to the zero vector by the linear transformation we're looking for.
One example of a linear transformation that has this kernel is the projection onto the plane orthogonal to ⎡ ⎣ −1 1 2 ⎤ ⎦. This transformation takes any vector in R^3 and projects it onto the plane that is perpendicular to the given vector.
To see why this works, let's call our given vector v = ⎡ ⎣ −1 1 2 ⎤ ⎦. We can find a basis for the plane orthogonal to v by finding the orthogonal complement of v. This is the set of all vectors w in R^3 that satisfy the equation v^T w = 0.
If we solve this equation, we get the set of all vectors of the form ⎡ ⎣ a -a/2 b ⎤ ⎦, where a and b are any real numbers. This is a basis for the plane orthogonal to v.
Now, we can define our linear transformation T as follows: T(x) = x - proj_v(x), where proj_v(x) is the projection of x onto the plane orthogonal to v.
Since proj_v(x) is in the plane orthogonal to v, it is also orthogonal to v. This means that v^T proj_v(x) = 0, so v^T T(x) = v^T x - v^T proj_v(x) = v^T x, which is not zero unless x is on the line spanned by v.
Therefore, the kernel of T is precisely the line spanned by v, as desired.

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A stereo costs $418.70, including 6% sales tax. How much was the sales tax itself?

Answers

Answer:

25.12

Step-by-step explanation:

Given the ______ of the z-distribution, the p-value for a two-tailed test is twice that of the p-value for a one-tailed test.

Answers

Answer:

the answer is symmetry.

SECTION A (20 MARKS) QUESTION 1 (a)Identify the relevant population for the below foci, and suggest the appropriate sampling design to investigate the issues, explaining why they are appropriate. Wherever necessary identify the sampling frame as well. 10 marks A public relations research department wants to investigate the initial reactions of heavy soft- drink users to a new all-natural soft drink'. (b) What type of sampling design is cluster sampling? What are the advantages and disadvantages of cluster sampling? Describe a situation where you would consider the use of cluster sampling. 10 marks

Answers

a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is  stratified random sampling. The list of all heavy soft-drink users is the sampling frame.

b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.

The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.

a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.

Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.

Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.

b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.

The advantages of cluster sampling are:

Cluster sampling is an efficient method of sampling large populations. It is much cheaper than other types of sampling methods.Cluster sampling is relatively easy to perform compared to other methods of sampling, such as simple random sampling.Cluster sampling can be used when the population is widely dispersed, and it would be difficult to cover the entire population.

The disadvantages of cluster sampling are:

Cluster sampling introduces sampling errors that could lead to biased results.Cluster sampling has a lower level of precision and accuracy compared to other types of sampling methods.Cluster sampling increases the standard error of the estimate, making it difficult to achieve the desired level of statistical significance.

A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.

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What is the equation of the line of best fit for Aiden’s data? Enter the correct answer in the box by replacing m and b in the equation. Round each number to the nearest tenth.

Answers

Answer:

Y= 2.3033x + 160.71

Step-by-step explanation:

The value of the slope m is 2.55 and the y-intercept of the line is 135.

What is a linear equation?

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + b

Where m is the slope of the line and b is the y-intercept of the line.

From the table, the two points will be (60, 288.1) and (100, 390).

Then the slope of the line will be

m = [(390 - 288.1) / (100 - 60)]

m = 101.9 / 40

m = 2.55

Then the equation of the line will be

y = 2.55x + b

The equation is passing through (100, 390). Then the value of b will be

390 = 2.55 (100) + b

390 = 255 + b

b = 135

Then the equation of the line will be

y = 2.55x + 135

The value of the slope m is 2.55 and the y-intercept of the line is 135.

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What is the equation of the line of best fit for Aidens data? Enter the correct answer in the box by
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