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1 year ago

Find the area of the regular octagon.

Mathematics

1 answer:

user100 [1]1 year ago

4 0

Answer:

236.59mm²

Step-by-step explanation:

The formula for the area of a regular polygon is 1/2ap, with a being the apothem and p being the perimeter.

To start, get the perimeter by multiplying 7 (one side of the polygon) by 8 to get 56.

Next, we have to find the apothem (the perpendicular segment from the center of the polygon to one of the sides).

First, create a right triangle on an of the polygon's sides, where the hypotenuse is equal to the radius of the polygon, one of the legs is the apothem, and the other leg is equivalent to half of the side.

Next, using the polygon angle formula (n-2(360)/n), we can get the base angle of the triangle, 1/2(135), or 67.5.

We can use this angle and some trigonometry to find the the apothem.

First, use SOHCAHTOA to figure out if you will use sine, cosine, or tangent (in this case, tangent).

Next, set up an equation using the tangent of 67.5 to find the apothem - tan67.5 = a/3.

And set the equation equal to a (a = 3.5tan67.5).

Now that you have the apothem, plug it into the area formula to get A = 1/2(56)(3.5tan67.5) and solve!

(28)(3.5tan67.5)

(28)(8.4497)

236.59mm²

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2x=4 what does x equal?

alex41 [277]

2x=4
Divide 2 on both sides so that the only thing remaining on the left side is the variable x.
Final Answer: x = 2

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2 years ago

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The average of Aaron's three test scores must be at least 93 to earn an A in the class. Aaron scored 89 on the first

victus00 [196]

Answer:

Aaron must obtain a 96 or higher to achieve the desired score to earn an A in the class.

Step-by-step explanation:

Given that the average of Aaron's three test scores must be at least 93 to earn an A in the class, and Aaron scored 89 on the first test and 94 on the second test, to determine what scores can Aaron get on his third test to guarantee an A in the class, knowing that the highest possible score is 100, the following inequality must be written:

93 x 3 = 279

89 + 94 + S = 279

S = 279 - 89 - 94

S = 96

Thus, at a minimum, Aaron must obtain a 96 to achieve the desired score to earn an A in the class.

4 0

2 years ago

If anyone can help with number 4

Klio2033 [76]

If you do 27-12 (which is 15) you add 15 to 13 and 20

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3 years ago

Consider the system of equations.

anzhelika [568]

Answer: You can multiply the top equation by -1 to eliminate the x variable.

And the solution is (2,4/3) in case you need it.

Step-by-step explanation:

2x + 3y = 8

2x + 6y = 12

If you multiply the upper equation or down equation by one, you will be able to eliminate the x variable.

-1( 2x + 3y) = -1(8) New equation: -2x -3y = -8.

Add the new equation you got by multiplying the top equation by -1 to the bottom equation.

Add them: -2x -3y = -8

2x + 6y = 12

3y = 4

y = 4/3

You can now input the value for y into the one of the equations and solve for x.

-2x - 3(4/3) = -8

-2x -4 = -8

+4 +4

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8 0

3 years ago

n=400 people under the age of 25 was asked whether they check social media sites right after they wake up. 42% check social medi

Aliun [14]

Answer:

Step-by-step explanation:

We would set up the hypothesis test.

For the null hypothesis,

p = 0.5

For the alternative hypothesis,

p < 0.5

Considering the population proportion, probability of success, p = 0.5

q = probability of failure = 1 - p

q = 1 - 0.5 = 0.5

Considering the sample,

P = 42/100 = 0.42

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

n = 400

z = (0.42 - 0.5)/√(0.5 × 0.5)/400 = - 3.2

Recall, population proportion, p = 0.5

We want the area to the left of 0.5 since the alternative hypothesis is lesser than 0.5. Therefore, from the normal distribution table, the probability of getting a proportion < 0.5 is 0.00069

So p value = 0.00069

Since alpha, 0.05 > than the p value, 0.00069, then we would reject the null hypothesis.

Therefore, there is significant evidence to conclude that that less than 50% of people under the age of 25 check social media sites right after they wake up.

7 0

2 years ago