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VLD [36.1K]
3 years ago
12

different sizes of regular pentagons are used in a stained glass window.each small pentagon has side lengths of 4 inches and an

area of 27.5 square inches.each large pentagon has a side lengths of 8 inches.what is the area of each large pentagon?
Mathematics
1 answer:
Liula [17]3 years ago
7 0
The goal is to find the area of a pentagon with side length 8.

We can find the area of a pentagon very easily by splitting it up into 10 congruent right triangles with the apothem as the height. The base of one of these triangles would be 4. The base angle would be 54 degrees, because it's half of the angle of a regular pentagon.

Using trig we find that the height of this triangle/apothem of the pentagon is equal to 4tan(54 degrees), which is about 5.506.

The area of a triangle is bh/2, so...4*5.506/2 = 11.011 in².
Times 10 triangles is 110.11 in².

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You would use division
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3 years ago
13. McKenzie gets a base pay of $1,800 per month. She also earns 12%
leva [86]

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The answer is 7,200...........

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The owner of a construction company would like to know if his current work teams can build room additions quicker than the time
frez [133]

Answer:

The claim that the current work teams can build room additions quicker than the time allotted for by the contract has strong statistical evidence.

Step-by-step explanation:

We have to test the hypothesis to prove the claim that the work team can build room additions quicker than the time allotted for by the contract.

The null hypothesis is that the real time used is equal to the contract time. The alternative hypothesis is that the real time is less thant the allotted for by the contract.

H_0: \mu=0\\\\H_1: \mu

The significance level, as a storng evidence is needed, is α=0.01.

The estimated standard deviation is:

s_M=\frac{s}{\sqrt{n}}=\frac{0.2}{\sqrt{16}} =0.2/4=0.05

As the standard deviation is estimated, we use the t-statistic with (n-1)=15 degrees of freedom.

For a significance level of 0.01, right-tailed test, the critical value of t is t=2.603.

Then, we calculate the t-value for this sample:

t=\frac{x-\mu}{s_M} =\frac{-0.32-0}{0.05}= -6.4

As the t-statistic lies in the rejection region, the null hypothesis is rejected. The claim that the current work teams can build room additions quicker than the time allotted for by the contract has strong statistical evidence.

8 0
3 years ago
In a destructive test of product quality, a briefcase manufacturer places each of a simple random sample of the day’s production
Pepsi [2]

Answer:

The lower confidence limit of 99% confidence interval for the mean breaking strength of the briefcases produced today would be equal to 331.09 pounds.

Step-by-step explanation:

Lower limit of confidence interval = mean - Error margin (E)

mean = 341.0 pounds

sd = 21.5 pounds

n = 35

degree of freedom = n - 1 = 35 - 1 = 34

confidence level = 99%

t-value corresponding to 34 degrees of freedom and 99% confidence level is 2.728

E = t × sd/√n = 2.728 × 21.5/√35 = 9.91 pounds

Lower limit = 341.0 - 9.91 = 331.09 pounds

6 0
3 years ago
Find the mean absolute deviation for the set {-32, 9, 11, 12}
Zolol [24]
<h3>Answer:</h3>

A

Step-by-step explanation:

{-32, 9, 11, 12}

first, find the mean (Find the sum of the data values, and divide the sum by the number of data values )

(-32) + 9 + 11 + 12 = 0

0/0 = 0

then, find the absolute value of the difference between each data value and the mean: |data value – mean|.

-32 - 0= -32

9 -0 = 9

11 -0 = 11

12 -0 = 0

finally, find the sum of the absolute values of the differences. Divide the sum of the absolute values of the differences by the number of data values.

0 - 0 / 4 = 0

answer is 0 (A)

7 0
3 years ago
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