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Rainbow [258]
2 years ago
14

A regular hexagon is inscribed in a circle and another regular hexagon is circumscribed about the same circle. What is the ratio

of the area of the larger hexagon to the area of the smaller hexagon
Mathematics
1 answer:
Anna007 [38]2 years ago
3 0

4/3 of the area of the larger hexagon to the area of the smaller hexagon

Let the sides of the interior hexagon be 2 cm long, then this hexagon is made up of 6 equilateral triangles of side = 2.

The area of this hexagon = 6 * 1 * sqrt3 = 6 sqrt3 ( as the triangle is made up of 2 60-30-90 triangles)

The exterior hexagon is made up of 6 equilateral triangles with altitude 2 and the area = 6 * 2 * (2 / sqrt3 ) = 24 / sqrt3

area exterior hex / interior hex = 24 / sqrt3 * 1 / 6sqrt3 = 24/18

= 4/3

Required ratio = 4/3 answer

Learn more about Equations:

brainly.com/question/16450098

#SPJ4

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A shirt that normally costs $35.00 is on sale for 28.00. What is the percent discount?
Olin [163]

Answer:

$25.20

Step-by-step explanation:

$35 x 0.28

= $9.80

35-9.80

= $25.20

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32.45 shirt; 15% discount.
Maurinko [17]
32.45-15%(4.8675)=27.5825
Hope this Helps ^.^

7 0
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Jim had three waffles. He ate 1/6 of one waffle, and. 2/3 of another waffle. How many waffles were left?
Troyanec [42]
So find how much was eaten
1/6 and 2/3=eaten
add 1/6 and 2/3
convert bottom number to same
2/3=4/6
1/6+4/6=5/6
5/6 eaten
3-5/6=
2+1-5/6=
2+6/6-5/6=
2+1/6
2 and 1/6 waffles left
7 0
3 years ago
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A researcher claims that the variation in the salaries of elementary school teachers is greater than the variation in the salari
guajiro [1.7K]

Answer:

a

The null hypothesis is  H_o :  \sigma^2_1 = \sigma^2 _2

The alternative hypothesis is H_a :  \sigma_1 ^2 > \sigma^2_2

b

F_{critical} = 1.8608

c

F = 2.9085

d

    The decision rule is  

Reject the null hypothesis

e

There is sufficient evidence to support the researchers claim

Step-by-step explanation:

From the question we are told that

 The first sample size is  n_1 = 30

 The sample variance for elementary school is  s^2_1 = 8324

 The second sample size is  n_2 = 30

  The sample variance for the secondary school is  s^2_2 = 2862

   The significance level is  \alpha = 0.05

The null hypothesis is  H_o :  \sigma^2_1 = \sigma^2 _2

The alternative hypothesis is H_a :  \sigma_1 ^2 > \sigma^2_2

Generally from the F statistics table  the critical value of \alpha = 0.05 at first and  second degree of freedom df_1 = n_1 - 1 = 30 - 1 = 29 and  df_2 = n_2 - 1 = 30 - 1 = 29 is  

         F_{critical} = 1.8608

Generally the test statistics is mathematically represented as

       F = \frac{s_1^2 }{s_2^2}

=>   F = \frac{8324 }{2862}

=>   F = 2.9085

Generally from the value obtained we see that  F >  F_{critical } Hence

   The decision rule is  

Reject the null hypothesis

    The conclusion is  

  There is sufficient evidence to support the researchers claim

   

4 0
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How do you write 5x - 4y = 1 in slope intercept form
Alexxandr [17]

First move the 4y to the right and the 1 to the left:

4y=5x-1

Then divide everything by 4:

y=5/4 x - 1/4

7 0
3 years ago
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