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olchik [2.2K]
3 years ago
12

50 seats on a train. 27 of the seats are empty. what is the percentage of the empty seats on the train

Mathematics
2 answers:
lorasvet [3.4K]3 years ago
8 0

Answer: 54%

Step-by-step explanation

25 is half of 50, so that would be 50%.

To find out the percentage of each seat, divide 100 by 50. You will get 2.

So now we know 2% equals 1 seat on the train. If 27 seats are empty, you would multiply 2% by 27%, giving you 54%.

navik [9.2K]3 years ago
3 0
27/50= the empty seats in fraction
Which converts to percentage =
27/50 x 2 = 54/100 = 54%
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Regular hexagon ABCDEF is inscribed in circle X and has an apothem that is 6√3 inches long. Use the length of the apothem to cal
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Answer:

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The radius of the circumscribing circle is 12 inches

Part B

The length of each side of the hexagon, 's', is;

s = a \times 2 \times tan \left(\dfrac{\pi}{n} \right)

Therefore;

s = 6 \cdot \sqrt{3}  \times 2 \times tan \left(\dfrac{\pi}{6} \right) = 6 \cdot \sqrt{3}  \times 2 \times \left(\dfrac{1}{\sqrt{3} } \right) = 12

s = 12 inches

The perimeter, P = n × s = 6 × 12 = 72 inches

The perimeter of the hexagon is 72 inches

Step-by-step explanation:

The given parameters of the regular hexagon are;

The length of the apothem of the regular hexagon, a = 6·√3 inches

The relationship between the apothem, 'a', and the circumradius, 'R', is given as follows;

a = R \cdot cos \left(\dfrac{\pi}{n} \right)

Where;

n = The number of sides of the regular polygon = 6 for a hexagon

'a = 6·√3 inches', and 'R' are the apothem and the circumradius respectively;

Part A

Therefore, we have;

The \ circumradius, \  R = \dfrac{a}{cos \left(\dfrac{\pi}{n} \right)}

Plugging in the values gives;

The \ circumradius, \  R = \dfrac{6 \cdot \sqrt{3} }{cos \left(\dfrac{\pi}{6} \right)} = \dfrac{6 \cdot \sqrt{3} }{\left(\dfrac{\sqrt{3} }{2} \right)} = 6 \cdot \sqrt{3}  \times \dfrac{2}{\sqrt{3} }  = 12

The circumradius, R = 12 inches

Part B

The length of each side of the hexagon, 's', is given as follows;

s = a \times 2 \times tan \left(\dfrac{\pi}{n} \right)

Therefore, we get;

s = 6 \cdot \sqrt{3}  \times 2 \times tan \left(\dfrac{\pi}{6} \right) = 6 \cdot \sqrt{3}  \times 2 \times \left(\dfrac{1}{\sqrt{3} } \right) = 12

The length of each side of the hexagon, s = 12 inches

The perimeter of the hexagon, P = n × s = 6 × 12 = 72 inches

The perimeter of the hexagon = 72 inches

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