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iren [92.7K]
3 years ago
8

An irregular hexagon has angles that measure the following. Angle 1: 2x + 15 Angle 2: 9x - 3 Angle 3: 77 Angle 4: 8x + 8 Angle 5

: 13x Angle 6: x - 4 What is the value of x?
Mathematics
1 answer:
Firdavs [7]3 years ago
8 0

Answer: 19

Step-by-step explanation:

1) You combine like terms with all the angles

Ex. 2x + 15 + 9x - 3 + 77 + 8x + 8 + 13x + x - 4, which equals 33x + 93

2) You set up an equation using the formula for the sum of the interior angles

Ex. 33x + 93 = 180(n - 2)

3) Since a hexagon has 6 sides, n is 6

Ex. 33x + 93 = 180(6 - 2)

4) Solve like a regular equation

Ex. 33x + 93 = 180(6 - 2)

33x + 93 = 720

- 93 = - 93

33x = 627

- Divide 627 by 33

x = 19

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We are given the following in the question:

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Standard deviation of probability distribution:

E(x^2) = 0^2(0.033)+ 1^2(0.149)+2^2(0.318)+3^2(0.318) +4^2(0.149) + 5^2(0.033)\\E(x^2) = 7.492\\\sigma^2 = E(x^2) - (E(x))^2\\\sigma^2 = 7.492 - (2.5)^2 = 1.242\\\sigma= \sqrt{1.242} = 1.11

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