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NeTakaya
3 years ago
12

PLS HALP on formulas involving polygons

Mathematics
1 answer:
jeyben [28]3 years ago
6 0
The sum of all five angles is 540 degrees.
A) 4*congruent angles + 5th angle = 540
B) (5th angle) -30 = 2*cong angle

A) 5th angle = 540 -4*cong angle
B) 5th angle  = 2*(cong angle)   -30
Multiplying B) by -1
B) -5th angle  = -2*(cong angle)   +30  then adding to A)
A) 5th angle = 540 -4*cong angle

-2*(cong angle)   +30  = 540 -4*cong angle
2*(cong angle) = 510
*****************************************
By trial and error I determined
each congruent angle = 95
5th angle = 160
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(a)\dfrac{92}{117}

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Number of Men, n(M)=24

Number of Women, n(W)=3

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Since you cannot appoint the same person twice, the probabilities are <u>without replacement.</u>

(a)Probability that both appointees are men.

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(b)Probability that one man and one woman are appointed.

To find the probability that one man and one woman are appointed, this could happen in two ways.

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P(One man and one woman are appointed)=P(MW)+P(WM)

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(c)Probability that at least one woman is appointed.

The probability that at least one woman is appointed can occur in three ways.

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P(at least one woman is appointed)=P(MW)+P(WM)+P(WW)

P(WW)=\dfrac{3}{27}X \dfrac{2}{26}=\dfrac{6}{702}

In Part B, P(MW)+P(WM)=\frac{8}{39}

Therefore:

P(MW)+P(WM)+P(WW)=\dfrac{8}{39}+\dfrac{6}{702}\\$P(at least one woman is appointed)=\dfrac{25}{117}

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