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swat32
3 years ago
15

Can anyone show me the steps in order solve this problem

Mathematics
1 answer:
STatiana [176]3 years ago
8 0
M∠A = 42°   [isosceles triangle]

m∠B = 180 - 42 - 42 = 96°  [in a triangle, the three interior angles always add to 180°]

m∠C = 180 - 96 - (x+12)
m∠C = 84 - x - 12
m∠C = 72 - x

2x+9 + 3x-1 + 72-x = 180
4x + 80 = 180
4x = 180 - 80
4x = 100
x = 100/4
x = 25

m∠C = 72 - x = 72 - 25 = 47°

<span>I hope this helped</span>

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The length of human pregnancies from conception to birth follows a distribution with mean 266 days and standard deviation 15 day
Katena32 [7]

Answer:

a) 81.5%

b) 95%

c) 75%

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 266 days

Standard Deviation, σ = 15 days

We are given that the distribution of  length of human pregnancies is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

a) P(between 236 and 281 days)

P(236 \leq x \leq 281)\\\\= P(\displaystyle\frac{236 - 266}{15} \leq z \leq \displaystyle\frac{281-266}{15})\\\\= P(-2 \leq z \leq 1)\\\\= P(z \leq 1) - P(z < -2)\\= 0.838 - 0.023 = 0.815 = 81.5\%

b) a) P(last between 236 and 296)

P(236 \leq x \leq 281)\\\\= P(\displaystyle\frac{236 - 266}{15} \leq z \leq \displaystyle\frac{296-266}{15})\\\\= P(-2 \leq z \leq 2)\\\\= P(z \leq 2) - P(z < -2)\\= 0.973 - 0.023 = 0.95 = 95\%

c) If the data is not normally distributed.

Then, according to Chebyshev's theorem, at least 1-\dfrac{1}{k^2}  data lies within k standard deviation of mean.

For k = 2

1-\dfrac{1}{(2)^2} = 75\%

Atleast 75% of data lies within two standard deviation for a non normal data.

Thus, atleast 75% of pregnancies last between 236 and 296 days approximately.

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Answer:

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Step-by-step explanation:

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