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3 years ago

Find the area of the polygon

Mathematics

1 answer:

larisa [96]3 years ago

3 0

Answer:

$687.5 \: {ft}^{2}$

Step-by-step explanation:

Area of polygon = Area of square + Area of triangle

$= {25}^{2} + \frac{1}{2} \times 25 \times (30 - 25) \\ \\ = 625 +\frac{1}{2} \times 25 \times5 \\ \\ = 625 + \frac{1}{2} \times 125 \\ \\ = 625 + 62.5 \\ \\ = 687.5 \: {ft}^{2}$

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(a^3)^2
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3 years ago

A population of monkeys' tail lengths is normally distributed with a mean of 25 cm with a standard deviation of 8 cm. I am prepa

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Answer:

The probability that the mean of my sample will be between 24 and 25 cm

P(24 ≤X⁻≤25) = 0.4772

Step-by-step explanation:

Step(i):-

Given mean of the Population 'μ'= 25c.m

Given standard deviation of the Population 'σ' = 8c.m

Given sample size 'n' = 256

Let X₁ = 24

$Z_{1} = \frac{x_{1}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{24-25}{\frac{8}{\sqrt{256} } } = -2$

Let X₂ = 25

$Z_{2} = \frac{x_{2}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{25-25}{\frac{8}{\sqrt{256} } } = 0$

Step(ii):-

The probability that the mean of my sample will be between 24 and 25 cm

P(24 ≤X⁻≤25) = P(-2≤ Z ≤0)

= P( Z≤0) - P(Z≤-2)

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= 0.000+ 0.4772

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Final answer:-

The probability that the mean of my sample will be between 24 and 25 cm

P(24 ≤X⁻≤25) = 0.4772

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