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3 years ago

44 points! Brainliest for correct answer!

Mathematics

1 answer:

Art [367]3 years ago

5 0

Answer:

5n + 25q = 200 - - - (1)

n = 5q - - - (2)

q = 40

n = 5(40) = 200

Step-by-step explanation:

Number of Nickels = n

Number of Quarters = q

$2.00 = $2 * 100 = 200 cent

Nickel = 5 cent

Quarter = 25 cent

5n + 25q = 200 - - - (1)

n = 5q - - - (2)

5(5q) + 25q = 200

25q + 25q = 200

50q = 200

q = 200/5

q = 40

n = 5(40) = 200

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<u />

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<h3><u>Standard Deviation</u></h3>

$\displaystyle \textsf{Standard Deviation }s=\sqrt{\dfrac{\sum X^2-\dfrac{(\sum X)^2}{n}}{n-1}}$

$\begin{aligned}\displaystyle \textsf{Standard Deviation (Nilo)} & =\sqrt{\dfrac{(5^2+6^2+14^2+15^2)-\dfrac{(5+6+14+15)^2}{4}}{4-1}}\\\\& = \sqrt{\dfrac{482-\dfrac{40^2}{4}}{3}}\\\\& = \sqrt{\dfrac{82}{3}}\\\\& = 5.23\end{aligned}$

$\begin{aligned}\displaystyle \textsf{Standard Deviation (Lisa)} & =\sqrt{\dfrac{(8^2+9^2+11^2+12^2)-\dfrac{(8+9+11+12)^2}{4}}{4-1}}\\\\& = \sqrt{\dfrac{410-\dfrac{40^2}{4}}{3}}\\\\& = \sqrt{\dfrac{10}{3}}\\\\& = 1.83\end{aligned}$

<h3><u>Summary</u></h3>

Nilo has a mean score of 10 and a standard deviation of 5.23.

Lisa has a mean score of 10 and a standard deviation of 1.83.

The <u>mean</u> scores are the <u>same</u>.

Nilo's standard deviation is higher than Lisa's. Therefore, Nilo's test scores are more <u>spread out</u> that Lisa's, which means Lisa's test scores are more <u>consistent</u>.

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