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Margaret [11]
3 years ago
12

Dina is making a logo and she decides to use a regular polygon. Each interior angle of the polygon measures 140°. What is the nu

mber of sides of this polygon?
Mathematics
1 answer:
OlgaM077 [116]3 years ago
6 0

Answer:

<em>The polygon has 9 sides (a regular nonagon).</em>

Step-by-step explanation:

<u>Angles in a Regular Polygon</u>

A polygon with n sides has a total sum of internal angles equal to 180°(n-2). This means that each angle (in a regular polygon) measures

\displaystyle \frac{180(n-2)}{n}

The regular polygon used by Dina for the logo is such that each interior angle measures 140°, thus:

\displaystyle \frac{180(n-2)}{n}=140

Multiply by n:

180(n-2)=140n

Operate:

180n-360=140n

Reducing:

40n=360

Solving:

n=9

The polygon has 9 sides (a regular nonagon).

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248.96

Step-by-step explanation:

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At Hogwarts School of Witchcraft and Wizardry, Professor Snape was concerned about grade inflation, and suggested that the schoo
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Answers:

The z scores are approximately:

  • Care of Magical Creatures:  z = 0.333
  • Defense Against the Dark Arts:  z = 0.583
  • Transfiguration:  z = -0.263
  • Potions: z = -0.533

From those scores, we can say:

  • Best grade = Defense Against the Dark Arts
  • Worst grade = Potions

=====================================================

Further Explanation:

We'll need to convert each given score to a corresponding standardized z score.

The formula to use is

z = (x - mu)/sigma

where,

  • x = given grade for each class
  • mu = mean
  • sigma = standard deviation

Let's find the z score for the Care of Magical Creatures class

z = (x - mu)/sigma

z = (3.80 - 3.75)/(0.15)

z = 0.333 approximately

Repeat this process for the Defense Against the Dark Arts score.

z = (x - mu)/sigma

z = (3.60 - 3.25)/(0.60)

z = 0.583 approximately

And for the Transfiguration class as well

z = (x - mu)/sigma

z = (3.10 - 3.20)/(0.38)

z = -0.263 approximately

The negative z score means his grade below the average, whereas earlier the other scores were above the average since he got positive z scores.

Now do the final class (Potions) to get this z score

z = (x - mu)/sigma

z = (2.50 - 2.90)/(0.75)

z = -0.533 approximately

This grade is below average as well.

----------------------------

To summarize, we have these z scores

  • Care of Magical Creatures:  z = 0.333
  • Defense Against the Dark Arts:  z = 0.583
  • Transfiguration:  z = -0.263
  • Potions: z = -0.533

Harry did his best in Defense Against the Dark Arts because the z score of 0.583 (approximate) is the largest of the four z scores. On the other hand, his worst grade is in Potions because -0.533 is the lowest z score.

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