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4 years ago

The completed construction of a regular hexagon is shown below. Explain why ACF is a 30º-60º-90º triangle.

Mathematics

1 answer:

LuckyWell [14K]4 years ago

5 0

We know that one regular hexagon is consist of the six equilateral triangles.

One of this is ΔAFM every angle in this triangle worth 60°, according to this

∡AFM=60°.

ΔABC is isosceles triangle with angle ∡ABC=120°, because every interior angle in regular hexagon worth 120°.

Angles ∡BAC=∡BCA=30°. Total sum of angles in one triangle is 180°.

∡ACF≅∡BCA=30° at the end we can conclud that angle ∡FAC=90° WHY?

Good luck!!!

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3 years ago

Consider a game in which players draw playing cards one at a time from a standard 52-card deck. If a player draws a face card (a

aev [14]

Answer:

Expected value of drawing a card in this game on the first turn = 6

Step-by-step explanation:

Given - Consider a game in which players draw playing cards one at a time from a standard 52-card deck. If a player draws a face card (a jack, a queen, or a king), the player is awarded 16 points. Any other card drawn earns the player 3 points.

To find - What is the expected value of drawing a card in this game on the first turn?

Formula used -

Expected value, E[x] = ∑ x p(x)

where p(x) is the probability

Proof -

Total cards in a standard deck = 52

Total face cards = 12 (a jack, a queen, or a king)

Other cards = 40

Now,

Probability of getting a face card = $\frac{12}{52}$

Probability of getting a other card = $\frac{40}{52}$

So,

Expected value, E[x] = ∑ x p(x)

= (16)( $\frac{12}{52}$ ) + (3)( $\frac{40}{52}$ )

= $\frac{192}{52} + \frac{120}{52}$

= $\frac{312}{52}$

= 6

∴ we get

Expected value of drawing a card in this game on the first turn = 6

So,

The correct option is - B. 6 points

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3 years ago

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<h2><u><em>Please mark brainliest!</em></u></h2>

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