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Strike441 [17]
3 years ago
7

Find the value of x and the value of y.

Mathematics
1 answer:
fomenos3 years ago
7 0

Answer:

C.

Step-by-step explanation:

x is bisecting the baseline (cutting it in 2 halves of 6).

the third angle in the main overall triangle is 60 degrees.

remember, all angles in a triangle always add up to 180 degrees.

so, 180 - 60 - 60 = 60.

that means that all 3 angles are of equal size (60). and that means that all 3 sides must have the same length.

=> y = 12

and now using Pythagoras to calculate the height (x) of the triangle :

y² = x² + 6² (remember, this side is only half the baseline)

12² = x² + 6²

144 = x² + 36

x² = 108

x = sqrt(108) = sqrt(36×3) = 6×sqrt(3)

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20 business cards are placed in a hat, 10 belong to women, 10 belong yo men If 2 cards are drawn at once. what's the probability
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Answer:

First choice:

               \large\boxed{\large\boxed{5/19}}

Explanation:

<em>The probability that the first is a man's card and the second, a woman's card</em> is calculated as the product of both probabilities, taking into account the fact that the second time the number of cards  in the hat has changed.

In spite of it is said that the cards are drawn at once, since it is stated a specific order for the cards (first is a man's card and the second, a woman's card) you can model the procedure as if the cards were drawn consecutively, instead of at once.

<u>1. Probability that the first is a man's card</u>

  • Number of cards in the hat = 20 (the 20 business card)

  • Number of man's card in the hat: 10

  • Probability = favorable oucomes / possible outcomes = 10/20 = 1/2.

<u />

<u>2. Probability that the second is a woman's card</u>

  • Number of cards in the hat = 19 (there is one less card in the hat)

  • Number of wonan's card in the hat: 10

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<u>3. Probability that the first is a man's card and the second, a woman's card</u>

<u />

  • (1/2) × (10/19) = 5/19

That is the first choice.

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