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svlad2 [7]
2 years ago
5

State whether the triangles are similar. Number 16

Mathematics
1 answer:
STatiana [176]2 years ago
4 0

Answer: \triangle ABD \sim \triangle CBD by SAS

Step-by-step explanation:

\overline{BD} \cong \overline{BD} by the reflexive property, so \triangle ABD \cong \triangle CBD by SAS. Since all congruent figures are similar, this means that \boxed{\triangle ABD \sim \triangle CBD} by <u>SAS</u>.

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The length of the diogonals of a rectangular garden is 34m. If it's longer side measures 30m, find the perimeter of garden. ​
MakcuM [25]

Answer:

92 m

Step-by-step explanation:

Use the Pythagorean theorem to find the length of the shorter side.

Let w = length of the shorter side.

w^{2}  + 30^{2}  =  34^{2} \\ w^{2}  + 900 = 1156\\w^{2}  =  256\\w = \sqrt{256} = 16

The perimeter is 2l + 2w = 2(30) + 2(16) = 60 + 32 = 92 m

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Given a standard deck of 52 cards, 3 cards are dealt without replacement. Using this situation, answer the questions below.&lt;b
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Given that <span>3 cards are dealt without replacement in a </span><span>standard deck of 52 cards.

Part A:

There are 4 queens in a standard deck of 52 card, thus the probability that the first card is a queen is given by 4 / 52 = 1 / 13.

Since, the first card is not replaced, thus there are 3 queens remaining and 51 ards remaining in total, thus the probability that the second card is a queen is given</span> by 3 / 51 = 1 / 17

Similarly the probability that the third card is a queen is given by 2 / 50 = 1 / 25.

Therefore, the probability that <span>all three cards are queens is given by

\frac{1}{13} \times \frac{1}{17} \times \frac{1}{25} = \frac{1}{5525}



Part B:

Yes the probability of drawing a queen of heart is independent of the probability of drawing a queen of diamonds because they are separate cards and drawing one of the cards does not in any way affect the chance of drawing the other card.



Part C:

Given that the first card is a queen, then there are 3 queens remaining out of 51 cards remaining, thus the number of cards that are not queen is 51 - 3 = 48 cards.

Therefore, </span>if the first card is a queen, the probability that the second card will not be a queen is given by 48 / 51 = 16 / 17



Part D:

<span>Given that the first two card are queens, then there are 2 queens remaining out of 50 cards remaining.

Therefore, </span>if two of the three cards are queens ,<span>the probability that you will be dealt three queens</span> is given by 2 / 50 = 1 / 25 = 0.04



Part E:

<span>Given that the first two card are queens, then there are 2 queens remaining out of 50 cards remaining, thus the number of cards that are not queen is 50 - 2 = 48 cards.

Therefore, </span>if two of the three cards are queens ,the probability that the other card is not a queen is given by 48 / 50 = 24 / 25 = 0.96
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