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kozerog [31]
1 year ago
14

Find probabilities using combinations and permutations. Tyler was feeling particularly adventurous at the hair salon one day, an

d decided to dye his hair. The stylist informed him that he had 10 colors to choose from, 6 of which were shades of purple . If Tyler randomly selects 5 colors and tells the stylist to choose from those, what is the probability that exactly 2 of the chosen hair dyes are shades of purple? Write your answer as a decimal rounded to four decimal places.
Mathematics
1 answer:
Blizzard [7]1 year ago
7 0

There are total of 10 colors to choose.

6 are shades of purple and

4 are not shades of purple.

Tyler selects 5 colors, and exactly 2 are shades of purple. Therefore, the 3 other colors are not shades of purple.

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Given right triangle A w/a hypotenuse length of 3y + x and a leg of y-x, and right triangle B, w/ a hypotense length of y+5 and
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Triangle A

hypotenuse: 3y + x
leg: y - x

Triangle B

hypotenuse: y + 5
leg: x + 5

Congruency => 3y + x = y + 5 and y - x = x + 5

Solve the system

3y + x = y + 5 -> 2y + x = 5
y - x = x + 5 -> y - 2x = 5

  2y + x = 5
-2y + 4x = -10

5x = -5
x = -1
y = (5 -(-1)) / 2 = 6/2 = 3

Verify:

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3y + x = 9 - 1 = 8
y + 5 = 3 + 5 = 8

Legs:

y - x = 3 -(-1) = 3 + 1 = 4
x + 5 = -1 + 5 = 4.

Then both hypotenuses and both legs are congruent.

Answer: x = -1 and y = 3


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