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kolezko [41]
3 years ago
10

The measure of a straight angle (2x+50) (6x+2)

Mathematics
1 answer:
fenix001 [56]3 years ago
7 0

Answer:

see below

Step-by-step explanation:

If the two angles form a straight angle, their sum is 180

2x+50  + 6x+2 = 180

Combine like terms

8x +52 = 180

Subtract 52 from each side

8x+52-52 = 180-52

8x =128

divide each side by 8

8x/8 = 128/8

x =16

2x+50 = 2(16)+50 = 32+50 = 82

6x+2 = 6(16)+2 =96+2 = 98

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A bag contains different colored candies. There are 50 candies in the bag, 28 are red, 10 are blue, 8 are green and 4 are yellow
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Answer:

\displaystyle \frac{54}{5405}.

Step-by-step explanation:

How many unique combinations are possible in total?

This question takes 5 objects randomly out of a bag of 50 objects. The order in which these objects come out doesn't matter. Therefore, the number of unique choices possible will the sames as the combination

\displaystyle \left(50\atop 5\right) = 2,118,760.

How many out of that 2,118,760 combinations will satisfy the request?

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\displaystyle \left( 28\atop 2\right) = 378.

Number of ways to choose 3 green candies out of a batch of 8:

\displaystyle \left(8\atop 3\right)=56.

However, choosing two red candies out of a batch of 28 red candies does not influence the number of ways of choosing three green candies out of a batch of 8 green candies. The number of ways of choosing 2 red candies and 3 green candies will be the product of the two numbers of ways of choosing

\displaystyle \left( 28\atop 2\right) \cdot \left(8\atop 3\right) = 378\times 56 = 21,168.

The probability that the 5 candies chosen out of the 50 contain 2 red and 3 green will be:

\displaystyle \frac{21,168}{2,118,760} = \frac{54}{5405}.

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