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Yuki888 [10]
3 years ago
8

the square root of a number is subtracted from the sum of the number and 12. the result is 42. what is the original number?

Mathematics
1 answer:
Akimi4 [234]3 years ago
3 0

x +12 -sqrt(x) = 42

-sqrt(x) = -x+30

-sqrt(x)^2 = (-x+30)^2

x^2 - 61x + 900 = 0

(x-36) (x-25) = 0

 x = 36

36+12 = 48 - sqrt(36) = 48-6 = 42

 X  = 36

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Answer:

Her first exam score was a 78, her second exam score was a 89, and his third exam score was a 94.

Step-by-step explanation:

Use the formula for the mean: sum of elements / number of elements

Let x represent her first exam score.

Her second exam score can be represented by x + 11, since it was 11 points better than her first.

Her third exam score can be represented by (x + 11) + 5, since it was 5 points better than her second.

Plug in all of these expressions into the mean formula. Plug in 87 as the mean, and plug in 3 as the number of elements (since there are 3 scores):

mean = sum of elements / number of elements

87 =  ( (x) + (x + 11) + (x + 11) + 5 ) / 3

Add like terms and solve for x:

87 = (3x + 27) / 3

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So, her first score was a 78.

Find her second score by adding 11 to this:

78 + 11 = 89

Find her third score by adding 5 to the second score:

89 + 5 = 94

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For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

In this question:

To obtain a valid approximation for probabilities about the average daily downtime, either the underlying distribution(of the downtime per day for a computing facility) must be normal, or the sample size must be of 30 or more.

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