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AVprozaik [17]
2 years ago
12

arrange the expressions in the correct sequence to rationalize the denominator of the expression -(2)/(\sqrt(x+y-2)-\sqrt(x+y+2)

)
Mathematics
2 answers:
cupoosta [38]2 years ago
6 0
We have to rationalize the denominator:
\frac{-2}{ \sqrt{x+y-2} - \sqrt{x+y+2} } = \\  \frac{-2}{ \sqrt{x+y-2} -  \sqrt{x+y+2} }* \frac{ \sqrt{x+y-2}+ \sqrt{x+y+2}  }{ \sqrt{x+y-2}+ \sqrt{x+y+2}  }= \\  \frac{-2*( \sqrt{x+y-2}+ \sqrt{x+y+2})  }{x+y-2-(x+y+2)}= \\  \frac{-2*( \sqrt{x+y-2}+ \sqrt{x+y+2})  }{x+y-2-x-y-2}= \\  \frac{-2*( \sqrt{x+y-2}+ \sqrt{x+y+2}  }{-4}= \\  \frac{ \sqrt{x+y-2}+ \sqrt{x+y+2}  }{2}
vovangra [49]2 years ago
4 0

Answer:

\frac{\sqrt{x+y-2}+\sqrt{x+y+2}}{2}

Step-by-step explanation:

Given expression :

\frac{-2}{\sqrt{x+y-2}-\sqrt{x+y+2}}

Now, we solve this expression by rationalizing method


\frac{-2}{\sqrt{x+y-2}-\sqrt{x+y+2}}\times\frac{\sqrt{x+y-2}+\sqrt{x+y+2}}{\sqrt{x+y-2}+\sqrt{x+y+2}}  


\frac{-2(\sqrt{x+y-2}+\sqrt{x+y+2})}{x+y-2-x-y-2}  

(using  (a+b)(a-b)=a^2-b^2)


\frac{-2(\sqrt{x+y-2}+\sqrt{x+y+2})}{-4}


\frac{\sqrt{x+y-2}+\sqrt{x+y+2}}{2}

this is the required arrangement which result the expression by rationalizing

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The sum of two numbers is 33.the larger number is 3 more than two times the smaller number.what are the numbers?
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Answer: The numbers are 10 and 23

Step-by-step explanation:

Let the smaller number be x

And the larger number be y

Ist sentence;

1. The sum of two numbers is 33.

X + y= 33 .........eqn 1

2. second sentence

the larger number is 3 more than two times the smaller number.

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Put y into eqn 1

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g Annual starting salaries in a certain region of the U. S. for college graduates with an engineering major are normally distrib
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Answer:

The probability that the sample mean would be at least $39000 is of 0.8665 = 86.65%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean $39725 and standard deviation $7320.

This means that \mu = 39725, \sigma = 7320

Sample of 125

This means that n = 125, s = \frac{7320}{\sqrt{125}}

The probability that the sample mean would be at least $39000 is about?

This is 1 subtracted by the pvalue of Z when X = 39000. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{39000 - 39725}{\frac{7320}{\sqrt{125}}}

Z = -1.11

Z = -1.11 has a pvalue of 0.1335

1 - 0.1335 = 0.8665

The probability that the sample mean would be at least $39000 is of 0.8665 = 86.65%.

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