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Alex73 [517]
3 years ago
14

If p varies directly with T and p =105 when T=400.Find p when T =500

Mathematics
1 answer:
kumpel [21]3 years ago
7 0

Answer:

<h3>p = 131.25</h3>

Step-by-step explanation:

The variation p varies directly with T is written as

p = kT

where k is the constant of proportionality

To find p when T =500 we must first find the formula for the variation

That's

when p = 105 and T = 400

105 = 400k

Divide both sides by 400

<h3>k =  \frac{21}{80}</h3>

So the formula for the variation is

<h2>p =  \frac{21}{80} T</h2>

when

T = 500

Substitute it into the above formula

That's

p =  \frac{21}{80}  \times 500

Simplify

The final answer is

<h3>p = 131.25</h3>

Hope this helps you

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Answer:

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We are given that the population mean for income is $50,000, while the population standard deviation is 25,000.

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<em>Let </em>\bar X<em> = sample mean</em>

The z-score probability distribution for sample mean is given by;

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The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

So, probability that the sample will have a mean that is greater than $52,000 is given by = P(\bar X > $52,000)

  P(\bar X > $52,000) = P( \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } > \frac{52,000-50,000}{\frac{25,000}{\sqrt{1,000} } } ) = P(Z > 2.53) = 1 - P(Z \leq 2.53)

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Therefore, probability that the sample will have a mean that is greater than $52,000 is 0.0057.

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