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Anni [7]
3 years ago
14

A formula is expressed as D= a(2+kt). Express k in the terms of D, a and t? (Show work)

Mathematics
1 answer:
Mariulka [41]3 years ago
7 0
SIMPLIFIED \: \: ALGEBRA \\ \\ \\\\We \: are \: given \: - \\ \\ \: \\ D \: = \: a \: ( \: 2 + kt \: ) \\ \\ D \: = \: 2a \: + \: akt \: \\ \\ D \: - \: 2a \: = \: akt \: \\ \\ \frac{D \: - \: 2a}{at} \: = \: k \\ \\ \\ Therefore \: , \: in \: terms \: of \: D \: , \: \: a \:, \: \: and \:  \: t \: \\ \\ k \: = \: \frac{D - 2a}{at \: } \: \: \: \: \: \: \: Ans.
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The diameter of a truck wheel is 56.5 inches. What is the circumference of<br> the wheel?
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Step-by-step explanation:

You simply divide the diameter by 2 to get the radius (28.25) and then plug into the circumference equation, 2*pi*r = Circumfrence.

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A small business owner estimates his mean daily profit as $970 with a standard deviation of $129. His shop is open 102 days a ye
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Answer:

The probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean <em>μ</em> and standard deviation <em>σ</em> and we select appropriately huge random samples (<em>n</em> ≥ 30) from the population with replacement, then the distribution of the sum of values of <em>X</em>, i.e ∑<em>X</em>, will be approximately normally distributed.  

Then, the mean of the distribution of the sum of values of X is given by,  

 \mu_{x}=n\mu

And the standard deviation of the distribution of the sum of values of X is given by,  

 \sigma_{x}=\sqrt{n}\sigma

The information provided is:

<em>μ</em> = $970

<em>σ</em> = $129

<em>n</em> = 102

Since the sample size is quite large, i.e. <em>n</em> = 102 > 30, the Central Limit Theorem can be used to approximate the distribution of the shopkeeper's annual profit.

Then,

\sum X\sim N(\mu_{x}=98940,\ \sigma_{x}=1302.84)

Compute the probability that the shopkeeper's annual profit will not exceed $100,000 as follows:

P (\sum X \leq  100,000) =P(\frac{\sum X-\mu_{x}}{\sigma_{x}}

                              =P(Z

*Use a <em>z</em>-table for the probability.

Thus, the probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.

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3 years ago
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