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Sphinxa [80]
3 years ago
8

NEED QUICK HELP.

Mathematics
1 answer:
Andrew [12]3 years ago
5 0

Hello!

The equation for an exponential deprecation model like this is y = a(1-r)^{x}, where a is the starting value, x is the number of years passed, and r is the amount the value deprecates each year.

We know what a and r are: a = 1600, as that is the original cost of the computer, and r = .18, as that's how much it decreases by. Substitute these two into the equation.

We get y = 1600(1-.18)^{x}. Now, subtract 1 - .18 to get our final answer.

y = 1600(.82)^{x} is therefore the final model.

Hope this helps!

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Step-by-step explanation:

1. 2/5

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Answer:

A sample of at least 545 adults is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

For this problem, we have that:

\pi = 0.15

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.  

If he wishes to be 95% confident that his estimate contains the population proportion, how large a sample will be necessary?

We need a sample of at least n.

n is found when M = 0.03. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.03 = 1.96\sqrt{\frac{0.15*0.85}{n}}

0.03\sqrt{n} = 1.96\sqrt{0.15*0.85}

\sqrt{n} = \frac{1.96\sqrt{0.15*0.85}}{0.03}

(\sqrt{n})^{2} = (\frac{1.96\sqrt{0.15*0.85}}{0.03})^{2}

n = 544.23

Rounding up

A sample of at least 545 adults is needed.

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2 years ago
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