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3 years ago

The sale tax on an item is %6. Express the total cost, C, in terms of the price of the item, P.

Mathematics

1 answer:

skelet666 [1.2K]3 years ago

5 0

<h3>Answer: C = 1.06P</h3>

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Explanation:

The sales tax is 6% of the price P

6% of P = 0.06P

Add on the original cost P to get P+0.06P = (1+0.06)P = 1.06P

The 1.06 indicates the final after tax cost is 106% of the original price.

You can think of it like 100% + 6% = 106% = 1.06

So that's how we end up with C = 1.06P

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An example using actual numbers:

Let P = $100 be the initial cost before tax

6% of P = 0.06*P = 0.06*100 = 6 dollars is the tax

100+6 = 106 is the final cost

Note how C = 1.06P = 1.06*100 = 106

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For many years businesses have struggled with the rising cost of health care. But recently, the increases have slowed due to les

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Answer:

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

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And replacing we got:

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And replacing into the confidence interval formula we got:

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$0.52 + 1.64*\sqrt{\frac{0.52(1-0.52)}{1000}}=0.5459$

And the 95% confidence interval would be given (0.4941;0.5459).

Step-by-step explanation:

Data given and notation

n=1000 represent the random sample taken

$\hat p=0.52$ estimated proportion of of U.S. employers were likely to require higher employee contributions for health care coverage

$\alpha=0.05$ represent the significance level (no given, but is assumed)

Solution to the problem

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

The margin of error for this case is given by:

$ME= z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

And replacing we got:

$ME = 1.64*\sqrt{\frac{0.52(1-0.52)}{1000}}=0.0259$

And replacing into the confidence interval formula we got:

$0.52 - 1.64*\sqrt{\frac{0.52(1-0.52)}{1000}}=0.4941$

$0.52 + 1.64*\sqrt{\frac{0.52(1-0.52)}{1000}}=0.5459$

And the 95% confidence interval would be given (0.4941;0.5459).

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Answer:

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Step-by-step explanation:

The height of the blade as a function f time can be written in the following way:

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Finally the equation that can be used to model h is:

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