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geniusboy [140]
3 years ago
6

Anthony decided to buy two DVDs that were not included in the deal. His price before tax was $19.99. What was the cost of the tw

o DVDs after the 8.25% tax was added?
Mathematics
1 answer:
galina1969 [7]3 years ago
8 0

Given:

Cost of 2 DVDs before tax = $19.99

Tax rate = 8.25%

To find:

The cost of 2 DVDs after the tax was added.

Solution:

We have,

Cost of 2 DVDs before tax = $19.99

Tax rate = 8.25%

So,

Tax = 8.25% of Cost of 2 DVDs before tax

Tax=\dfrac{8.25}{100}\times 19.99

Tax=1.649175

Tax\approx 1.65

Now,

Cost of 2 DVDs after tax = Cost of 2 DVDs before tax + Tax

                                         = $19.99 + $1.65

                                         = $21.64

Therefore, the cost of 2 DVDs after the tax is $21.64.

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The answer assumes that the question is about the <em>normal distribution</em>.

Answer:

96% of the data in any data set <em>normally distributed</em> is 2.05 <em>standard deviations</em> <em>above</em> and <em>below</em> the mean.

Step-by-step explanation:

The key to solving this question is having into account that exists the <em>standard normal distribution</em> that permits obtaining any probability from any normally distributed data, doing the following transformation:

\\ z = \frac{x-\mu}{\sigma}

That is, in this case, we subtract a given value <em>x</em> from the <em>population mean</em> and then divide the result by the <em>population standard deviation</em>. This is a z-score, and this value is associated with the probability for a <em>standard normal distribution</em>, with a population mean = 0 and population standard deviation = 1.

Fortunately, for the <em>standard normal distribution</em>, there is associated a ubiquitous <em>standard normal table</em> for possible values of <em>z</em> and the corresponding probability. Then, knowing that the data are <em>normally distributed</em> and having both distribution <em>parameters</em>, namely, the <em>population mean</em> and <em>population standard deviation</em>, we can consult any standard normal table to find the probabilities for any data distributed following the normal distribution.

However, even without previously know the values of the normal parameters, the standard normal distribution can tell us how many standard deviations from the mean are 96.00% of the data for every normally distributed population.

<h3>Solving the question</h3>

Having all this information at hand, we know that <em>the z-score value tells us how many standard deviations</em> <em>from the mean</em> are the data normally distributed. As a result, we can determine how many standard deviations below and above the population mean represent the 96.00% of the cases for this normal distribution consulting a <em>cumulative standard normal table from the mean</em>.

If we divide 96.00/2 = 48, that is, 0.48, we need to find the z-score for this probability consulting a <em>cumulative standard normal table from the mean</em>. The values for a z-score for that probability is z=2.05, approximately. So, since the normal distribution is also symmetrical, those values are above and below the mean, that is, z =2.05 (above) and z=-2.05(below).

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To find this, we must first note that the original slope is -8. Parallel lines have the same slope, so we know that the new line will also have the slope of -8.

Given this information, we can use the point and slope and put them into the base form of point-slope form.

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Answer:

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