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3 years ago

John bought an iPad for $480 and pain $31.20 in sales tax. What was the sales tax rate?

Mathematics

1 answer:

tia_tia [17]3 years ago

8 0

The sales tax rate was 6.5%

Step-by-step explanation:

Given,

Price of iPad = $480

Sales tax on iPad = $31.20

Sales tax rate = $\frac{sales\ tax}{Price\ of\ iPad}*100$

$Sales\ tax\ rate=\frac{31.20}{480}*100\\Sales\ tax\ rate=\frac{3120}{480}\\Sales\ tax\ rate=6.5\%$

The sales tax rate was 6.5%

Keywords: sales tax, division

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Step-by-step explanation:

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2 years ago

According to the National Vital Statistics, full-term babies' birth weights are Normally distributed with a mean of 7.5 pounds a

Sav [38]

Answer:

68.26% probability that a randomly selected full-term pregnancy baby's birth weight is between 6.4 and 8.6 pounds

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 7.5, \sigma = 1.1$

What is the probability that a randomly selected full-term pregnancy baby's birth weight is between 6.4 and 8.6 pounds

This is the pvalue of Z when X = 8.6 subtracted by the pvalue of Z when X = 6.4. So

X = 8.6

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{8.6 - 7.5}{1.1}$

$Z = 1$

$Z = 1$ has a pvalue of 0.8413

X = 6.4

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{6.4 - 7.5}{1.1}$

$Z = -1$

$Z = -1$ has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

68.26% probability that a randomly selected full-term pregnancy baby's birth weight is between 6.4 and 8.6 pounds

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3 years ago

What is the quotient of 2 3/4 and 5 1/2?

Juli2301 [7.4K]

Answer:

1/2

Step-by-step explanation:

This can be done several ways. Perhaps the easiest is to use the decimal equivalents:

(2 3/4)/(5 1/2) = 2.75/5.5 = 0.5

If you want to use the numbers given, the usual procedure is to convert them to improper fractions and do the division that way:

2 3/4 = (4·2 +3)/4 = 11/4

5 1/2 = (2·5 +1)/2 = 11/2

Now, the problem can be written as ...

(2 3/4) / (5 1/2) = (11/4) / (11/2)

This sort of division problem can be solved two ways:

invert and multiply (the denominator is inverted)

= (11/4) × (2/11) = (11·2)/(11·4) = 2/4 = 1/2

use a common denominator (for the two fractions)

= (11/4) / (11/2) = (11/4) / (22/4) = 11/22 = 1/2

The quotient is 1/2.

_____

Additional comments

It is helpful in many cases to just use decimal equivalents for the calculation. To do that, you need to be familiar with the equivalents of commonly used fractions. I find it is usually sufficient to know the unit fractions in each case. Then you can multiply or add to find the others.

1/9 = 0.1...(1-digit repeat), 1/8 = 0.125, 1/7 = 0.142857...(6-digit repeat), 1/6 = 0.16...(1-digit repeat), 1/5 = 0.2, 1/4 = 0.25, 1/3 = 0.3...(1-digit repeat), 1/2 = 0.5

I learned the "invert and multiply" method for dividing fractions when I was in school. The Common Core math apparently also teaches the method of matching the denominators of a compound fraction. Then the result is the ratio of numerators. (A variation not taught is that you can match the numerators and use the inverse of the ratio of denominators. Both of these methods can be validated using the "invert and multiply" method. (11/4)/(11/2) = 2/4)

"Invert and multiply" is another way of saying that division is the same as multiplication by the reciprocal. This applies everywhere, not just in fraction problems.

8 0

3 years ago