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3 years ago

A fuel tank contains 1 3/4 gallons of gasoline. Casey adds 33 1/3 gallons of

Mathematics

1 answer:

romanna [79]3 years ago

5 0

Answer:

The gallons of gas the tank contain now is 35 1/12.

Step-by-step explanation:

Given:

Fuel tank contains 1 3/4 gallons of gasoline.

Casey adds 33 1/3 gallons of gasoline to the tank.

Now, to find the total gallons of gas the tank contain.

Converting the mixed fractions into improper.

Gallons of gasoline in fuel tank $=1\frac{3}{4}=\frac{7}{4}$ .

Gallons of gasoline Casey adds $=33\frac{1}{3} =\frac{100}{3}$ .

According to question:

By adding we get the total gallons of gasoline now tank contain:

$\frac{7}{4} +\frac{100}{3}$

$=\frac{7\times 3+100\times 4}{12}$

$=\frac{21+400}{12}$

$=\frac{421}{12}$

$=35\frac{1}{12}$

Therefore, the gallons of gas the tank contain now is 35 1/12.

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Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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$\bar X$ represent the sample mean

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$\sigma$ represent the population standard deviation

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Solution to the problem

Part a

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

For this case we can calculate the mean like this:

$\bar X =\frac{46+54}{2}=50$

And the margin of error is given by:

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$z_{\alpha/2} = 2.05$

And if we solve for the deviation like this:

$\sigma = ME * \frac{\sqrt{n}}{z_{\alpha/2}}$

And replacing we got:

$\sigma =4 *\frac{\sqrt{80}}{2.05} =17.45$

Part b

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