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Some wine is [tex]13\%[/tex] alcohol by volume. If you have a 0.750 L bottle of wine, how many quarts ([tex]qt[/tex]) of alcohol are in the bottle?

Note: [tex]1 \, qt = 946 \, mL[/tex]

Answer :

To find out how many quarts of alcohol are in a 0.750 L bottle of wine that is 13% alcohol by volume, we can follow these steps:

1. Determine the amount of alcohol in the wine:
- The wine is 13% alcohol by volume. This means that 13% of the total volume of the wine is alcohol.
- Calculate the volume of alcohol in the bottle:
[tex]\[
\text{Volume of alcohol (L)} = 0.13 \times 0.750 \, \text{L}
\][/tex]
- This gives us 0.0975 L of alcohol.

2. Convert the volume of alcohol from liters to milliliters:
- Since 1 liter is equivalent to 1000 milliliters, we multiply the volume in liters by 1000:
[tex]\[
\text{Volume of alcohol (mL)} = 0.0975 \, \text{L} \times 1000 \, \text{mL/L} = 97.5 \, \text{mL}
\][/tex]

3. Convert milliliters to quarts:
- We are given that 1 quart is equivalent to 946 milliliters.
- To convert milliliters to quarts, divide the volume in milliliters by the conversion factor:
[tex]\[
\text{Volume of alcohol (qt)} = \frac{97.5 \, \text{mL}}{946 \, \text{mL/qt}}
\][/tex]
- This results in approximately 0.10307 quarts.

So, the 0.750 L bottle of wine contains about 0.10307 quarts of alcohol.

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