Answer:
Karen's company makes $94,608,000 per year.
Step-by-step explanation:
We must convert the given measurement of 3 dollars per second to per year. "Per" can be rewritten as a fraction, so our given measurement of their profit is $3/second. It is assumed that it is per 1 second.
[tex]\frac{\${3}}{\text{sec}}[/tex]
First, there are 60 seconds in a minute, so we can use this as the first conversion factor. 60 sec/min. In dimensional analysis, a unit must be on both sides of the fraction bar in order to be canceled out. Since our first fraction has seconds on the bottom, the conversion factor must have seconds on top.
[tex]\frac{\${3}}{\text{sec}} * \frac{60 \text{sec}}{1 \text{min}}[/tex]
Now, we need to covert minutes into hours. There are 60 minutes in an hour and the minutes are currently on the bottom, so our conversion factor is 60 min/hour.
[tex]\frac{\${3}}{\text{sec}} * \frac{60 \text{sec}}{1 \text{min}} * \frac{60\text{min}}{\text{1 hr}}[/tex]
There are 24 hours in a day, so the next conversion factor is 24 hr/1 day.
[tex]\frac{\${3}}{\text{sec}} * \frac{60 \text{sec}}{1 \text{min}} * \frac{60\text{min}}{\text{1 hr}}*\frac{24 \text{ hr}}{\text{1 day}}[/tex]
There are 365 days in a year, so the next (and final!) conversion factor is 365 days/1 year.
[tex]\frac{\${3}}{\text{sec}} * \frac{60 \text{sec}}{1 \text{min}} * \frac{60\text{min}}{\text{1 hr}}*\frac{24 \text{ hr}}{\text{1 day}} * \frac{365\text{ days}}{1 \text{ year}}[/tex]
We can confirm that we are left with the units $ per year by checking that all other units have been canceled out. Seconds, minutes, hours, and days have all be written in both the numerator and denominator, so they have all been canceled out, which leaves us with our desired dollars per year.
Now multiply across. The denominator only has 1s, and any number over one is equal to itself so our answer will simply be the product of the numerators.
[tex]3 * 60 * 60 * 24 * 365 = 94,608,000[/tex]
Karen's company makes $94,608,000 per year.
