12 * 20% = 12 * 0.20 = 2.4 hours
It will not last his entire shift.
Approximately 1718 have a score within that range.
We calculate the z-score for each end of this spectrum:
z = (X-μ)/σ = (2.5-3.1)/0.3 = -0.6/0.3 = -2
Using a z-table (http://www.z-table.com) we see that the area to the left of, less than, this z-score is 0.0228.
For the upper end:
z = (3.7-3.1)/0.3 = 0.6/0.3 = 2
Using a z-table, we see that the area to the left of, less than, this z-score is 0.9772.
The probability between these is given by subtracting these:
0.9772 - 0.0228 = 0.9544.
This means the proportion of people that should fall between these is 0.9544:
0.9544*1800 = 1717.92 ≈ 1718
We have been given that fuel efficiency for a 2007 passenger car was 31.2 mi/gal and the same model of car, the fuel efficiency increased to 35.6 mi/gal in 2012. Also, the gas tank for this car holds 16 gallons of gas.
We need to write a function and graph a linear function that models the distance that each car can travel for a given amount of gas up to one tankful.
Let represent the functions as
and
where
and
represent the distances traveled by car in years 2007 and 2012 and x represents the number of gallons. Therefore, we can express the required functions as:

Domain of both these functions are [0,16] and ranges are [0,499.2] and [0,569.6] respectively for years 2007 and 2012.
The difference function will be:


Domain of this function is [0,16] and range is [0,67.2].
The graphs are shown below.