The fee Jack Duffy charges per mile is $0.278, making option B correct.
Detailed explanation:
Given:
Jack Duffy's travel distance = d = 12,568 miles
Fixed costs amount to = $1,485.00
Variable costs amount to = $2,015.75
Let the cost per mile charged by Jack Duffy be = $x
According to the provided information
Total cost = Fixed costs + Variable costs
Thus, Total cost = $1,485.00 + $2,015.75
This equates to Total cost = $3,500.75
Therefore,
The cost Jack Duffy charges per mile = 
Hence, x = $0.278 per mile
This leads us to conclude that Jack Duffy’s charging rate is $0.278 per mile, confirming option B.
The average speed for his entire journey from York to Blackpool is about 61.41 km/h.
Here’s a breakdown of how we arrive at this:
The distance he travelled from York to Leeds is 45 km,
and the speed during that section was 54 km/h.
Therefore, the time taken to travel from York to Leeds is 45/54 hours (since Time = Distance/Speed).
Next, the distance from Leeds to Blackpool is 42 km,
and the time for that leg of the journey is 35 minutes, which is 35/60 hours.
This leads to the total duration for his trip as
hours.
The cumulative distance covered equals 45 + 42 = 87 km.
Thus, his average speed is calculated as:
Apply the Pythagorean theorem
x^2 + x^2 = 2x^2
sqrt(2x^2)=x sqrt(2)
(5r - 4)(r² - 6r + 4)
uses the distributive property for multiplication.
This expands to 5r(r² - 6r + 4) - 4(r² - 6r + 4)
which results in 5r³ - 30r² + 20r - 4r² + 24r - 16
as you combine like terms and simplify.
The outcome is 5r³ - 30r² - 4r² + 20r + 24r - 16
leading to a final expression of 5r³ - 34r² + 44r - 16. Choice A.
