Question

1. the area of canada is approximately 9 984 670 km². the area of manitoba is about 6½% of the area of canada. what is the area of manitoba to the nearest square kilometre? 12. a manufacturer of electric hybrid vehicles claims its vehicle will travel 200% as far as its regular vehicle on a full tank of gas. if the regular vehicle travels an average of 550 km on a full tank, how far will the hybrid go?

Explanation:

Question 11

Step 1: Convert the percentage to a decimal

The percentage is \(6\frac{1}{2}\%\), which is equal to \(6.5\%\). To convert a percentage to a decimal, we divide by 100. So, \(6.5\% = \frac{6.5}{100}=0.065\).

Step 2: Multiply the area of Canada by the decimal

The area of Canada is \(9984670\space km^2\). To find the area of Manitoba, we multiply the area of Canada by \(0.065\): \(9984670\times0.065\).
Calculating this: \(9984670\times0.065 = 9984670\times\frac{65}{1000}=\frac{9984670\times65}{1000}\).
First, calculate \(9984670\times65 = 9984670\times(60 + 5)=9984670\times60+9984670\times5 = 599080200+49923350 = 648903550\).
Then, divide by 1000: \(\frac{648903550}{1000}=648903.55\).
Since we need to round to the nearest square kilometre, and the decimal part is \(0.55\), which is more than \(0.5\), we round up. So the area of Manitoba is \(648904\space km^2\).

Step 1: Understand the percentage

The hybrid vehicle travels \(200\%\) as far as the regular vehicle. To find the distance the hybrid travels, we need to find \(200\%\) of the distance the regular vehicle travels.

Step 2: Convert the percentage to a multiplier

To find a percentage of a number, we convert the percentage to a decimal (or fraction) and multiply. \(200\%=\frac{200}{100} = 2\).

Step 3: Multiply the regular vehicle's distance by the multiplier

The regular vehicle travels \(550\space km\) on a full tank. So the hybrid vehicle travels \(550\times2 = 1100\space km\).

Answer:

\(648904\space km^2\)

Question 12