6. The figure shows rectangle ABCD in the coordinate plane with point A(0, 2.76), B(3.87, 2.76), C(3.87,0, and D(0,0). Rectangle ABCD can be used to approximate the size of the state of Colorado with x and y scales representing hundreds of miles. At the end of 2010, the population of Colorado was 5,029,196 people. Based on this information given, what was the population density at the end of 2010 in people per square mile? Enter your answer in the box.​

Answer:

Population density = 47 people per square miles

Step-by-step explanation:

From the picture attached,

Coordinates of vertex B → (3.87, 2.76)

Which represents length of vertex A from origin O (AD)= 2.76 units ≈ 276 miles

Length of vertex B from origin O (CD) = 3.87 units ≈ 3.87 miles

Area of rectangle ABCD = Length × Width

                                         = CD × AD

                                         = 387 × 276

                                         = 106812 square miles

Population of Colorado = 5029196 people

Population density of Colorado = [tex]\frac{\text{Total population}}{\text{Total area}}[/tex]

                                                     = [tex]\frac{5029196}{106812}[/tex]

                                                     = 47.08

                                                     ≈ 47 people per square miles

The population density at the end of 2010 in people per square mile is 47.

Length of vertex A from origin O (AD)= 2.76 units ≈ 276 miles

Length of vertex B from origin O (CD) = 3.87 units ≈ 3.87 miles

Now  

Area of rectangle ABCD = Length × Width

 = CD × AD

= 387 × 276

= 106812 square miles

And,

Population of Colorado = 5029196 people

So,  the population density is

[tex]= 5029196 \div 106812[/tex]

= 47

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