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Flashcards: Apply concepts of density in modeling situations

A farmer has to make a square pen to hold chickens. If each chicken has to have $1 \;\textup{m}^2$ of area to roam and there are chickens total, what is the length of the amount of fencing required to pen in the chickens?

$25 \;\textup{m}$

$50 \;\textup{m}$

$20\;\textup{m}$

$75 \;\textup{m}$

$83\;\textup{m}$

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Flashcards: Apply concepts of density in modeling situations

Your answer:

$25 \;\textup{m}$

Your answer:

$50 \;\textup{m}$

Your answer:

$75 \;\textup{m}$

Your answer:

$83\;\textup{m}$

Correct answer:

$20\;\textup{m}$

Explanation:

A square has area formula

A = l^2

The total area required for the chickens will be

$25 \;\textup{m}^2$

since each chicken requires $1\;\textup{m}^2$ of space and there are chickens.

Thus, we have

25 = l^2

for the length of our chicken fence.

$\sqrt{25}=\sqrt{l^2}^$

l = 5

Since there are four sides of a square and each side has a length of 5, the total length of fence required is

$5\times4 = 20\;\textup{m}$ .

Flashcards: Apply concepts of density in modeling situations

Census

Source: United States Census Bureau

The average population density of a geographic area is defined to be the average number of residents per square mile.

Above is a table with the land areas and populations of five states.Which state among the five has the greatest population density?

Tennessee

Mississippi

Alabama

Kentucky

Arkansas

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Flashcards: Apply concepts of density in modeling situations

The average population density of a geographic area is defined to be the average number of residents per square mile.

Above is a table with the land areas and populations of five states.Which state among the five has the greatest population density?

Your answer:

Mississippi

Your answer:

Alabama

Your answer:

Kentucky

Your answer:

Arkansas

Correct answer:

Tennessee

Explanation:

For each state, divide the population by the land area. We can round each figure to the nearest whole for simplicity's sake.

Alabama:

$4,860,000 \div 50,645 \approx 96$ persons per square mile.

Arkansas:

$2,980,000 \div 52,035 \approx 57$ persons per square mile.

Kentucky:

$4,430,000 \div 39,486 \approx 112$ persons per square mile.

Mississippi:

$2,990,000 \div 46,923 \approx 64$ persons per square mile.

Tennessee:

$6,600,000 \div 41,235 \approx 160$ persons per square mile.

Tennessee has the greatest population density among the five states.

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Flashcards: Apply concepts of density in modeling situations

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