Answer:
2. 3.913 kg (3 dp)
3. light cream
4. 240 CoffeeStops
5. 7 CoffeeStops per square mile
6. 2,861 cups of coffee each day
Step-by-step explanation:
Given:
- Skim milk density at 20 °C = 1.033 kg/l
- Light cream density at 20 °C = 1.012 kg/l
- 1 liter = 0.264 gallons
Question 2
[tex]\begin{aligned}\textsf{1 gallon} & = \sf \dfrac{1}{0.264}\:liters\\\\\implies \textsf{Mass (1 gallon of skim milk)} & = \sf Density \times Volume\\& = \sf 1.033\:kg/l \times \dfrac{1}{0.264}\:l\\& = \sf 3.913\:kg\:(3\:dp)\end{aligned}[/tex]
Therefore, the mass of 1 gallon of skim milk is 3.913 kg (3 dp)
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Question 3
Given:
- Volume of liquid = 9 liters
- Mass of liquid = 9.108 kg
[tex]\begin{aligned}\implies \sf Density & = \sf \dfrac{Mass}{Volume}\\\\& = \sf \dfrac{9.108\:kg}{9\:l}\\\\& = \sf 1.012\:kg/l \end{alilgned}[/tex]
Therefore, the container holds light cream.
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Question 4
Given:
- 15 CoffeeStops per 100,000 people
- Population of Manhattan ≈ 1,602,000 people
[tex]\begin{aligned}\implies \textsf{Number of Coffeestops} & = \sf \dfrac{population}{density}\\\\& = \sf \dfrac{1,602,000}{100,000/15}\\\\& = \sf \dfrac{1,602,000}{100,000} \times 15\\\\& = \sf 240.3\end{aligned}[/tex]
Therefore, there are 240 CoffeeStops.
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Question 5
Given
- Manhattan ≈ 34 square miles
[tex]\begin{aligned}\implies \textsf{CoffeeStops density} & = \sf \dfrac{number\:of\:stores}{land\:area}\\\\& = \sf \dfrac{240}{34}\\\\& \approx \sf 7 \: \textsf{CoffeeStops per square mile}\end{aligned}[/tex]
Therefore, the density of CoffeeStops is 7 per square mile.
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Question 6
Given:
- Each person buys 3 cups of coffee per week
[tex]\begin{aligned}\implies \textsf{Cups served each week} & = \textsf{number of people} \times \textsf{number of cups per week}\\& = \sf 1,602,000 \times 3\\& = \sf 4,806,000\: \textsf{cups per week}\\\\\implies \textsf{Cups per day} & = \sf \dfrac{\textsf{cups per week}}{\textsf{days in a week}}\\\\& = \sf \dfrac{4,806,000}{7}\\\\& = \sf 686,571\:\textsf{(nearest whole number)}\end{aligned}[/tex]
[tex]\begin{aligned}\implies \textsf{Cups served per day per shop} & = \dfrac{\textsf{cups per day}}{\textsf{number of shops}}\\\\& = \sf \dfrac{686,571}{240}\\\\& = \sf 2,861\: \textsf{(nearest whole number)} \end{aligned}[/tex]
Therefore, each Manhattan CoffeeStop serves approximately 2,861 cups of coffee each day.
