For Uncle Joe's dairy farm with 200 cows the cost of a methan digester is about 400 dollars. ASsume that the farm uses 800,000 kilowatt hours of electricity each year at a cost of $0.20 per kwh. The waste from a single cow can produce 2.0 kwh of electricity each day. Assuming the cost of electricity stays the same and Farmer Joe starts using manure from the cows in an aneorbic digester :

Question

For Uncle Joe's dairy farm with 200 cows the cost of a methan digester is about 400 dollars. ASsume that the farm uses 800,000 kilowatt hours of electricity each year at a cost of $0.20 per kwh. The waste from a single cow can produce 2.0 kwh of electricity each day. Assuming the cost of electricity stays the same and Farmer Joe starts using manure from the cows in an aneorbic digester :

Calculate :

The number of KwH of electricity that can be produced in one year

The amount of money Farmer Joe will save in one year NOT counting the installation cost of the digester (round to nearest $1000)

The amount of time in years it will take to recover the cost of installing the digester on the farm (you may need to record your ansewr to nearest whole number)

Answer 1

200cows * 2kwh/cow/day = 400kwh/day * 365 days/yr = 146000 kwh/yr

multiply by the value of a kwh to get the savings

Now figure the cost of running the digester for a year.

divide the cost by the savings to get the recovery time.

Answer 2

By how much does the mean of the data set below change if the outlier is removed round your answer to the nearest tenth if necassary

8,6,9,12,19,7,10,8
A. 0.5
B. 0.6
C. 1.3
D. 2.4

Answer 3

First, we need to find the mean of the entire data set:

Mean = (8+6+9+12+19+7+10+8)/8 = 9.875

Now, let's remove the outlier (19) and find the mean of the new data set:

Mean = (8+6+9+12+7+10+8)/7 = 8.57

The difference between the original mean and the new mean is:

9.875 - 8.57 = 1.305

Rounding to the nearest tenth, we get:

1.3

Therefore, the answer is C. 1.3.

Answer 4

To calculate the number of kWh of electricity that can be produced in one year, we need to multiply the number of cows by the daily electricity production per cow and then multiply it by the number of days in a year.

Number of kWh produced per year = (Number of cows) x (Daily electricity production per cow) x (Number of days in a year)

Number of cows = 200
Daily electricity production per cow = 2.0 kWh
Number of days in a year = 365

Number of kWh produced per year = 200 x 2.0 kWh x 365 days = 146,000 kWh

The amount of money Farmer Joe will save in one year (not counting the installation cost of the digester) can be calculated by multiplying the number of kWh produced per year by the cost per kWh.

Money saved per year = (Number of kWh produced per year) x (Cost per kWh)

Number of kWh produced per year = 146,000 kWh
Cost per kWh = $0.20

Money saved per year = 146,000 kWh x $0.20/kWh = $29,200

The amount of time it will take to recover the cost of installing the digester on the farm can be calculated by dividing the cost of the digester by the savings per year (not counting the installation cost).

Time to recover cost = (Cost of digester) / (Money saved per year)

Cost of digester = $400
Money saved per year = $29,200

Time to recover cost = $400 / $29,200 = 0.01369 years

Since we are asked to round to the nearest whole number, the time to recover the cost of installing the digester is approximately 0 years.