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musickatia [10]
3 years ago
5

A certain region currently has wind farms capable of generating a total of 2200 megawatts (2.2 gigawatts) of power. Assuming win

d farms can generate 25% of their capacity, how much energy, in kilowatt-hours, can the region's wind farm generate in one year?
Given that the average household in the region uses about 10,000 kilowatt-hours of energy each year, how many households can be powered by these wind farms?
Mathematics
1 answer:
sveta [45]3 years ago
8 0

Answer:

<u>The correct answer is A. 4,818'000,000 kilowatt-hours per year and B. 481,800 households.</u>

Step-by-step explanation:

1. Let's review the information provided to us for solving the questions:

Power capacity of the wind farms = 2,200 Megawatts or 2.2 Gigawatts

2. Let's resolve the questions A and B:

Part A

Assuming wind farms typically generate 25​% of their​ capacity, how much​ energy, in​ kilowatt-hours, can the​ region's wind farms generate in one​ year?

2,200 * 0.25 = 550 Megawatts

550 Megawatts = 550 * 1,000 Kilowatts = 550,000 Kilowatts

Now we calculate the amount of Kilowatts per hour, per day and per year:

550,000 Kw generated by the farms means that are capable of produce 550,000 kw per hour of energy

550,000 * 24 = 13'200,000 kilowatt-hours per day

<u>13'200,000 * 365 = 4,818'000,000 kilowatt-hours per year</u>

Part B

Given that the average household in the region uses about​ 10,000 kilowatt-hours of energy each​ year, how many households can be powered by these wind​ farms?

For calculating the amount of households we divide the total amount of energy the wind farms can generate (4,818'000,000 kilowatt-hours) and we divide it by the average household consumption (10,000 kilowatt-hours)

<u>Amount of households =  4,818'000,000/10,000 = 481,800</u>

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Answer:

The answer is B

Step-by-step explanation:

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3 years ago
A bank advertises that it compounds money quarterly and that it will take Double your money in 10 years. what is the interest-ra
S_A_V [24]

The interest rate is 6.992%, if a bank advertises that it compounds money quarterly and that it will take Double your money in 10 years.

Step-by-step explanation:

The given is,

                          Compounds money quarterly

                          Double your money in 10 years

Step:1

              Formula to calculate future investment with compounded quarterly,

                                                        A =P(1+\frac{r}{n} )^{nt}...............................(1)

              Where, A - Future amount

                           P - Initial investment\

                            r - Rate of interest

                            n - No. of compounding in a year

                             t - No. of years

Step:2

               Let, P = X

                      A = 2X ( Double your money )

              From given, n - 4 ( for compounding quarterly )

                                    t - 10 years

               From equation (1)

                                                        2X =X(1+\frac{r}{4} )^{(4)(10)}

                                                         \frac{2X}{X}  =(1+\frac{r}{4} )^{(4)(10)}

                                                            2  =(1+\frac{r}{4} )^{40}

          Take root 40^{th} root on both side,

                                                         \sqrt[40]{2} = (1+\frac{r}{4} )

                                            1.017479692 = (\frac{4+r}{4} )

                                     (1.017479692)(4) = (r+4)

                                                  4.06992=(r+4)

                                                              r = 4.06992 -4

                                                              r =( 0.06992)(100)

                                                              r = 6.992 %

Result:

             The interest rate is 6.992%, if a bank advertises that it compounds money quarterly and that it will take Double your money in 10 years.

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