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lubasha [3.4K]
3 years ago
10

Solar energy is considered by many to be the energy of the future. A recent survey was taken to compare the cost of solar energy

to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $120 and a standard deviation of $11. If the distribution can be considered bell shaped, what percentage of homes will have a monthly utility bill of more than $109? Group of answer choices approximately 16% approximately 32% approximately 84% approximately 95%
Mathematics
1 answer:
ycow [4]3 years ago
8 0

Answer:

The answer is 132

Step-by-step explanation:

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Find the value of x. Give your answer in simplest radical form.
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Answer: x = 5*sqrt(10)
"sqrt" stands for "square root"

-------------------------------------------------------

Refer to the attached image. The figure is not to scale. Notice how I've added in y and z (blue and red respectively)
The length y is the bottom horizontal leg for the triangle on the right.
The length z is the bottom horizontal leg for the triangle on the left.

To find x, we need to find y first, which will help us find z, and then we can finally get to x.

Let's find y first
To do this, we use the pythagorean theorem
a^2 + b^2 = c^2
y^2 + 9^2 = 15^2
y^2 + 81 = 225
y^2 + 81-81 = 225-81
y^2 = 144
sqrt(y^2) = sqrt(144)
y = 12 ... keep in mind that y is a length, so it needs to be positive

Notice how the y and z lengths combine to form a total length of 25 units
Therefore,
y+z = 25
12+z = 25
12+z-12 = 25-12
z = 13

Now that we know z = 13, we can find x. Again we use the pythagorean theorem one last time
a^2 + b^2 = c^2
z^2 + 9^2 = x^2
13^2 + 9^2 = x^2
169 + 81 = x^2
250 = x^2
x^2 = 250
sqrt(x^2) = sqrt(250)
x = sqrt(250)
x = sqrt(25*10)
x = sqrt(25)*sqrt(10)
x = 5*sqrt(10)
This is in simplest radical form as we can't factor 10 any further (there are no perfect square factors that go into 10). This is the exact length of side x

Note: using a calculator, 5*sqrt(10) = 15.8113883008419 approximately

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