Based on the population mean, the mean of the distribution sample means would be 204.6. The standard deviation would be 0.22.
<h3>What are the mean and standard deviation of the distribution?</h3>
The mean of the distribution sample means is the same as the population means which is 204.6.
The standard deviation can be found as:
σₓ = σ / √n
= 3.1 / √197
= 0.22
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The volume of the cone that has a radius of 8 in. and a height of 10.5 in. is: 703.7 in.³
<h3>What is the Volume of a Cone?</h3>
Volume = 1/3πr²h
Given the parameters:
- Height (h) = 10.5 in.
- Radius (r) = 8 in.
Volume of the cone = 1/3πr²h = 1/3π(8²)(10.5)
Volume of the cone = 1/3π(64)(10.5)
Volume of the cone = 703.7 in.³
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Answer:
The profit will be maximum on x = 250.
Step-by-step explanation:
From the given information:
Revenue = 1500x - x²
Cost = 1500 + 1000x
As we know that
Profit = Revenue - Cost ; Let say it equation 1
Then after putting the values of revenue and cost in equation 1 we have:
Profit = (1500x - x²) - (1500 + 1000x)
Profit = 1500x - x² - 1500 - 1000x
Profit = -x² + 500x - 1500
We know that at the max or min the slope of the graph formed by the profit function will be zero, therefore we find the slope of profit function by taking the first derrivative w.r.t. x as under:
d(Profit)/dx = d/dx(-x² + 500x - 1500)
d(Profit)/dx = -2x + 500
By putting the above slope equal to zero we get:
d(Profit)/dx = -2x + 500 = 0
-2x + 500 = 0
-2x = -500
x = 250
Therefore it is concluded that the profit will be maximum when x will be equal to 250.
577,000, there is an average change of 577,000 people per year.
To find the average rate of change of the population of people per year, we first need to find the population change per any amount of time, and then divide by how much time that is (in this case, three years). We can find the population change by <u>subtracting </u>the values 17,334,000 and 19,065,000. Subtracting them, we get a change of 1,731,000 in three years. Now, to find the average rate of change of the population in people per year, we divide by three, which gives us our answer of 577,000 people, on average, per year.
