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2 answers:
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Answer:
Step-by-step explanation:
The work is define as the integral of the force times distance. So we have:
Now, we can write the force in terms of density.
V is the volume (V=2*1*1=2 m³)
So the work will be:
The limit of integration is between 0 and 0.5 because we want to pump half of the water out of the aquarium.
I hope it helps you!
Answer:
5.59 times per second.
Step-by-step explanation:
Direct variation is in the form:
Where <em>k</em> is the constant of variation.
Inverse variation is in the form:
In the given problem, the frequency of a vibrating guitar string varies inversely as its length. In other words, using <em>f</em> for frequency and <em>l</em> for length:
We can solve for the constant of variation. We know that the frequency <em>f</em> is 4.3 when the length is 0.65 meters long. Thus:
Solve for <em>k: </em>
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So, our equation becomes:
Then when the length is 0.5 meters, the frequency will be:
Answer:
There is not enough evidence to conclude that average starting salary for clerical employees in the state is less than $35,000 per year.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 35,000 dollars per year
Sample mean, = 34,700 dollars per year
Sample size, n = 100
Alpha, α = 0.10
Population standard deviation, σ = 3,500 dollars per year
First, we design the null and the alternate hypothesis
We use one-tailed z test to perform this hypothesis.
Formula:
Putting all the values, we have
Now,
Since,
We fail to reject the null hypothesis and accept the null hypothesis.
Thus, there is not enough evidence to conclude that average starting salary for clerical employees in the state is less than $35,000 per year.