I need help on this question please!
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Answer:
And we can find the nnumber of deviations from the mean for each limit given:
So we are 3 deviation from the mean and using the empirical rule we know that within 3 deviations from the mean we have 99.7% of the values
Step-by-step explanation:
Let X the random variable that represent the amount of time it takes him to arrive, and for this case we know the distribution for X is given by:
Where and
We want to find this probability:
And we can use the z score formula given by:
And we can find the nnumber of deviations from the mean for each limit given:
So we are 3 deviation from the mean and using the empirical rule we know that within 3 deviations from the mean we have 99.7% of the values
[a] Dye is removed from the pool at a rate of
(250 gal/min) * (<em>q</em>/60,000 g/gal) = -<em>q</em>/240 g/gal
where <em>q</em> denotes the amount of dye in the pool at time <em>t</em>. Clean water is pumped back into the pool, so no dye is being re-added.
So the net rate of change of the amount of dye in the pool is given by the differential equation,
with the intial value, <em>q</em>(0) = 6000 g (or 6 kg).
[b] The ODE above is separable as
Integrate both sides to get
Now plug in the initial condition:
so the particular solution to the IVP is
[c] The acceptable concentration of the dy is 0.03 g/gal, which in a pool containing 60,000 gal of water corresponds to
(0.03 g/gal) * (60,000 gal) = 1800 g = 1.8 kg
of dye. Find the time <em>t</em> when this occurs:
so the amount of dye in the pool is within the acceptable tolerance after about 289 min have passes, or about 4.82 hrs. So no, the filtration system is not up to the task.