A 100-liter tank initially full of water develops a leak at the bottom. Given that 10% of the water leaks out in the first 5 minutes, find the amount of water left in the tank 20 minutes after the leak develops if the water drains off at a rate that is proportional to the amount of water present.

And we want to find the amount remaining after t = 20 minutes so we just need to replace into the model and we got:

Step-by-step explanation:

For this case if we assume the proportional model we have the following differential equation:

Where A represent the amount in the tank, t the time and k the proportional constant.

We can reorder the differential equation like this:

If we integrate both sides we got:

Using exponential on both sides we got:

And for this case  we have the following conditions given:

Using the first condition we have that:

Using the second condition we have:

And we can solve for k like this:

So then our model would be given by:

And we want to find the amount remaining after t = 20 minutes so we just need to replace into the model and we got:

answer: it's d

step-by-step explanation:

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;