Answer:
y'(t) = k(700,000-y(t)) k>0 is the constant of proportionality
y(0) =0
Step-by-step explanation:
(a.) Formulate a differential equation and initial condition for y(t) = the number of people who have heard the news t days after it has happened.
If we suppose that news spreads through a city of fixed size of 700,000 people at a time rate proportional to the number of people who have not heard the news that means
<em>dy/dt = k(700,000-y(t)) </em>where k is some constant of proportionality.
Since no one has heard the news at first, we have
<em>y(0) = 0 (initial condition)
</em>
We can then state the initial value problem as
y'(t) = k(700,000-y(t))
y(0) =0
The median is 4.5. the median is the number in the middle
Answer:
There are 89% of healthy adults with body temperatures that are within 3 standard deviations of the mean
The minimum value that is within 3 standard deviations of the mean is 96.57.
The maximum value that is within 3 standard deviations of the mean is 100.11.
Step-by-step explanation:
Chebyshev's theorem states that a minimum of 89% of the values lie within 3 standard deviation of the mean.
So
Using Chebyshev's theorem, what do we know about the percentage of healthy adults with body temperatures that are within 3 standard deviations of the mean?
There are 89% of healthy adults with body temperatures that are within 3 standard deviations of the mean.
What are the minimum and maximum possible body temperatures that are within 3 standard deviations of the mean?
We have that the mean
is 98.34 and the standard deviation
is 0.59. So:
Minimum

Maximum

For this case we have by definition that:

In this case we must find
so:
(
We must apply distributive property that states that:

So:

Answer:
