If
and
, separate variables in the differential equation to get

Integrate both sides:

Use the initial condition to solve for
:

Then the particular solution to the initial value problem is

(A)
Answer:
answer in the pic
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask me in the comments below ;)
We have been given that the lifespans of lions in a particular zoo are normally distributed. The average lion lives 12.5 years; the standard deviation is 2.4 years. We are asked to find the probability of a lion living longer than 10.1 years using empirical rule.
First of all, we will find the z-score corresponding to sample score 10.1.
, where,
z = z-score,
x = Random sample score,
= Mean
= Standard deviation.



Since z-score of 10.1 is
. Now we need to find area under curve that is below one standard deviation from mean.
We know that approximately 68% of data points lie between one standard deviation from mean.
We also know that 50% of data points are above mean and 50% of data points are below mean.
To find the probability of a data point with z-score
, we will subtract half of 68% from 50%.


Therefore, the probability of a lion living longer than 10.1 years is approximately 16%.
<span>1. 3a²-a = a(3a - 1)
2. 7ab³-14b = 7b(ab^2 - 2)
3. x³-x²+x = x(x^2 - x + 1)
4. 12x³-xy² = x(12x^2 - y^2)
5. 5x-6x²+7x³ = x(5 - 6x + 7x^2)
6. 7a+8ab+9a² = a(7 + 8b + 9a)
7.3x²-3xy+6xy²
</span>= 3x(x - y + 2y^2)