Let

be the random variable for the weight of any given can, and let

and

be the mean and standard deviation, respectively, for the distribution of

.
You have

Recall that for any normal distribution, approximately 99.7% of it lies within three standard deviations of the mean, i.e.

. This means 0.3% must lie outside this range,

. Because the distribution is symmetric, it follows that

.
Also recall that for any normal distribution, about 95% of it falls within two standard deviations of the mean, so

, which means 5% falls outside, and by symmetry,

.
Together this means

Solving for the mean and standard deviation gives

and

.

Look for an integrating factor
:

Multiply both sides by
:

Condense the left side as the derivative of a product:
![\dfrac{\mathrm d}{\mathrm dt}\left[(t+1)^{-7/9}y\right]=\dfrac{14}9t(t+1)^{-16/9}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dt%7D%5Cleft%5B%28t%2B1%29%5E%7B-7%2F9%7Dy%5Cright%5D%3D%5Cdfrac%7B14%7D9t%28t%2B1%29%5E%7B-16%2F9%7D)
Integrate both sides:

For the integral on the right, substitute






Given that
, we get


Answer:
Step-by-step explanation:
First solve -5x+9y=-12 for x:
-5x+9y=-12
-5x+9y-9y=-12-9y
-5x=-12-9
-5x=-9-12
-5x/-5=-9/5-12/-5
x=9/5y+12/6
Substitute x into an equation
3(-9/5y+12/6)+2y=22
37/5y+36/5=22
37/5y+36/5-36/5=22-36/5
37/5y=74/5
37/5y/37/5=74/5/37/5
y=2
Substitute y in x=-9/5y+12/6
9/5(2)+12/6
x=6
Solution Set: (6,2)
xoxo
2x+6<u><</u>x+5
subtract x from both sides
x+6<u><</u>5
subtract 6 from both sides
x<u><</u>-1
so x<u><</u>-1
solution set
S={x|x<u><</u>-1}