You would use PEMDAS, which means Parenthesis, exponents, multiplication, division, addition" and then subtraction. You would solve the problem in that order
pretty much about the same as before.
a = weight of a large box
b = weight of a small box.
we know their combined weight is 65 lbs, thus a + b = 65.
we also know that the truck has 60 large ones, and 55 small ones, thus 60*a is the total weight for the large ones and 55*b is the total weight for the small ones, and we know that is a total of 3775, 60a + 55b = 3775.
![\bf \begin{cases} a+b=65\\ \boxed{b}=65-a\\ \cline{1-1} 60a+55b=3775 \end{cases}\qquad \qquad \stackrel{\textit{substituting on the 2nd equation}}{60a+55\left( \boxed{65-a} \right)=3775} \\\\\\ 60a+3575-55a=3775\implies 5a+3575=3775\implies 5a=200 \\\\\\ a=\cfrac{200}{5}\implies \blacktriangleright a = 40 \blacktriangleleft \\\\\\ \stackrel{\textit{since we know that}}{b=65-a\implies }b=65-40\implies \blacktriangleright b=25\blacktriangleleft](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%20a%2Bb%3D65%5C%5C%20%5Cboxed%7Bb%7D%3D65-a%5C%5C%20%5Ccline%7B1-1%7D%2060a%2B55b%3D3775%20%5Cend%7Bcases%7D%5Cqquad%20%5Cqquad%20%5Cstackrel%7B%5Ctextit%7Bsubstituting%20on%20the%202nd%20equation%7D%7D%7B60a%2B55%5Cleft%28%20%5Cboxed%7B65-a%7D%20%5Cright%29%3D3775%7D%20%5C%5C%5C%5C%5C%5C%2060a%2B3575-55a%3D3775%5Cimplies%205a%2B3575%3D3775%5Cimplies%205a%3D200%20%5C%5C%5C%5C%5C%5C%20a%3D%5Ccfrac%7B200%7D%7B5%7D%5Cimplies%20%5Cblacktriangleright%20a%20%3D%2040%20%5Cblacktriangleleft%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bsince%20we%20know%20that%7D%7D%7Bb%3D65-a%5Cimplies%20%7Db%3D65-40%5Cimplies%20%5Cblacktriangleright%20b%3D25%5Cblacktriangleleft)
1) Mean
The mean is given by the sum of the data divided by the number of data (4, in this case):
![\mu = \frac{1}{N} \sum x_i = \frac{1}{4}(72.42+91.50+58.99+69.02) = \frac{291.93}{4}=72.98 $](https://tex.z-dn.net/?f=%5Cmu%20%3D%20%20%20%5Cfrac%7B1%7D%7BN%7D%20%5Csum%20x_i%20%3D%20%5Cfrac%7B1%7D%7B4%7D%2872.42%2B91.50%2B58.99%2B69.02%29%20%3D%20%5Cfrac%7B291.93%7D%7B4%7D%3D72.98%20%24%20%20)
2) Standard deviation
The standard deviation is given by:
![\sigma = \sqrt{ \frac{1}{N} \sum (x_i-\mu)^2 }](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%20%5Csqrt%7B%20%5Cfrac%7B1%7D%7BN%7D%20%5Csum%20%28x_i-%5Cmu%29%5E2%20%7D%20%20)
where
![\mu](https://tex.z-dn.net/?f=%5Cmu)
is the mean, that we already found at point 1), and N=4. Substituting data, we have:
![\sigma = \sqrt{ \frac{1}{4} ((-0.56)^2+(18.52)^2+(-13.99)^2+(-3.96)^2) } =](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%20%5Csqrt%7B%20%5Cfrac%7B1%7D%7B4%7D%20%28%28-0.56%29%5E2%2B%2818.52%29%5E2%2B%28-13.99%29%5E2%2B%28-3.96%29%5E2%29%20%7D%20%3D)
32 divided by 4/5=32*5/4/
simplify:8*5=40
there are 40 4/5 foot pieces in 32 feet