Answer:
D. 150 pounds
Step-by-step explanation:
For be directly proportional, it has to be that as one value increases the other does it equally, so
If 138 pound box has a volume of 23 gallons for 25 gallons ?. For being directly proportional tha value must be higest
138 → 23 ![x=\frac{25*138}{23} = 150](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B25%2A138%7D%7B23%7D%20%3D%20150)
x → 25
It is hard to comprehend your question. As far as I understand:
f(x,y) = e^(-x)
Find the volume over region R = {(x,y): 0<=x<=ln(6), -6<=y <= 6}.
That is all I understood. It would be easier to understand with a picture or some kind of visual aid.
Anyways, to find the volume between the surface and your rectangular region R, we must evaluate a double integral of f on the region R.
![\iint_{R}^{ } e^{-x}dA=\int_{-6}^{6} \int_{0}^{ln(6)} e^{-x}dx dy](https://tex.z-dn.net/?f=%5Ciint_%7BR%7D%5E%7B%20%7D%20e%5E%7B-x%7DdA%3D%5Cint_%7B-6%7D%5E%7B6%7D%20%5Cint_%7B0%7D%5E%7Bln%286%29%7D%20e%5E%7B-x%7Ddx%20dy)
Now evaluate,
![\int_{0}^{ln(6)}e^{-x}dx](https://tex.z-dn.net/?f=%5Cint_%7B0%7D%5E%7Bln%286%29%7De%5E%7B-x%7Ddx)
which evaluates to, 5/6 if I did the math correct. Correct me if I am wrong.
Now integrate this w.r.t. y:
![\int_{-6}^{6}\frac{5}{6}dy = 10](https://tex.z-dn.net/?f=%5Cint_%7B-6%7D%5E%7B6%7D%5Cfrac%7B5%7D%7B6%7Ddy%20%3D%2010)
So,
![\iint_{R}^{ } e^{-x}dA=\int_{-6}^{6} \int_{0}^{ln(6)} e^{-x}dx dy = 10](https://tex.z-dn.net/?f=%5Ciint_%7BR%7D%5E%7B%20%7D%20e%5E%7B-x%7DdA%3D%5Cint_%7B-6%7D%5E%7B6%7D%20%5Cint_%7B0%7D%5E%7Bln%286%29%7D%20e%5E%7B-x%7Ddx%20dy%20%3D%2010)
The product of powers property.
Answer:
102 students
Step-by-step explanation:
Note that 65% and 71% are both 1 standard deviation from the mean (71%). According to the empirical rule, 68% of scores lie within 1 std. dev. of the mean.
68% of 150 students would be 0.68(150 students) = 102 students