Answer:
Step-by-step explanation:
1) True. This is because the divergence of F is 1, thus, F is a linear function. Orientation is given outward to the surface. Linear function double integrated over a surface with outward orientation gives volume enclosed by the surface.
2) True. This is primarily what the Divergence theorem is.
3) False. If F was 3/pi instead of div(F), then the statement would have been true.
4) False. The gradient of divergence can be anything. The curl of divergence of a vector function is 0, not the gradient o divergence.
5) False. While finding Divergence, derivatives are taken for different variables. Since the derivatives of constants are 0, therefore, both the vector functions F and G can be different constant parts of there components even if their divergences are equal.
The answer would be 331 weeks rounded. Just divide.
Answer:
0.3085 = 30.85% probability that a randomly selected pill contains at least 500 mg of minerals
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean 
and standard deviation 
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean 490 mg and variance of 400.
This means that 
What is the probability that a randomly selected pill contains at least 500 mg of minerals?
This is 1 subtracted by the p-value of Z when X = 500. So
has a p-value of 0.6915.
1 - 0.6915 = 0.3085
0.3085 = 30.85% probability that a randomly selected pill contains at least 500 mg of minerals
We are given a volume of 160 fluid ounces of chemical which is added to a container that holds 120,000 gallons of water. Assuming that the chemical has the same density as water, we just need to convert 120,000 gallons to ounces.
A conversion factor is taken from literature, 1 gallon is equivalent to 128 fluid ounces. So 160 fluid ounces is only 1.25 gallons, thus occupying minimal space in the container. The employee could add more of the chemical in the container. He can actually add 15360000 fluid ounces in total.
