Find the height of a square pyramid that has a volume of 12 cubic feet and a base length of 3 feet.
2 answers:
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Answer:
The mean would be $322,343 and the median would be $196,723.
Step-by-step explanation:
Since the distribution of individual incomes is skewed to the right, it means that the distribution has a long right tail.
Drawing a distribution with this characteristic, we can see how the majority of the data falls into the left side of the graphic, meaning that a lot of people receive less income. Following this reasoning, the mean which is the amount of the data (in this case individual income) divided by the amount of people, would be the higher number, meaning that the few people who earn more money would influence in making this number higher.
Following this reasoning, the median (which is not influenced by this difference) would be the less high number.
Answer:
The value of x that gives the maximum transmission is 1/√e ≅0.607
Step-by-step explanation:
Lets call f the rate function f. Note that f(x) = k * x^2ln(1/x), where k is a positive constant (this is because f is proportional to the other expression). In order to compute the maximum of f in (0,1), we derivate f, using the product rule.
We need to equalize f' to 0
- k*(2x ln(1/x) - x) = 0 -------- We send k dividing to the other side
- 2x ln(1/x) - x = 0 -------- Now we take the x and move it to the other side
- 2x ln(1/x) = x -- Now, we send 2x dividing (note that x>0, so we can divide)
- ln(1/x) = x/2x = 1/2 ------- we send the natural logarithm as exp
- 1/x = e^(1/2)
- x = 1/e^(1/2) = 1/√e ≅ 0.607
Thus, the value of x that gives the maximum transmission is 1/√e.