If 35% of a natural area is to be developed, leaving 500 acres untouched, how many acres are to be developed?
2 answers:
Answer:
Area to be developed = 269.23 acres
Step-by-step explanation:
Let there is A acres natural area to be developed.
If 35% of A acres is developed then untouched area will be (100 - 35 = 65%)
Now it has been given in the question that 65% of A (untouched area) = 500 acres
So area of the natural field = 769.23 acres
Now 35% of the natural area which is to be developed = A×35%
Area of the natural area to be developed is 269.23 acres
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Answer:
(B) At Maryland, the mean number of points per player per game is greater than the median number of points per player per game.
(D)The mean number of points per player per game is the same at all 3 schools.
Step-by-step explanation:
<u>Baylor University</u>
6 players who each score 12 points per game
6 players who each score 0 points per game.
The Scores are: 0,0,0,0,0,0,12,12,12,12,12,12
<u>University of Maryland</u>
1 player scores 58 points per game,
1 player scores 14 points per game,
The rest(10) of the players score 0 points per game.
The Scores are: 0,0,0,0,0,0,0,0,0,0,14,58
<u> Dartmouth College</u>
4 players score 5 points per game,
4 players score 6 points per game,
4 players score 7 points per game.
The Scores are: 5,5,5,5,6,6,6,6,7,7,7,7
The following applies:
(B) At Maryland, the mean number of points per player per game is greater than the median number of points per player per game.
(D)The mean number of points per player per game is the same at all 3 schools.
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.