A gardener is planning to fill her garden with mulch. She plots it on a grid to plan how much she will need. The garden is in th
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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.
Answer:
34.86% probability that it will be huge success
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Receiving a favorable review.
Event B: Being a huge success.
Information on previous textbooks published show that 20 % are huge successes
This means that
99 % of the huge successes received favorable reviews
This means that
Probability of receiving a favorable review:
20% are huge successes. Of those, 99% receive favorable reviews.
30% are modest successes. Of those, 70% receive favorable reviews.
30% break even. Of those, 40% receive favorable reviews.
20% are losers. Of those, 20% receive favorable reviews.
Then
Finally
34.86% probability that it will be huge success
Answer:
0 and 5 minutes
Step-by-step explanation:
Median is the middle observation of given data. It can be found by following steps:
Arranging data in ascending or descending order.
Taking the average of middle two value if the total number of observation is even, and this average is our median.
or, if we odd number of observation then the most middle value is our median.
The mode is the observation which has a high number of repetitions (frequency).
We have given 8 numbers and we have to find the other two numbers a minute late for each bus to arrive at the bus stop.
Also, we have given the median and mode of all 10 buses i.e. 3.5 and 0 respectively.
Since the mode is 0, so the frequency of 0 must be greater than 2 times and less than or equal to 4 times.
The frequency of 0 is 4 is not possible as then we didn't get a median 3.5 then.
So the frequency of 0 is 3.
Hence one of number is 0 in two unknown number of a minute late for each bus arrive at the bus stop.
Now, we have the number of minutes late for each bus after arranging them in ascending order is: 0 0 0 2 2 6 8 8 9
For getting a median 3.5 we must have a number between 2 and 6. Let it be x then:
⇒x = 5
Hence the number of minutes late for each bus is: 0 0 0 2 2 5 6 8 8 9
Thus, 0 and 5 are minutes late for the two-afternoon buses.