1991987
23.04.2020 •
Mathematics
3. Graph the following line 3x – 4y +12 = 0
(put in y=mx+b form first)
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Ответ:
The answer to your question is below
Step-by-step explanation:
Data
Line: 3x - 4y + 12 = 0
Process
1.- Subtract 3x in both sides
3x - 4y - 3x + 12 = -3x
2.- Simplify
- 4y + 12 = -3x
3.- Subtract 12 in both sides
-4y + 12 - 12 = -3x - 12
4.- Simplify
-4y = -3x - 12
5.- Divide by -4 both sides
-4y/-4 = -3x/-4 - 12/-4
6.- Simplify
y = 3/4x + 3
7.- Graph y-intersept (3)
8.- From the number three, count trhee units up and four units to the right (3/4).
9.- Join the points
Ответ:
a) What is the probability that the duration of a particular rainfall event at this location is at least 2 hours?
We want this probability"
At most 3 hours?
b) What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations?
What is the probability that it is less than the mean value by more than one standard deviation?
Step-by-step explanation:
Previous concepts
The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:
The cumulative distribution for this function is given by:
We know the value for the mean on this case we have that :
Solution to the problem
Part a
What is the probability that the duration of a particular rainfall event at this location is at least 2 hours?
We want this probability"
At most 3 hours?
Part b
What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations?
The variance for the esponential distribution is given by:
And the deviation would be:
And the mean is given by
Two deviations correspond to 5.540, so we want this probability:
What is the probability that it is less than the mean value by more than one standard deviation?
For this case we want this probablity: