Help! I'm unsure as to how to solve this... True or false? Can a polygon with 21 sides have 432 possible diagonals.

NO, it can have only 189 possible diagonals

Step-by-step explanation:

No. of diagonals in a polygon is given by n(n-3)/2

where n is the number of sides in the polygon.

Given

polygon has 21 sides

thus, no. of diagonals for 21 sided polygon is = 21(21-3)/2 = 21*18/2 = 189

while in the problem it is asking if it has 432 possible diagonals

which is wrong.

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: