Answer:
a) The probability that at least 3 months elapse before the first earthquake of destructive magnitude occurs is P=0.7788
b) The probability that at least 7 months elapsed before the first earthquake of destructive magnitude occurs knowing that 3 months have already elapsed is P=0.7165
Step-by-step explanation:
Tha most appropiate distribution to model the probability of this events is the exponential distribution.
The cumulative distribution function of the exponential distribution is given by:

The destructive earthquakes happen in average once a year. This can be expressed by the parameter λ=1/year.
We can express the probability of having a 3 month period (t=3/12=0.25) without destructive earthquakes as:

Applying the memory-less property of the exponential distribution, in which the past events don't affect the future probabilities, the probability of having at least 7 months (t=0.58) elapsed before the first earthquake given that 3 months have already elapsed, is the same as the probability of having 4 months elapsed before an earthquake.


Answer: The cost of child's ticket = $10
The cost of adult ticket = $ 13
Step-by-step explanation:
Let x be the cost of a child ticket and y be the cost of an adult ticket.
Then According to the question, we have

Multiply equation (1) by 3 and equation (2) by 2, then we have

Subtract equation (1) from equation (2), we have

Substitute the value of x in equation (1), we get

Hence, the cost of child's ticket = $10
The cost of adult ticket = $ 13
The Lateral Surface Area of Square based pyramid whose height= 71 feet Slant height= 90 feet and Base= 115 feet is 20700
.
The Lateral Surface Area is 20700 
<h3 /><h3>What Lateral Surface Area of Square based pyramid?</h3>
The word "lateral" means "belonging to the side". So the lateral area of a square pyramid is the sum of the areas of its side faces. This is also known as the lateral surface area (LSA) of the square pyramid. We know that a square pyramid has:
- a base which is a square.
- 4 side faces, each of which is a triangle.
It is given that,
- height, h= 71 feet
- Slant height, l= 90 feet
- Base, b= 115 feet
Lateral Surface Area of square pyramid is,
LSA= 
Where p= perimeter of base
l= slant height
Perimeter of base = 4 x side
= 4 x 115
= 460 feet
Now, Lateral Surface Area of square pyramid is,
= 
= 460 x 45
= 20700 
Hence the Lateral Surface Area of square pyramid is 20700 
Learn more about Lateral Surface Area of Pyramid here:
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Answer:
5x >=45. x>= 9 is correct