Slope-intercept form
1 answer:
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<h3>Answer:</h3>
<em>Try the answers</em>
You can try the answers to see what works. You can expect all of the choices to match the first two terms, so try some farther down. Let's see if we can get -25 from -7.
a) 3*(-7) -4 = -21 -4 = -25 . . . . this one works
b) -7 -2 = -9 . . . . ≠ -25
c) -3(-7) +2 = 21 +2 = 23 . . . . ≠ -25
d) -2(-7) +1 = 14 +1 = 15 . . . . ≠ -25
The formula that works is the first one.
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<em>Derive it</em>
All these formulas depend on the previous term only, so we can write equations that show the required relationships. Let the unknown coefficients in our recursion formula be p and q, as in ...
Then, to get the second term from the first, we have
... 1·p +q = -1
And to get the third term from the second, we have
... -1·p +q = -7
Subtracting the second equation from the first gives ...
... 2p = 6
... p = 3 . . . . . . . this is sufficient to identify the first answer as correct
We can find q from the first equation.
... q = -1 -p = -1 -3 = -4
So, our recursion relation is ...
Answer:
15.24% probability that at least 2 will still stand after 35 years
Step-by-step explanation:
To solve this question, we need to understand the binomial distribution and the exponential distribution.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
In which is the decay parameter.
The probability that x is lower or equal to a is given by:
Which has the following solution:
The probability of finding a value higher than x is:
Probability of a single tower being standing after 35 years:
Single tower, so exponential.
Mean of 25 years, so
We have to find
What is the probability that at least 2 will still stand after 35 years?
Now binomial.
Each tower has a 0.2466 probability of being standing after 35 years, so
3 towers, so
We have to find:
In which
15.24% probability that at least 2 will still stand after 35 years