Does the graph represent a function?
2 answers:
Answer: Not a Function
Step-by-step explanation: For a function, each x term
must correspond to exactly one y term.
We can use the vertical line test to determine whether
or not that holds true for the graph shown here.
If each x term corresponds to exactly one y term, then any vertical line
that we draw on the graph should hit the graph at only one point.
Notice below that many of the vertical lines that we draw
on this graph will hit the graph at more than one point.
Thus, we can conclude that no, the graph shown here is <em>not a function</em>.
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Answer:
66.76% probability that the levee will NEVER fail in the next 20 years.
Step-by-step explanation:
For each year, there are only two possible outcomes. Either a levee fails during the year, or no levees fail. In each year, the probabilities of levees failing are independent from each other. So we use the binomial probability distribution to solve this problem.
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.
In this problem we have that:
A levee was designed to protect against floods with an annual exceedance probability of 0.02. This means that
What is the risk that the levee will NEVER fail in the next 20 years?
This is when
. So
66.76% probability that the levee will NEVER fail in the next 20 years.