Which of the following expressions represents a function?
1 answer:
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Answer:
This a circle centered at the point , and of radius "3" as it is shown in the attached image.
Step-by-step explanation:
Recall that the standard formula for a circle of radius "R", and centered at the point is given by:
Therefore, in our case, by looking at the standard equation they give us, we extract the following info:
1) since the radius must be a positive number and (
) is not a viable answer.
2) for (
) to equal
3) for (
) to equal
Therefore, we are in the presence of a circle centered at the point , and of radius "3". That is what we draw as seen in the attached image.
1) 4.55
2) Short hit
Step-by-step explanation:
1)
The table containing the score and the relative probability of each score is:
Score 3 4 5 6 7
Probability 0.15 0.40 0.25 0.15 0.05
Here we call
X = Miguel's score on the Water Hole
The expected value of a certain variable X is given by:
where
are all the possible values that the variable X can take
is the probability that
Therefore in this problem, the expected value of MIguel's score is given by:
2)
In this problem, we call:
X = Miguel's score on the Water Hole
Here we have that:
- If the long hit is successfull, the expected value of X is
- Instead, if the long hit fails, the expected value of X is
Here we also know that the probability of a successfull long hit is
Which means that the probabilty of an unsuccessfull long hit is
Therefore, the expected value of X if Miguel chooses the long hit approach is:
In part 1) of the problem, we saw that the expected value for the short hit was instead
Since the expected value for X is lower (=better) for the short hit approach, we can say that the short hit approach is better.