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2 answers:
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The function f(x) is vertically compressed to form g(x) while the function f(x) is vertically compressed and then reflected across the x-axis to form h(x)
<h3>How to compare both functions?</h3>The functions are given as
f(x) =x^2
g(x) =3x^2
h(x) = -3x^2
Substitute f(x) =x^2 in g(x) =3x^2 and h(x) = -3x^2
g(x) =3f(x)
h(x) = -3f(x)
This means that the function f(x) is vertically compressed to form g(x)
Also, the function f(x) is vertically compressed and then reflected across the x-axis to form h(x)
See attachment for the functions g(x) and h(x)
Also, functions f(x) and g(x) have the same domain and range
While functions f(x) and h(x) have the same domain but different range
The complete table is:
x -2 -1 0 1 2
g(x) 12 3 0 3 12
h(x) -12 -3 0 -3 -12
Read more about function transformation at:
#SPJ1
Answer:
There is a 97.585% probability that a fisherman catches a spotted seatrout within the legal limits.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by
After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.
In this problem, we have that:
The lengths of the spotted seatrout that are caught, are normally distributed with a mean of 22 inches, and a standard deviation of 4 inches, so .
What is the probability that a fisherman catches a spotted seatrout within the legal limits?
They must be between 10 and 30 inches.
So, this is the pvalue of the Z score of subtracted by the pvalue of the Z score of
X = 30
has a pvalue of 0.9772
X = 10
has a pvalue of 0.00135.
This means that there is a 0.9772-0.00135 = 0.97585 = 97.585% probability that a fisherman catches a spotted seatrout within the legal limits.