I need help with math Please
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The true statement about the directrix is that each directrix of this ellipse is 31.25 units from the center on the major axis.
<h3>How to determine the distance of the directrix?</h3>The equation of the ellipse is given as:
The above means that:
a^2 = 625
a = 25
b^2 = 225
b = 15
Calculate c using:
c^2 = a^2 - b^2
This gives
c^2 = 625 - 225
Evaluate the difference
c^2 = 400
Evaluate the square root
c = 20
The equation of the directrix is
x - x₀ = ± a²/c
So, we have:
x - x₀ = ± 625/20
Evaluate the quotient
x - x₀ = ± 31.25
This means that, each directrix is 31.25 units from the center on the major axis.
Read more about directrix at:
Complete question;
<em>The distribution of lengths of salmon from a certain river is approximately normal with a standard deviation of 3.5 inches. If 10 percent of salmon are longer than 30 inches, which of the following is closest to the mean of the distribution? 26 inches A 28 inches B 30 inches C 33 inches D 34 inches</em>
Option B is correct. The value that is closest to the mean of the distribution is 30inches.
The formula for calculating the z-score is expressed as:
Given the following parameters
If 10 percent of salmon are longer than 30 inches, then:
- P(x>30) = 0.1
Using the z table to get the value corresponding to the mean area 0.1.
- The required z-score will be -1.285
Substitute the resulting parameters into the formula to get the mean of the distribution.
Hence the value that is closest to the mean of the distribution is 30inches.
Learn more here: brainly.com/question/15295437