That is a rational number.
Answer:
II and II only.
Step-by-step explanation:
The first series converges because the common ratio r is 0.8 (<1).
II diverges as |r| > 1.
III is an alternating series with r = -4 - that is |r| = 4 so it diverges.
It would be: -12 + 15x = 3(-4+5x)
So, after common factor out, your answer is 3(-4+5x)
Hope this helps!
Answer:
incenter
Step-by-step explanation:
We have been given that the ages of students in a school are normally distributed with a mean of 15 years and a standard deviation of 2 years.
We are asked to find the percentage of students that are between 14 and 18 years old.
First of all, we will find z-score corresponding to 14 and 18 using z-score formula.
![z=\frac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
![z=\frac{14-15}{2}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B14-15%7D%7B2%7D)
![z=\frac{-1}{2}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B-1%7D%7B2%7D)
![z=-0.5](https://tex.z-dn.net/?f=z%3D-0.5)
Similarly, we will find the z-score corresponding to 18.
![z=\frac{18-15}{2}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B18-15%7D%7B2%7D)
![z=\frac{3}{2}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B3%7D%7B2%7D)
![z=1.5](https://tex.z-dn.net/?f=z%3D1.5)
Now we will find the probability of getting a z-score between
and
that is
.
![P(-0.5](https://tex.z-dn.net/?f=P%28-0.5%3Cz%3C1.5%29%3DP%28z%3C1.5%29-P%28z%3C-0.5%29)
Using normal distribution table, we will get:
![P(-0.5](https://tex.z-dn.net/?f=P%28-0.5%3Cz%3C1.5%29%3D0.93319-0.30854)
![P(-0.5](https://tex.z-dn.net/?f=P%28-0.5%3Cz%3C1.5%29%3D0.62465)
Let us convert
into percentage.
![0.62465\times 100\%=62.465\%\approx 62.5\%](https://tex.z-dn.net/?f=0.62465%5Ctimes%20100%5C%25%3D62.465%5C%25%5Capprox%2062.5%5C%25)
Therefore, approximately
of the students are between 14 and 18 years old.