1 foot = 12 inches
7 1/2 feet = 12 * 7 1/2
15/2 feet = 12 * 15/2
15/2 feet = 90 inches
SO, OPTION B IS YOUR ANSWER....
Answer:
Step-by-step explanation:
Given is a differential equation of III order,
![y''' + 6y'' + y' - 34y = 0](https://tex.z-dn.net/?f=y%27%27%27%20%2B%206y%27%27%20%2B%20y%27%20-%2034y%20%3D%200)
The characteristic equation would be cubic as
![m^3+6m^2+m-34=0](https://tex.z-dn.net/?f=m%5E3%2B6m%5E2%2Bm-34%3D0)
By trial and error, we find that
![f(2) = 2^3+6(2^2)+2-34 =0\\](https://tex.z-dn.net/?f=f%282%29%20%3D%202%5E3%2B6%282%5E2%29%2B2-34%20%3D0%5C%5C)
Thus m=2 is one solution
Since given that
is one solution we get
m = -4+i and hence other root is conjugate ![m=-4-i](https://tex.z-dn.net/?f=m%3D-4-i)
Hence general solution would be
![y=Ae^{2x} +e^{-4x} (Bcosx +C sinx)](https://tex.z-dn.net/?f=y%3DAe%5E%7B2x%7D%20%2Be%5E%7B-4x%7D%20%28Bcosx%20%2BC%20sinx%29)
If they drive an average of 60 miles per hour the last day it will take them 2.5 hours.
4 hours at 60 miles per hour = 4*60 = 240 miles
6 hours at 65 miles per hour = 6*65 = 390 miles
This is a total of 630 miles. There are 780-630=150 miles left; if they average 60 miles per hour, that would be 150/60 = 2.5 hours.
Using the Central Limit Theorem, the standard deviation of the sampling distribution of sample means would be of 0.86.
<h3>What does the Central Limit Theorem state?</h3>
It states that the standard deviation of the sampling distribution of sample means is given by:
![s = \frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=s%20%3D%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
In which:
is the standard deviation of the population.
The parameters for this problem are given as follows:
.
Hence:
![s = \frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=s%20%3D%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
![s = \frac{6.8}{\sqrt{63}}](https://tex.z-dn.net/?f=s%20%3D%20%5Cfrac%7B6.8%7D%7B%5Csqrt%7B63%7D%7D)
s = 0.86.
More can be learned about the Central Limit Theorem at brainly.com/question/16695444
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The answer is D
Really hoped this helped <3