The algebraic equation is
X/8=5
The value of x is
X=40
Answer:
![\bar X= \frac{1.83+1.85+1.79+1.73+1.69+1.74+1.76+1.70}{8}= 1.76125](https://tex.z-dn.net/?f=%5Cbar%20X%3D%20%5Cfrac%7B1.83%2B1.85%2B1.79%2B1.73%2B1.69%2B1.74%2B1.76%2B1.70%7D%7B8%7D%3D%201.76125)
Now we can estimate the population variance with the sample variance given by:
![s^2 = \frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}](https://tex.z-dn.net/?f=s%5E2%20%3D%20%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5En%20%28x_i%20-%5Cbar%20X%29%5E2%7D%7Bn-1%7D)
And replacing we got:
![s^2 = 0.0033839](https://tex.z-dn.net/?f=%20s%5E2%20%3D%200.0033839)
And the estimator for the population deviation
is given by :
![\hat \sigma = \sqrt{s^2}= \sqrt{0.0033839}= 0.058172](https://tex.z-dn.net/?f=%5Chat%20%5Csigma%20%3D%20%5Csqrt%7Bs%5E2%7D%3D%20%5Csqrt%7B0.0033839%7D%3D%200.058172)
Step-by-step explanation:
For this case we have the following data given:
1.83,1.85,1.79,1.73,1.69,1.74,1.76,1.70
First we need to calculate the mean with the following formula:
![\bar X= \frac{\sum_{i=1}^n X_i}{n}](https://tex.z-dn.net/?f=%5Cbar%20X%3D%20%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5En%20X_i%7D%7Bn%7D)
And replacing we got:
![\bar X= \frac{1.83+1.85+1.79+1.73+1.69+1.74+1.76+1.70}{8}= 1.76125](https://tex.z-dn.net/?f=%5Cbar%20X%3D%20%5Cfrac%7B1.83%2B1.85%2B1.79%2B1.73%2B1.69%2B1.74%2B1.76%2B1.70%7D%7B8%7D%3D%201.76125)
Now we can estimate the population variance with the sample variance given by:
![s^2 = \frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}](https://tex.z-dn.net/?f=s%5E2%20%3D%20%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5En%20%28x_i%20-%5Cbar%20X%29%5E2%7D%7Bn-1%7D)
And replacing we got:
![s^2 = 0.0033839](https://tex.z-dn.net/?f=%20s%5E2%20%3D%200.0033839)
And the estimator for the population deviation
is given by :
![\hat \sigma = \sqrt{s^2}= \sqrt{0.0033839}= 0.058172](https://tex.z-dn.net/?f=%5Chat%20%5Csigma%20%3D%20%5Csqrt%7Bs%5E2%7D%3D%20%5Csqrt%7B0.0033839%7D%3D%200.058172)
Treat "13 4/5 feet below sea level" as a negative quantity. Then add the increase, "1542 feet," obtaining
(1542 - 13 4/5) feet = 1528 1/5 feet above sea level.
The total volume I suppose is what you are asking.
You can simplify this into 1/3 = .33
2.5 + .33 = 2.88 cups.