In statistics, ANOVA means Analysis of Variance. This is a statistical tool that helps in determining if the effect of the independent variable on the dependent variable is significant or not. It uses the F-distribution to determine the difference of means. That is why the other name for ANOVA is the F-test. It was named in honor of Ronald Fisher. It is a table consisting of F values which is simply the ratio of two variances. It depends on the degrees of freedom and the α to be used. A sample of the F-table is shown in the picture.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the information above :
A) Cost equation for Newton Telephone company :
y = 8x
Where x = number of minutes used
y = total cost for x minutes
Cost equation for Tryus telephone company :
y = connection fee + (fee per minute * number of minutes)
y = 42 + (2x)
Where x = number of minutes used
y = total cost for x minutes
Amount is in cent
Answer:
2
Step-by-step explanation:
You can divide both of them by 2
Answer:
![4\sqrt[3]{2}x(\sqrt[3]{y}+3xy\sqrt[3]{y} )](https://tex.z-dn.net/?f=4%5Csqrt%5B3%5D%7B2%7Dx%28%5Csqrt%5B3%5D%7By%7D%2B3xy%5Csqrt%5B3%5D%7By%7D%20%29)
Step-by-step explanation:
Let's start by breaking down each of the radicals:
![\sqrt[3]{16x^3y}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B16x%5E3y%7D)
Since we're dealing with a cube root, we'd like to pull as many perfect cubes out of the terms inside the radical as we can. We already have one obvious cube in the form of 
, and we can break 16 into the product 8 · 2. Since 8 is a cube root -- 2³, to be specific, we can reduce it down as we simplify the expression. Here our our steps then:
![\sqrt[3]{16x^3y}\\=\sqrt[3]{2\cdot8\cdot x^3\cdot y}\\=\sqrt[3]{2} \sqrt[3]{8} \sqrt[3]{x^3} \sqrt[3]{y} \\=\sqrt[3]{2} \cdot2x\cdot \sqrt[3]{y} \\=2x\sqrt[3]{2}\sqrt[3]{y}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B16x%5E3y%7D%5C%5C%3D%5Csqrt%5B3%5D%7B2%5Ccdot8%5Ccdot%20x%5E3%5Ccdot%20y%7D%5C%5C%3D%5Csqrt%5B3%5D%7B2%7D%20%5Csqrt%5B3%5D%7B8%7D%20%5Csqrt%5B3%5D%7Bx%5E3%7D%20%5Csqrt%5B3%5D%7By%7D%20%5C%5C%3D%5Csqrt%5B3%5D%7B2%7D%20%5Ccdot2x%5Ccdot%20%5Csqrt%5B3%5D%7By%7D%20%5C%5C%3D2x%5Csqrt%5B3%5D%7B2%7D%5Csqrt%5B3%5D%7By%7D)
We can apply this same technique of "extracting cubes" to the second term:
![\sqrt[3]{54x^6y^5} \\=\sqrt[3]{2\cdot27\cdot (x^2)^3\cdot y^3\cdot y^2} \\=\sqrt[3]{2}\sqrt[3]{27} \sqrt[3]{(x^2)^3} \sqrt[3]{y^3} \sqrt[3]{y^2}\\=\sqrt[3]{2}\cdot 3\cdot x^2\cdot y \cdot \sqrt[3]{y^2} \\=3x^2y\sqrt[3]{2} \sqrt[3]{y}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B54x%5E6y%5E5%7D%20%5C%5C%3D%5Csqrt%5B3%5D%7B2%5Ccdot27%5Ccdot%20%28x%5E2%29%5E3%5Ccdot%20y%5E3%5Ccdot%20y%5E2%7D%20%5C%5C%3D%5Csqrt%5B3%5D%7B2%7D%5Csqrt%5B3%5D%7B27%7D%20%5Csqrt%5B3%5D%7B%28x%5E2%29%5E3%7D%20%5Csqrt%5B3%5D%7By%5E3%7D%20%5Csqrt%5B3%5D%7By%5E2%7D%5C%5C%3D%5Csqrt%5B3%5D%7B2%7D%5Ccdot%203%5Ccdot%20x%5E2%5Ccdot%20y%20%5Ccdot%20%5Csqrt%5B3%5D%7By%5E2%7D%20%5C%5C%3D3x%5E2y%5Csqrt%5B3%5D%7B2%7D%20%5Csqrt%5B3%5D%7By%7D)
Replacing those two expressions in the parentheses leaves us with this monster:
![2(2x\sqrt[3]{2}\sqrt[3]{y})+4(3x^2y\sqrt[3]{2} \sqrt[3]{y})](https://tex.z-dn.net/?f=2%282x%5Csqrt%5B3%5D%7B2%7D%5Csqrt%5B3%5D%7By%7D%29%2B4%283x%5E2y%5Csqrt%5B3%5D%7B2%7D%20%5Csqrt%5B3%5D%7By%7D%29)
What can we do with this? It seems the only sensible thing is to look for terms to factor out, so let's do that. Both terms have the following factors in common:
![4, \sqrt[3]{2} , x](https://tex.z-dn.net/?f=4%2C%20%5Csqrt%5B3%5D%7B2%7D%20%2C%20x)
We can factor those out to give us a final, simplified expression:
Not that this is the same sum as we had at the beginning; we've just extracted all of the cube roots that we could in order to rewrite it in a slightly cleaner form.
