97.8-63.65
97.80
-63.65
-----------
34.15
Answer:
97.68 %
z(lower) = .0227
z(upper) = .999
Step-by-step explanation:
The greatest common factor is the biggest number taken from the values.
Q1. The answer is <span>A. 5y^6
</span>
![20 y^{9} +5 y^{6}= 4*5 y^{9}+5 y^{6}](https://tex.z-dn.net/?f=20%20y%5E%7B9%7D%20%2B5%20y%5E%7B6%7D%3D%204%2A5%20y%5E%7B9%7D%2B5%20y%5E%7B6%7D)
Since
![x^{a}* x^{b} =x^{a+b}](https://tex.z-dn.net/?f=x%5E%7Ba%7D%2A%20x%5E%7Bb%7D%20%20%3Dx%5E%7Ba%2Bb%7D%20)
, then
![x^{9}= x^{3}* x^{6}](https://tex.z-dn.net/?f=%20x%5E%7B9%7D%3D%20x%5E%7B3%7D%2A%20x%5E%7B6%7D%20%20%20)
Back to our expression:
![4*5 y^{9}+5 y^{6}=4*5 y^{3}*y^{6}+5 y^{6}=4 y^{3}*5y ^{6}+ 5y ^{6}*1=5 y^{6} (4y ^{3} +1)](https://tex.z-dn.net/?f=4%2A5%20y%5E%7B9%7D%2B5%20y%5E%7B6%7D%3D4%2A5%20y%5E%7B3%7D%2Ay%5E%7B6%7D%2B5%20y%5E%7B6%7D%3D4%20y%5E%7B3%7D%2A5y%20%5E%7B6%7D%2B%20%205y%20%5E%7B6%7D%2A1%3D5%20y%5E%7B6%7D%20%284y%20%5E%7B3%7D%20%2B1%29)
The greatest common factor is thus
![5 y^{6}](https://tex.z-dn.net/?f=5%20y%5E%7B6%7D)
Q2. The answer is <span>D. 12xy^2
</span>
![12x y^{5}+60 x^{4} y^{2} -24 x^{3} y^{3}=12x y^{5}+5*12 x^{4} y^{2} -2*12 x^{3} y^{3}](https://tex.z-dn.net/?f=12x%20y%5E%7B5%7D%2B60%20x%5E%7B4%7D%20y%5E%7B2%7D%20-24%20x%5E%7B3%7D%20y%5E%7B3%7D%3D12x%20y%5E%7B5%7D%2B5%2A12%20x%5E%7B4%7D%20y%5E%7B2%7D%20-2%2A12%20x%5E%7B3%7D%20y%5E%7B3%7D)
We will use the rule
![x^{a}* x^{b} =x^{a+b}](https://tex.z-dn.net/?f=x%5E%7Ba%7D%2A%20x%5E%7Bb%7D%20%3Dx%5E%7Ba%2Bb%7D%20)
to factorise the exponents:
![12x y^{5}+5*12 x^{4} y^{2} -2*12 x^{3} y^{3}= \\ =12x*y^{2}*y^{3}+5*12*x* x^{3} *y^{2}-2*12x* x^{2} *y*y^{2}= \\ =12xy^{2}*y^{3}+12xy^{2}*5 x^{3} -12xy^{2}*2 x^{2} y= \\ =12xy^{2}(y^{3}+5 x^{3}-2 x^{2} y)](https://tex.z-dn.net/?f=12x%20y%5E%7B5%7D%2B5%2A12%20x%5E%7B4%7D%20y%5E%7B2%7D%20-2%2A12%20x%5E%7B3%7D%20y%5E%7B3%7D%3D%20%5C%5C%20%3D12x%2Ay%5E%7B2%7D%2Ay%5E%7B3%7D%2B5%2A12%2Ax%2A%20x%5E%7B3%7D%20%2Ay%5E%7B2%7D-2%2A12x%2A%20x%5E%7B2%7D%20%2Ay%2Ay%5E%7B2%7D%3D%20%5C%5C%20%3D12xy%5E%7B2%7D%2Ay%5E%7B3%7D%2B12xy%5E%7B2%7D%2A5%20x%5E%7B3%7D%20-12xy%5E%7B2%7D%2A2%20x%5E%7B2%7D%20y%3D%20%5C%5C%20%3D12xy%5E%7B2%7D%28y%5E%7B3%7D%2B5%20x%5E%7B3%7D-2%20x%5E%7B2%7D%20y%29%20)
The greatest common factor is thus
Answer:
![m \leq 4.3](https://tex.z-dn.net/?f=m%20%5Cleq%204.3)
Step-by-step explanation:
We need to get m on one side all by itself. To achieve this, let's subtract both sides by 1.2 to get
.