A) she incorrectly determined the GCF.
The GCF of 32ab - ab would be ab, not 8b.
Simplify, and you'll get the answer 2:4
Answer: The answer is 3/2x^2+3/10x+17/20
Answer:
Confidence Interval = (23.776, 24.224)
Step-by-step explanation:
Restaurant chain claims that its bottles of ketchup contain 24 ounces of ketchup on average.
⇒ Mean = 24 ounces.
Standard Deviation = 0.8
Number of bottles used for sample = 49
⇒ n = 49
Confidence level = 95%
Corresponding z value with 95% confidence level = 1.96
Now, confidence interval is given by the following expression :
![Mean \pm z^*\times \frac{\sigma}{\sqrt{n}}\\\\=24\pm1.96\times \frac{0.8}{\sqrt{49}}\\\\=24\pm 0.224](https://tex.z-dn.net/?f=Mean%20%5Cpm%20z%5E%2A%5Ctimes%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%5C%5C%5C%5C%3D24%5Cpm1.96%5Ctimes%20%5Cfrac%7B0.8%7D%7B%5Csqrt%7B49%7D%7D%5C%5C%5C%5C%3D24%5Cpm%200.224)
Hence, Confidence Interval = (23.776, 24.224)
Answer:
Part 1) ![(10x+15y)^{2}=(6x+9y)^{2}+(8x+12y)^{2}](https://tex.z-dn.net/?f=%2810x%2B15y%29%5E%7B2%7D%3D%286x%2B9y%29%5E%7B2%7D%2B%288x%2B12y%29%5E%7B2%7D)
Part 2) The answer in the procedure
Step-by-step explanation:
Part 1)
we know that
Applying the Pythagoras Theorem
![c^{2}=a^{2}+b^{2}](https://tex.z-dn.net/?f=c%5E%7B2%7D%3Da%5E%7B2%7D%2Bb%5E%7B2%7D)
we have
![c=(10x+15y)](https://tex.z-dn.net/?f=c%3D%2810x%2B15y%29)
![a=(6x+9y)](https://tex.z-dn.net/?f=a%3D%286x%2B9y%29)
![b=(8x+12y)](https://tex.z-dn.net/?f=b%3D%288x%2B12y%29)
substitute the values
![(10x+15y)^{2}=(6x+9y)^{2}+(8x+12y)^{2}](https://tex.z-dn.net/?f=%2810x%2B15y%29%5E%7B2%7D%3D%286x%2B9y%29%5E%7B2%7D%2B%288x%2B12y%29%5E%7B2%7D)
Part 2) Transform each side of the equation to determine if it is an identity
![(10x+15y)^{2}=(6x+9y)^{2}+(8x+12y)^{2}\\ \\100x^{2}+150xy+225y^{2}=36x^{2}+54xy+81y^{2}+64x^{2}+96xy+144y^{2}\\ \\100x^{2}+150xy+225y^{2}=100x^{2}+150xy+225y^{2}](https://tex.z-dn.net/?f=%2810x%2B15y%29%5E%7B2%7D%3D%286x%2B9y%29%5E%7B2%7D%2B%288x%2B12y%29%5E%7B2%7D%5C%5C%20%5C%5C100x%5E%7B2%7D%2B150xy%2B225y%5E%7B2%7D%3D36x%5E%7B2%7D%2B54xy%2B81y%5E%7B2%7D%2B64x%5E%7B2%7D%2B96xy%2B144y%5E%7B2%7D%5C%5C%20%5C%5C100x%5E%7B2%7D%2B150xy%2B225y%5E%7B2%7D%3D100x%5E%7B2%7D%2B150xy%2B225y%5E%7B2%7D)
The left side is equal to the right side
therefore
Is an identity