Answer:

Step-by-step explanation:
Given: 
To convert: the given sum into product
Solution:
Use formula: 
![cosx + cos3x + cos5x + cos7x=2\cos \left ( \frac{x+3x}{2} \right )\cos \left ( \frac{x-3x}{2} \right )+2\cos \left ( \frac{5x+7x}{2} \right )\cos \left ( \frac{5x-7x}{2} \right )\\=2\cos (2x)\cos (-x)+2\cos (6x)\cos (-x)\\=2\cos (2x)\cos (x)+2\cos (6x)\cos (x)\\=2\cos x\left [ \cos (2x)+\cos (6x) \right ]](https://tex.z-dn.net/?f=cosx%20%2B%20cos3x%20%2B%20cos5x%20%2B%20cos7x%3D2%5Ccos%20%5Cleft%20%28%20%5Cfrac%7Bx%2B3x%7D%7B2%7D%20%5Cright%20%29%5Ccos%20%5Cleft%20%28%20%5Cfrac%7Bx-3x%7D%7B2%7D%20%5Cright%20%29%2B2%5Ccos%20%5Cleft%20%28%20%5Cfrac%7B5x%2B7x%7D%7B2%7D%20%5Cright%20%29%5Ccos%20%5Cleft%20%28%20%5Cfrac%7B5x-7x%7D%7B2%7D%20%5Cright%20%29%5C%5C%3D2%5Ccos%20%282x%29%5Ccos%20%28-x%29%2B2%5Ccos%20%286x%29%5Ccos%20%28-x%29%5C%5C%3D2%5Ccos%20%282x%29%5Ccos%20%28x%29%2B2%5Ccos%20%286x%29%5Ccos%20%28x%29%5C%5C%3D2%5Ccos%20x%5Cleft%20%5B%20%5Ccos%20%282x%29%2B%5Ccos%20%286x%29%20%5Cright%20%5D)
![cosx + cos3x + cos5x + cos7x=2\cos \left ( \frac{x+3x}{2} \right )\cos \left ( \frac{x-3x}{2} \right )+2\cos \left ( \frac{5x+7x}{2} \right )\cos \left ( \frac{5x-7x}{2} \right )\\=2\cos x\left [ \cos (2x)+\cos (6x) \right ]\\=2\cos x\left [2 \cos \left ( \frac{2x+6x}{2} \right )\cos \left ( \frac{2x-6x}{2} \right ) \right ]\\=2\cos x\left [ 2\cos (4x) \cos (-2x) \right ]\\=4\cos x\cos (4x)\cos (2x)](https://tex.z-dn.net/?f=cosx%20%2B%20cos3x%20%2B%20cos5x%20%2B%20cos7x%3D2%5Ccos%20%5Cleft%20%28%20%5Cfrac%7Bx%2B3x%7D%7B2%7D%20%5Cright%20%29%5Ccos%20%5Cleft%20%28%20%5Cfrac%7Bx-3x%7D%7B2%7D%20%5Cright%20%29%2B2%5Ccos%20%5Cleft%20%28%20%5Cfrac%7B5x%2B7x%7D%7B2%7D%20%5Cright%20%29%5Ccos%20%5Cleft%20%28%20%5Cfrac%7B5x-7x%7D%7B2%7D%20%5Cright%20%29%5C%5C%3D2%5Ccos%20x%5Cleft%20%5B%20%5Ccos%20%282x%29%2B%5Ccos%20%286x%29%20%5Cright%20%5D%5C%5C%3D2%5Ccos%20x%5Cleft%20%5B2%20%5Ccos%20%5Cleft%20%28%20%5Cfrac%7B2x%2B6x%7D%7B2%7D%20%5Cright%20%29%5Ccos%20%5Cleft%20%28%20%5Cfrac%7B2x-6x%7D%7B2%7D%20%5Cright%20%29%20%5Cright%20%5D%5C%5C%3D2%5Ccos%20x%5Cleft%20%5B%202%5Ccos%20%284x%29%20%5Ccos%20%28-2x%29%20%5Cright%20%5D%5C%5C%3D4%5Ccos%20x%5Ccos%20%284x%29%5Ccos%20%282x%29)
Your should be 24/7 because you multiply three times seven get twenty one add twenty one with three and get your answer.
Complete Question
The option to the blank space are shown on the first uploaded image
Answer:
Neal's decision is to <u>fail to reject </u> the <u>null hypothesis</u> (p 0.066). There is <u>no sufficient </u> evidence to <u>prove</u> the claim that the average electricity consumption of <u>all Ledee household </u>is <u>greater than</u> , <u>854.28 kWh</u>
Step-by-step explanation:
From the question we are told that
The population mean is 
The sample size is 
The sample mean is 
The standard deviation is 
The level of significance is 
The null hypothesis is 
The alternative hypothesis is 
The t-statistics is 
The p-value is 
Now from the given data we can see that

Generally when this is the case , we fail to reject the null hypothesis
So
Neal's decision is to <u>fail to reject </u> the <u>null hypothesis</u> (p 0.066). There is <u>no sufficient </u> evidence to <u>prove</u> the claim that the average electricity consumption of <u>all Ledee household </u>is <u>greater than</u> , <u>854.28 kWh</u>
Answer:
Well, any number that is not 5 for the y-intercept
Step-by-step explanation:
As you could tell not matter how I change the y-intercept it is always parallel to the line y=2x + 5
3/4 is greater than 2/3 is the right one. Because 1/2 is more than 1/3. -1/4 is not less than -2/3, and -1 is not greater than 3/4s. I hope it helps