Answer:
Both methods give 1/(12x + 32)
Step-by-step explanation:
Given 1/4(x + 2x + 16 - 8)
First Method.
Summing the like terms of the quantities in the denominator we are building, then multipying the root by 4.
Adding like terms in the denominator
1/4(x + 2x + 16 - 8) = 1/4(3x + 8)
Multiply denominator byv4
= 1/(12x + 32)
Second Method.
Multiply the quantities in the denominator by 4, and add the like terms together.
Multiplying denominator by 4.
1/4(x + 2x + 16 - 8) = 1/(4x + 8x + 64 - 32)
Adding like terms in denominator.
= 1/(12x + 32)
Step-by-step explanation:
75% of 60 is 45
45-1=44
3/4=75
Answer
• Line m: x = 3
,
• Line n: y = –4
Explanation
If a line has no y-intercept, it means it must be parallel to the y - axis. Thus, it is a vertical line that will only cross the x-axis once (in this case).
As we are given that the x-intercept is (3,0), then the equation of line m is:
![x=3](https://tex.z-dn.net/?f=x%3D3)
Following the same logic, if a line has no x-intercept, it will be parallel to the x-axis and it will be a vertical line.
As we are given that the y-intercept is (0,-4), then the equation of line n is:
Answer:
188 weeks of data must be sampled.
Step-by-step explanation:
From the information given, we can deduce that:
The Margin of error is within = 200
The confidence interval = 95%
The level of significance = 1 - C.I
= 1 - 0.95
= 0.05
The standard deviation = 1400
The number of weeks the data must be sampled can be determined by using the formula for sample size which is:
![n =( \dfrac{Z_{\alpha/2} \times \sigma}{E} )^2](https://tex.z-dn.net/?f=n%20%3D%28%20%5Cdfrac%7BZ_%7B%5Calpha%2F2%7D%20%5Ctimes%20%5Csigma%7D%7BE%7D%20%29%5E2)
![n =( \dfrac{Z_{0.05/2} \times 1400}{200} )^2](https://tex.z-dn.net/?f=n%20%3D%28%20%5Cdfrac%7BZ_%7B0.05%2F2%7D%20%5Ctimes%201400%7D%7B200%7D%20%29%5E2)
![n =( \dfrac{1.96 \times 1400}{200} )^2](https://tex.z-dn.net/?f=n%20%3D%28%20%5Cdfrac%7B1.96%20%5Ctimes%201400%7D%7B200%7D%20%29%5E2)
![n =( \dfrac{2744}{200} )^2](https://tex.z-dn.net/?f=n%20%3D%28%20%5Cdfrac%7B2744%7D%7B200%7D%20%29%5E2)
![n =( 13.72)^2](https://tex.z-dn.net/?f=n%20%3D%28%2013.72%29%5E2)
n = 188.24
n ≅ 188
Thus, 188 weeks of data must be sampled.