1/2x = 2/3x - 8...multiply everything by common denominator of 6
3x = 4x - 48
3x - 4x = -48
-x = -48
x = 48 <== ur number
Answer:
See attachment
Step-by-step explanation:
Answer:
y = 4x - 3
Step-by-step explanation:
Firstly rearrange into the form y = mx + c;
⇒ ![y = -\frac{1}{4}x + 2](https://tex.z-dn.net/?f=y%20%3D%20-%5Cfrac%7B1%7D%7B4%7Dx%20%2B%202)
Secondly, find the gradient of the line using the formula for perpendicular lines;
⇒ ![m_{1}m_{2} = -1](https://tex.z-dn.net/?f=m_%7B1%7Dm_%7B2%7D%20%3D%20-1)
⇒ ![-\frac{1}{4}m_{2} = -1](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B4%7Dm_%7B2%7D%20%3D%20-1)
⇒ ![m_{2} = 4](https://tex.z-dn.net/?f=m_%7B2%7D%20%3D%204)
Now substitute into the formula for a straight line;
⇒ ![y - y_{1} = m(x - x_{1})](https://tex.z-dn.net/?f=y%20-%20y_%7B1%7D%20%3D%20m%28x%20-%20x_%7B1%7D%29)
⇒ ![y + 11 = 4(x + 2)](https://tex.z-dn.net/?f=y%20%2B%2011%20%3D%204%28x%20%2B%202%29)
⇒ ![y = 4x - 3](https://tex.z-dn.net/?f=y%20%3D%204x%20-%203)
Answer:
c
Step-by-step explanation:
c
Answer: ![(19.48,\ 21.32)](https://tex.z-dn.net/?f=%2819.48%2C%5C%2021.32%29)
Step-by-step explanation:
The confidence interval for population mean is given by :-
![\mu\ \pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=%5Cmu%5C%20%5Cpm%20z_%7B%5Calpha%2F2%7D%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
Given : Sample size : ![n=50](https://tex.z-dn.net/?f=n%3D50)
![\mu=20.4\text{ minutes}](https://tex.z-dn.net/?f=%5Cmu%3D20.4%5Ctext%7B%20minutes%7D)
![\sigma=2.1\text{ minutes}](https://tex.z-dn.net/?f=%5Csigma%3D2.1%5Ctext%7B%20minutes%7D)
Significance level : ![1-0.99.8=0.002](https://tex.z-dn.net/?f=1-0.99.8%3D0.002)
Critical value : ![z_{\alpha/2}=3.090](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3D3.090)
Now, the 99.8% confidence interval for the mean time taken for all students to fill out the form will be :-
![20.4\ \pm (3.09)\dfrac{2.1}{\sqrt{50}}\\\\\approx20.4\pm0.92\\\\=(19.48,\ 21.32)](https://tex.z-dn.net/?f=20.4%5C%20%5Cpm%20%283.09%29%5Cdfrac%7B2.1%7D%7B%5Csqrt%7B50%7D%7D%5C%5C%5C%5C%5Capprox20.4%5Cpm0.92%5C%5C%5C%5C%3D%2819.48%2C%5C%2021.32%29)
Hence, a 99.8% confidence interval for the mean time taken for all students to fill out the form = ![(19.48,\ 21.32)](https://tex.z-dn.net/?f=%2819.48%2C%5C%2021.32%29)