Answer:
Therefore,
![Length=12\ cm](https://tex.z-dn.net/?f=Length%3D12%5C%20cm)
![Width= 7\ cm](https://tex.z-dn.net/?f=Width%3D%207%5C%20cm)
Step-by-step explanation:
Let the Width of rectangle be 'x' cm.
Then the length of a rectangle will be (x + 5) cm.
Area of rectangle given is 84 cm squared.
To Find:
Length = (x+5) = ?
Width = x = ?
Solution:
We have area of rectangle given as
![\textrm{Area of Rectangle}=Length\times Width](https://tex.z-dn.net/?f=%5Ctextrm%7BArea%20of%20Rectangle%7D%3DLength%5Ctimes%20Width)
Substituting the given values we get
![84=(x+5)x\\x^{2} +5x-84=0\\](https://tex.z-dn.net/?f=84%3D%28x%2B5%29x%5C%5Cx%5E%7B2%7D%20%2B5x-84%3D0%5C%5C)
On factorizing we get
![x^{2} +12x-7x-84=0\\x(x+12)-7(x+12)=0\\(x+12)(x-7)=0\\(x+12)=0\ or\ (x-7)=0\\x=-12\ or\ x=7\\\therefore x =7\ cm\ \textrm{As x cannot be negative}](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B12x-7x-84%3D0%5C%5Cx%28x%2B12%29-7%28x%2B12%29%3D0%5C%5C%28x%2B12%29%28x-7%29%3D0%5C%5C%28x%2B12%29%3D0%5C%20or%5C%20%28x-7%29%3D0%5C%5Cx%3D-12%5C%20or%5C%20x%3D7%5C%5C%5Ctherefore%20x%20%3D7%5C%20cm%5C%20%5Ctextrm%7BAs%20x%20cannot%20be%20negative%7D)
Therefore,
![Length=x+5=7+5=12\ cm](https://tex.z-dn.net/?f=Length%3Dx%2B5%3D7%2B5%3D12%5C%20cm)
Therefore,
![Length=12\ cm](https://tex.z-dn.net/?f=Length%3D12%5C%20cm)
![Width= 7\ cm](https://tex.z-dn.net/?f=Width%3D%207%5C%20cm)
Answer: (0.00027144, 0.00036176)
Step-by-step explanation:
The sample proportion of cell phone users who develop cancer of the brain or nervous system = ![\dfrac{133}{420027}=0.0003166](https://tex.z-dn.net/?f=%5Cdfrac%7B133%7D%7B420027%7D%3D0.0003166)
Sample size : 420027
Confidence interval for p:
, where
= sample proportion , n= sample size , z* = crirical z value.
For 90% confidence interval , z*= 1.645
Required confidence interval:
![0.0003166\pm (1.645)\sqrt{\dfrac{0.0003166(1-0.0003166)}{420027}}\\\\=0.0003166\pm 0.00004516\\\\=(0.0003166-0.00004516,\ 0.0003166+ 0.00004516)\\\\=(0.00027144, \ 0.00036176)](https://tex.z-dn.net/?f=0.0003166%5Cpm%20%281.645%29%5Csqrt%7B%5Cdfrac%7B0.0003166%281-0.0003166%29%7D%7B420027%7D%7D%5C%5C%5C%5C%3D0.0003166%5Cpm%200.00004516%5C%5C%5C%5C%3D%280.0003166-0.00004516%2C%5C%200.0003166%2B%200.00004516%29%5C%5C%5C%5C%3D%280.00027144%2C%20%5C%200.00036176%29)
A 90% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system = (0.00027144, 0.00036176)
Answer:
A. 50.24
Step-by-step explanation:
f(4) = 3.14 times 4²
f(4) = 3.14(16)
f(4) = 50.24
<h2><u><em>xoxo, </em></u></h2><h2><u><em>your highness...</em></u></h2>