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Answer:
16
Step-by-step explanation:
<u>Given:</u>
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<u>To find:</u>
<u></u>
<u></u>
<u></u>
<u>Formula:</u>
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Here,
![a=x\\b=y](https://tex.z-dn.net/?f=a%3Dx%5C%5Cb%3Dy)
Squaring both sides of: ![x+y=6](https://tex.z-dn.net/?f=x%2By%3D6)
![\Rightarrow (x+y)^2 = 6^2](https://tex.z-dn.net/?f=%5CRightarrow%20%28x%2By%29%5E2%20%3D%206%5E2)
Using formula written above on LHS:
![x^{2} +y^{2} +2xy = 36](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2By%5E%7B2%7D%20%2B2xy%20%3D%2036)
Given ![xy=10](https://tex.z-dn.net/?f=xy%3D10)
![\Rightarrow x^{2} +y^{2} + 2 \times 10 = 36\\\Rightarrow x^{2} +y^{2} + 20= 36\\\Rightarrow x^{2} +y^{2}= 36-20\\\Rightarrow x^{2} +y^{2}= 16](https://tex.z-dn.net/?f=%5CRightarrow%20x%5E%7B2%7D%20%2By%5E%7B2%7D%20%2B%202%20%5Ctimes%2010%20%3D%2036%5C%5C%5CRightarrow%20x%5E%7B2%7D%20%2By%5E%7B2%7D%20%2B%2020%3D%2036%5C%5C%5CRightarrow%20x%5E%7B2%7D%20%2By%5E%7B2%7D%3D%2036-20%5C%5C%5CRightarrow%20x%5E%7B2%7D%20%2By%5E%7B2%7D%3D%2016)
So, correct answer is:
![x^{2} +y^{2} = 16](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2By%5E%7B2%7D%20%3D%2016)
Answer:
(0.215,0.33)
Step-by-step explanation:
The 99% confidence interval can be calculated as
![p- z_{\frac{\alpha }{2} } \sqrt{\frac{pq}{n} }](https://tex.z-dn.net/?f=p-%20z_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%7D%20%5Csqrt%7B%5Cfrac%7Bpq%7D%7Bn%7D%20%7D%20%3CP%3Cp%2Bz_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%7D%20%5Csqrt%7B%5Cfrac%7Bpq%7D%7Bn%7D%20%7D)
Where p is the estimated sample proportion that can be calculated as
p=x/n
where x=109 and n=400
p=109/400=0.2725
q=1-p=1-0.273=0.7275
![z_{\frac{\alpha }{2} } =z_{\frac{\0.01 }{2} }=z_{0.005}=2.5758](https://tex.z-dn.net/?f=z_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%7D%20%3Dz_%7B%5Cfrac%7B%5C0.01%20%7D%7B2%7D%20%7D%3Dz_%7B0.005%7D%3D2.5758)
The 99% confidence interval is
![0.2725-2.5758 \sqrt{\frac{0.2725(0.7275)}{400} }](https://tex.z-dn.net/?f=0.2725-2.5758%20%5Csqrt%7B%5Cfrac%7B0.2725%280.7275%29%7D%7B400%7D%20%7D%20%3CP%3C0.2725%2B2.5758%20%5Csqrt%7B%5Cfrac%7B0.2725%280.7275%29%7D%7B400%7D%20%7D)
0.2725-2.5758(0.022262 )< P < 0.2725+2.5758(0.022262)
02725-0.057343 < P < 0.2725+0.057343
0.215157 < P < 0.329843
Rounding the obtained answer to three decimal places
0.215 < P < 0.33
Thus, the 99% confidence interval for the proportion of fatal accidents that involved the use of a cell phone is (0.215,0.33).
We are 99% confident that population the proportion of fatal accidents that involved the use of a cell phone will lie in this interval (0.215,0.33).
Since carter multiplies by 10 and then by 2 and adds the two, here we have been given 16 * 12
Step 1: Carter would first multiply the number by 10. This would be = 16*10
Step 2: Carter would multiply the number by 2. This would be = 16*2
Step 3: He would add the two. This would be = (16*10) + (16*2)
Carter's solution would be:
=16*12
=(16*10) + (16*2)
= 160 + 32
= 192
4x - 8 = 3x + 12
x - 8 = 12
x= 20