Answer:
E B D
Step-by-step explanation:
E B and D are true, all the other statements are false
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The given quadratic has real roots if its discriminant is non-negative, so the probability is
![P(16Y^2-16(Y+2)\ge0)=P(16Y^2-16Y-32\ge0)](https://tex.z-dn.net/?f=P%2816Y%5E2-16%28Y%2B2%29%5Cge0%29%3DP%2816Y%5E2-16Y-32%5Cge0%29)
![=P(Y^2-Y-2\ge0)](https://tex.z-dn.net/?f=%3DP%28Y%5E2-Y-2%5Cge0%29)
Complete the square:
![Y^2-Y-2=Y^2-Y+\dfrac14-\dfrac94=\left(Y-\dfrac12\right)^2-\dfrac94](https://tex.z-dn.net/?f=Y%5E2-Y-2%3DY%5E2-Y%2B%5Cdfrac14-%5Cdfrac94%3D%5Cleft%28Y-%5Cdfrac12%5Cright%29%5E2-%5Cdfrac94)
![\implies P(Y^2-Y-2\ge0)=P\left(\left(Y-\dfrac12\right)^2-\dfrac94\ge0\right)](https://tex.z-dn.net/?f=%5Cimplies%20P%28Y%5E2-Y-2%5Cge0%29%3DP%5Cleft%28%5Cleft%28Y-%5Cdfrac12%5Cright%29%5E2-%5Cdfrac94%5Cge0%5Cright%29)
![=P\left(\left(Y-\dfrac12\right)^2\ge\dfrac94\right)](https://tex.z-dn.net/?f=%3DP%5Cleft%28%5Cleft%28Y-%5Cdfrac12%5Cright%29%5E2%5Cge%5Cdfrac94%5Cright%29)
![=P\left(\left|Y-\dfrac12\right|\ge\dfrac32\right)](https://tex.z-dn.net/?f=%3DP%5Cleft%28%5Cleft%7CY-%5Cdfrac12%5Cright%7C%5Cge%5Cdfrac32%5Cright%29)
![=P\left(Y-\dfrac12\ge\dfrac32\text{ and }Y-\dfrac12\ge-\dfrac32\right)](https://tex.z-dn.net/?f=%3DP%5Cleft%28Y-%5Cdfrac12%5Cge%5Cdfrac32%5Ctext%7B%20and%20%7DY-%5Cdfrac12%5Cge-%5Cdfrac32%5Cright%29)
![=P\left(Y\ge2\text{ and }Y\ge-1\right)](https://tex.z-dn.net/?f=%3DP%5Cleft%28Y%5Cge2%5Ctext%7B%20and%20%7DY%5Cge-1%5Cright%29)
![=P\left(Y\ge2\right)](https://tex.z-dn.net/?f=%3DP%5Cleft%28Y%5Cge2%5Cright%29)
![=\displaystyle\int_2^\infty f_Y(y)\,\mathrm dy](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%5Cint_2%5E%5Cinfty%20f_Y%28y%29%5C%2C%5Cmathrm%20dy)
where
is the PDF of
,
![f_Y(y)=\begin{cases}\frac15&\text{for }0\le y\le5\\0&\text{otherwise}\end{cases}](https://tex.z-dn.net/?f=f_Y%28y%29%3D%5Cbegin%7Bcases%7D%5Cfrac15%26%5Ctext%7Bfor%20%7D0%5Cle%20y%5Cle5%5C%5C0%26%5Ctext%7Botherwise%7D%5Cend%7Bcases%7D)
![\implies P(Y\ge2)=\displaystyle\int_2^5\frac{\mathrm dy}5=\boxed{\frac35}](https://tex.z-dn.net/?f=%5Cimplies%20P%28Y%5Cge2%29%3D%5Cdisplaystyle%5Cint_2%5E5%5Cfrac%7B%5Cmathrm%20dy%7D5%3D%5Cboxed%7B%5Cfrac35%7D)
Answer:
$55.48
Step-by-step explanation:
nice to help you.hope it helps