E[Y] = 11 ((11)/(120)) + (4)/(3)

$$ E[Y] = 11 \left(\frac{11}{120}\right) + \frac{4}{3} $$ $$ E[Y] = \frac{121}{120} + \frac{4}{3} $$ To add these fractions, find a common denominator, which is $120$: $$ E[Y] = \frac{121}{120} + \frac{4 \times 40}{3 \times 40} $$ $$ E[Y] = \frac{121}{120} + \frac{160}{120} $$ $$ E[Y] = \frac{121 + 160}{120} $$ $$ E[Y] = \frac{281}{120} $$ Now, calculate $E[2Y + 4]$ using the property $E[aY + b] = aE[Y] + b$: $$ E[2Y + 4] = 2E[Y] + 4 $$ Substitute the value of $E[Y]$: $$ E[2Y + 4] = 2 \left(\frac{281}{120}\right) + 4 $$ $$ E[2Y + 4] = \frac{2 \times 281}{120} + 4 $$ $$ E[2Y + 4] = \frac{562}{120} + 4 $$ Simplify the fraction $\frac{562}{120}$ by dividing both numerator and denominator by $2$: $$ E[2Y + 4] = \frac{281}{60} + 4 $$ Convert $4$ to a fraction with a denominator of $60$: $$ E[2Y + 4] = \frac{281}{60} + \frac{4 \times 60}{60} $$ $$ E[2Y + 4] = \frac{281}{60} + \frac{240}{60} $$ $$ E[2Y + 4] = \frac{281 + 240}{60} $$ $$ E[2Y + 4] = \frac{521}{60} $$ The value of $E[2Y + 4]$ is $\boxed{\frac{521}{60}}$. That's 2 down. 3 left today — send the next one.