A $27-$inch monitor contains $1920$ x $1080$ picture elements, or pixels. Each pixel is represented in $24$ bits of memory. A byte of memory is $8$ bits.a$.$ How many megabytes $($MB$)$ of memory are required to store the information displayed on the monitor?b$.$ Suppose it takes $10$ ms to refresh the monitor. How fast must the image data be moved from memory to the monitor? Express your answer in gigabits per second $($Gbps$).$c$.$ A $27-$inch monitor is $24$ inches wide and $14$ inches high. What is the size of an individual pixel in square millimeters $($mm$2)?1\mathrm{.}4$ A tablet screen displays $1024$ x $600$ picture elements $($pixels$)$ in each frame of a video. Each pixel requires $3$ bytes of memory. Videos are displayed at a rate of $60$ frames per second. How many minutes of video will fit in a $128-$gigabyte memory?$1\mathrm{.}5$ Approximately $5\mathrm{.}4$ million hybrid passenger vehicles have been sold in the United States since $1999.$ Approximately $1\mathrm{.}4$ million plug$-$in electric passenger vehicles have been sold in the United States since $2010.$ Assume the average energy stored in a hybrid vehicle battery is $1\mathrm{.}5$ kilowatt$-$hours $($kWh$),$ and assume the average energy stored in a plug$-$in electric vehicle battery is $45$ kWh$.$ If $80\%$ of the hybrid vehicles and $90\%$ of the plug$-$in electric vehicles are still in service, estimate the total energy stored in these vehicles in gigawatt$-$hours $($GWh$)\mathrm{.}1\mathrm{.}6$ Suppose a plug$-$in electric vehicle has a $64$ kWh battery. The energy consumption of the vehicle is $16$ kWh$/100$ km$.$ a$.$ If the battery is charged to $60\%$ of its capacity, how many miles can be driven before recharging the battery? b$.$ If you want to travel $200$ miles before recharging the battery, you will need to charge the battery to what percent of its capacity before starting your trip