You need to use a Modulus $11$ check$-$digit application for one of your important parts used for your Rocket ship production. This metal part has been assigned a $3$ digit part number $275.$ We want the modulus $11$ software to create the $4$ th number. When done, our part number will have $4$ numbers and not $3.$ What is the $4^{th}$ digit part number? Show your calculations.

$\backslash$table$[[$GIVEN:$,,,],[$part#$,2,7,5],[$Multipliers$,13,22,35,$ what is the $4$th part number?$]]$