Problem $1(19\mathrm{.}12)$:

The geodetic height at Station Apple is $243\mathrm{.}983m,$ and the modeled geoid height is $-31\mathrm{.}70m.$ What is its orthometric height?

Problem $2(19\mathrm{.}13)$:

The orthometric height of a particular benchmark is $2513\mathrm{.}68ft,$ and the modeled geoid height at the station is $-25\mathrm{.}03m.$ What is the geodetic height of the benchmark? Draw a sketch depicting the geoid, ellipsoid, and benchmark.

Problem $3(20\mathrm{.}13$ & $20\mathrm{.}15)$:

What are the SPCS$83$ coordinates $($in sft$)$ and the scale factor for a station in the North zone of Pennsylvania with geodetic coordinates of $41{14}^{\text{'}}{14\mathrm{.}22063}^{\text{'}\text{'}}N$ and