Methane, CH$4,$ is burned with dry air. The molar analysis of the products on a dry basis is CO$2,7\mathrm{.}49\%$; CO$,0\mathrm{.}34\%$; O$2,2\mathrm{.}70\%$; and N$2,89\mathrm{.}47\%.$ Determine:

$($a$)$ the air$$fuel ratio on a molar basis, rounded to $2$ decimal places,

$($b$)$ the percent theoretical air, rounded to $2$ decimal places,

$($c$)$ the mole fraction of the water vapor, rounded to $3$ decimal places, and

$($d$)$ the amount of water vapor present, in lbmol per lbmol of fuel consumed, if the products are cooled to $90\backslash$deg F at $1$ atm, rounded to $3$ decimal places.