Answer
The tension in the cord is $~~4.6~N$
Work Step by Step
Since the two boxes are tied together, the acceleration of each box has the same magnitude.
We can find an expression for the acceleration of the FedEx box:
$F - m_2~g~sin~\theta-F_T = m_2~a$
$a = \frac{F - m_2~g~sin~\theta-F_T}{m_2}$
We can find an expression for the acceleration of the UPS box:
$F_T = m_1~a$
$a = \frac{F_T}{m_1}$
We can equate the two expressions to find $F_T$:
$\frac{F - m_2~g~sin~\theta-F_T}{m_2} = \frac{F_T}{m_1}$
$(F - m_2~g~sin~\theta-F_T)(m_1) = (F_T)(m_2)$
$(F - m_2~g~sin~\theta)(m_1) = (F_T)(m_1+m_2)$
$F_T = \frac{(F - m_2~g~sin~\theta)(m_1)}{m_1+m_2}$
$F_T = \frac{[12~N - (1.0~kg)~(9.8~m/s^2)~(sin~37^{\circ})~](3.0~kg)}{3.0~kg+1.0~kg}$
$F_T = 4.6~N$
The tension in the cord is $~~4.6~N$
