Recombinant E. coli (bacteria) or yeast are engineered to produce human insulin (Humulin). Bacteria are most common for large-scale production.

Notice $P = I + N$ where $N=\begin{pmatrix}0&0&0\\3&0&0\\9&3&0\end{pmatrix}$ (strictly lower triangular, so $N^3=0$).

$P^5 = (I+N)^5 = I + 5N + 10N^2$ (since $N^3=0$).

$N^2 = \begin{pmatrix}0&0&0\\0&0&0\\9&0&0\end{pmatrix}$... computing: $(N^2)_{31}=3\cdot3=9$, others 0.

$P^5 = I + 5N + 10N^2$. So $Q = P^5 + I = 2I + 5N + 10N^2$.

$q_{21} = 5\cdot3 = 15$, $q_{31} = 5\cdot9+10\cdot9=45+90=135$... wait: $q_{31}=(5N)_{31}+(10N^2)_{31}=5\cdot9+10\cdot9=45+90=135$. Wait $N_{31}=9, N^2_{31}=9$: $q_{31}=5(9)+10(9)=135$. $q_{32}=(5N)_{32}=5\cdot3=15$.

$\dfrac{q_{21}+q_{31}}{q_{32}} = \dfrac{15+135}{15} = \mathbf{10}$

Option A (all three) is correct.

• Contra entry should be a credit (reduces receivables), not debit.
• Discount allowed should be a credit (reduces amount owed by customers), not debit.
• Irrecoverable debts written off should be a credit (reduces receivable), not debit.

Using $l = L + \frac{TL}{AY} = L + kT$:

• $l_1 = L + kT_1$ and $l_2 = L + kT_2$ [cite: 506]
• Solving for $L$ by eliminating $k$: $L = \frac{T_2l_1 - T_1l_2}{T_2 - T_1}$[cite: 515].

Flextime is the practice of permitting employees to choose, with certain limitations, their own working hours. This helps organizations attract qualified individuals by allowing both employment and family needs to be addressed.

Using $\vec{s} = \vec{r}_0 + \vec{u}t + \frac{1}{2}\vec{a}t^2$:

• $x = 2 + 5(2) + \frac{1}{2}(4)(2^2) = 2 + 10 + 8 = 20$
• $y = 4 + 4(2) + \frac{1}{2}(4)(2^2) = 4 + 8 + 8 = 20$
• Distance from origin $D = \sqrt{20^2 + 20^2} = 20\sqrt{2}\text{ m}$.

Ball 1 falls for 18 s: $h_1 = \dfrac{1}{2}(10)(18)^2 = 1620\text{ m}$

Ball 2 falls for $18 - 6 = 12\text{ s}$: $h_2 = 12v + \dfrac{1}{2}(10)(12)^2 = 12v + 720$

Setting $h_1 = h_2$: $12v + 720 = 1620 \Rightarrow 12v = 900 \Rightarrow v = \mathbf{75\text{ m/s}}$