First convert $2.5$ pounds to ounces. Since $1$ pound $=16$ ounces, $2.5$ pounds $=2.5(16)=40$ ounces. The recipe makes $18$ cookies with $12$ ounces, so the rate is $\frac{18}{12}=1.5$ cookies per ounce. With $40$ ounces, the number of cookies is $40(1.5)=60$. Since $60>50$, the baker's claim is true. Therefore, the statement that must be true is that the batch will yield exactly $60$ cookies.

The original area is $x(0.8x)=0.8x^2$. Increasing each dimension by $25\%$ means multiplying each by $1.25$. The new length is $1.25x$, and the new width is $1.25(0.8x)=1.0x$. The new area is $(1.25x)(1.0x)=1.25x^2$. The increase in area is $1.25x^2-0.8x^2=0.45x^2$. As a percent of the original area, this is $\frac{0.45x^2}{0.8x^2}=0.5625=56.25\%$. So the correct answer is $56.25\%$.

Let $x$ be the number of milliliters of the $30\%$ solution used before the spill. Then $750-x$ milliliters of the $12\%$ solution were used.

The spill happens after the solutions are mixed, so it does not change the percent composition of the mixture. Therefore, the original $750$-milliliter mixture must already have been $18\%$ active ingredient.

Set up an equation using amount of active ingredient:

Now solve:

So the mixture originally contained $250$ milliliters of the $30\%$ solution.

The amount of acid stays the same because only water evaporates. Initially, the solution is $12\%$ acid, so the amount of acid is $0.12V$. After evaporation, the solution is $15\%$ acid. Let the final volume be $F$ milliliters. Then

Solving for $F$ gives

So the final volume is $\frac{4}{5}V$, meaning the amount of water evaporated is

Therefore, the correct expression is $\frac{V}{5}$.

Let $x$ be the number of liters of $20\%$ solution and $y$ be the number of liters of $35\%$ solution.

Because the final mixture is $30$ liters,

The amount of active ingredient in the final mixture must be $26\%$ of $30$ liters:

The active ingredient equation is

Now solve the system. From $x+y=30$, we get

Substitute into the second equation:

So the laboratory should use $18$ liters of the $20\%$ solution. Then $y=30-18=12$, which satisfies the safety rule since $12\ge 8$.

Therefore, the correct answer is $18$.