Lasts is the correct verb. We use last to describe the duration of an event: “The storm lasts 45 minutes.” Ends would mean it terminates at 45 minutes (doesn’t convey duration). Remains means to stay or continue existing, which is awkward here. Last is the idiomatic choice for expressing how long something continues.

Correct Answer: B — lasts.

At constant volume: $\dfrac{P_1}{T_1} = \dfrac{P_2}{T_2}$ (Gay-Lussac's Law)

$P_1 = 35\ \text{psi},\ T_1 = 27 + 273 = 300\ \text{K}$

$P_2 = 40\ \text{psi}$

$T_2 = T_1 \times \dfrac{P_2}{P_1} = 300 \times \dfrac{40}{35} = 300 \times 1.1\overline{428} \approx 342.86\ \text{K}$

$T_2\ (°C) = 342.86 - 273 \approx \mathbf{72}°\text{C}$

Note: ${}^{50}C_r \cdot {}^{50-r}C_{25-r} = \dfrac{50!}{r!(50-r)!} \cdot \dfrac{(50-r)!}{(25-r)!(25)!} = \dfrac{50!}{r!(25-r)!25!} = {}^{50}C_{25}\cdot{}^{25}C_r$

So the sum $= {}^{50}C_{25}\displaystyle\sum_{r=0}^{25}{}^{25}C_r = {}^{50}C_{25}\cdot 2^{25}$

Therefore $K = \mathbf{2^{25}}$.

The diagonal of the rectangle is 10 and one side is 6.

Using the Pythagorean theorem: $\text{diagonal}^2 = \text{length}^2 + \text{width}^2$

$10^2 = 6^2 + w^2 \Rightarrow 100 = 36 + w^2 \Rightarrow w^2 = 64 \Rightarrow w = 8$

Perimeter $= 2(6 + 8) = 2 \times 14 = 28$.