39) Draw the net of the cone. Step 1: Determine the radius of the base of the cone. The cone has a slant height $L = 7\,\text{cm}$ and a vertex angle of $60^\circ$. Consider the isosceles triangle formed by the slant heights and the diameter of the base. Since the two equal sides are $7\,\text{cm}$ and the angle between them is $60^\circ$, this is an equilateral triangle. Therefore, the diameter of the base is $7\,\text{cm}$. The radius of the base $r = \frac{\text{diameter}}{2} = \frac{7}{2}\,\text{cm} = 3.5\,\text{cm}$. Step 2: Determine the angle of the sector for the lateral surface. The radius of the sector is the slant height $L = 7\,\text{cm}$. The arc length of the sector is equal to the circumference of the base circle. Circumference $C = 2\pi r = 2\pi (3.5\,\text{cm}) = 7\pi\,\text{cm}$. The angle $\theta$ of the sector (in degrees) is given by the formula: $$\theta = \frac{r}{L} \times 360^\circ$$ $$\theta = \frac{3.5\,\text{cm}}{7\,\text{cm}} \times 360^\circ$$ $$\theta = \frac{1}{2} \times 360^\circ$$ $$\theta = 180^\circ$$ Step 3: Describe the net. The net of the cone consists of two parts: A circular base with a radius of $3.5\,\text{cm}$. A sector of a circle with a radius of $7\,\text{cm}$ and an angle of $180^\circ$ (a semicircle). 40) Maureen tossed a die once. Determine the probability that she obtained an even number. Step 1: Identify the sample space. When a standard die is tossed once, the possible outcomes are the integers from 1 to 6. The sample space $S = \{1, 2, 3, 4, 5, 6\}$. The total number of possible outcomes is $n(S) = 6$. Step 2: Identify the favorable outcomes. We are looking for the probability of obtaining an even number. The even numbers in the sample space are $\{2, 4, 6\}$. The number of favorable outcomes is $n(E) = 3$. Step 3: Calculate the probability. The probability $P(E)$ of an event $E$ is given by the formula: $$P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$ $$P(\text{even number}) = \frac{n(E)}{n(S)}$$ $$P(\text{even number}) = \frac{3}{6}$$ $$P(\text{even number}) = \frac{1}{2}$$ The probability that she obtained an even number is $\boxed{\frac{1}{2}}$.