The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 6 have in common.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{675mi}{75mph} \)
9 hours

To add these radicals together their radicands must be the same:

3\( \sqrt{45} \) + 9\( \sqrt{5} \)
3\( \sqrt{9 \times 5} \) + 9\( \sqrt{5} \)
3\( \sqrt{3^2 \times 5} \) + 9\( \sqrt{5} \)
(3)(3)\( \sqrt{5} \) + 9\( \sqrt{5} \)
9\( \sqrt{5} \) + 9\( \sqrt{5} \)

Now that the radicands are identical, you can add them together:

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{65}{100} \) = \( \frac{65 x 10}{100} \) = \( \frac{650}{100} \) = 6 shots

The center makes 50% of his shots so he'll have to take:

shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)

to make as many shots as the guard. Plugging in values for the center gives us:

center shots taken = \( \frac{6}{\frac{50}{100}} \) = 6 x \( \frac{100}{50} \) = \( \frac{6 x 100}{50} \) = \( \frac{600}{50} \) = 12 shots

to make the same number of shots as the guard and thus score the same number of points.

To fill a 12 gallon tank exactly halfway you'll need 6 gallons of fuel. Each fuel can holds 2 gallons so:

cans = \( \frac{6 \text{ gallons}}{2 \text{ gallons}} \) = 3