A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:

44,000 fans x \( \frac{5}{6} \) = \( \frac{220000}{6} \) = 36,667 fans.

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{62}{13} \) = 4\(\frac{10}{13}\)

So, it will take 4 full vans and one partially full van to transport the entire team making a total of 5 vans.

To multiply terms with radicals, multiply the coefficients and radicands separately:

8\( \sqrt{7} \) x 5\( \sqrt{4} \)
(8 x 5)\( \sqrt{7 \times 4} \)
40\( \sqrt{28} \)

Now we need to simplify the radical:

40\( \sqrt{28} \)
40\( \sqrt{7 \times 4} \)
40\( \sqrt{7 \times 2^2} \)
(40)(2)\( \sqrt{7} \)
80\( \sqrt{7} \)

To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 400 meters to kilometers, divide the distance by 1000 to get 0.4km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.4km + 40.7km + 6.2km
total distance = 47.3km

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $1,400
i = 0.07 x $1,400
i = $98