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 100 meters to kilometers, divide the distance by 1000 to get 0.1km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.1km + 50.1km + 11.6km
total distance = 61.8km

The equation for this sequence is:

a_n = a_n-1 + 2(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 2(6 - 1)
a₆ = 21 + 2(5)
a₆ = 31

The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 54 meters so the equation becomes: 2w + 2h = 54.

Putting these two equations together and solving for width (w):

2w + 2h = 54
w + h = \( \frac{54}{2} \)
w + h = 27
w = 27 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 27 - 2w
3w = 27
w = \( \frac{27}{3} \)
w = 9

Since h = 2w that makes h = (2 x 9) = 18 and the area = h x w = 9 x 18 = 162 m²

The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:

\( \frac{5}{100} \) x 8 = \( \frac{5 \times 8}{100} \) = \( \frac{40}{100} \) = 0.4 errors per hour

So, in an average hour, the machine will produce 8 - 0.4 = 7.6 error free parts.

The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 7.6 = 121.6 error free parts were produced yesterday.

To raise a term with an exponent to another exponent, retain the base and multiply the exponents: