To fill a 25 gallon tank exactly halfway you'll need 12\(\frac{1}{2}\) gallons of fuel. Each fuel can holds 2\(\frac{1}{2}\) gallons so:

cans = \( \frac{12\frac{1}{2} \text{ gallons}}{2\frac{1}{2} \text{ gallons}} \) = 5

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

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

\( \frac{7}{100} \) x 7 = \( \frac{7 \times 7}{100} \) = \( \frac{49}{100} \) = 0.49 errors per hour

So, in an average hour, the machine will produce 7 - 0.49 = 6.51 error free parts.

The machine ran for 24 - 9 = 15 hours yesterday so you would expect that 15 x 6.51 = 97.6 error free parts were produced yesterday.

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

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

7\( \sqrt{63} \) + 6\( \sqrt{7} \)
7\( \sqrt{9 \times 7} \) + 6\( \sqrt{7} \)
7\( \sqrt{3^2 \times 7} \) + 6\( \sqrt{7} \)
(7)(3)\( \sqrt{7} \) + 6\( \sqrt{7} \)
21\( \sqrt{7} \) + 6\( \sqrt{7} \)

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