To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

-7b⁵ - 1b⁵
(-7 - 1)b⁵
-8b⁵

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 60% the radius (and, consequently, the total area) increases by \( \frac{60\text{%}}{2} \) = 30%

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

\( \frac{4}{100} \) x 10 = \( \frac{4 \times 10}{100} \) = \( \frac{40}{100} \) = 0.4 errors per hour

So, in an average hour, the machine will produce 10 - 0.4 = 9.6 error free parts.

The machine ran for 24 - 5 = 19 hours yesterday so you would expect that 19 x 9.6 = 182.4 error free parts were produced yesterday.

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

vans = \( \frac{63}{7} \) = 9

To simplify a radical, factor out the perfect squares:

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