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

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 75mph \times 1h \)
75 miles

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

-6x⁷ x 4x²
(-6 x 4)x^{(7 + 2)}
-24x⁹

If a single cook can bake 2 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 2 x 3 = 6 large cakes during that time. 25 large cakes are needed for the party so \( \frac{25}{6} \) = 4\(\frac{1}{6}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 13 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 13 x 3 = 39 small cakes during that time. 300 small cakes are needed for the party so \( \frac{300}{39} \) = 7\(\frac{9}{13}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 5 + 8 = 13 cooks.

The amount of flour you need is (3\(\frac{1}{2}\) - \(\frac{3}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{28}{8} \) - \( \frac{3}{8} \)) cups
\( \frac{25}{8} \) cups
3\(\frac{1}{8}\) cups

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.