91Ó°ÊÓ

Use the Binomial Theorem to expand the complex number. Simplify your result. $$(5+\sqrt{-9})^{3}$$

Determine the seating capacity of an auditorium with 36 rows of seats when there are 15 seats in the first row, 18 seats in the second row, 21 seats in the third row, and so on.

A triangular brick wall is made by cutting some bricks in half to use in the first column of every other row (see figure). The wall has 28 rows. The top row is one-half brick wide and the bottom row is 14 bricks wide. How many bricks are in the finished wall?

Use sigma notation to write the sum. $$\frac{1}{3(1)}+\frac{1}{3(2)}+\frac{1}{3(3)}+\cdots+\frac{1}{3(9)}$

Consider a job offer with the given starting salary and the given annual raise. (a) Determine the salary during the sixth year of employment. (b) Determine the total compensation from the company through six full years of employment. Starting Salary \(\qquad\) Annual Raise \(\$ 32,500\) \(\qquad\) \(\$ 1500\)

Solve for \(n\) $$14 \cdot_{n} P_{3}=_{n+2} P_{4}$$

Consider a job offer with the given starting salary and the given annual raise. (a) Determine the salary during the sixth year of employment. (b) Determine the total compensation from the company through six full years of employment. Starting Salary \(\qquad\) Annual Raise \(\$ 36,800\) \(\qquad\) \(\$ 1750\)

Use the Binomial Theorem to approximate the quantity accurate to three decimal places. For example, in Exercise \(79,\) use the expansion \(\begin{aligned}(1.02)^{8} &=(1+0.02)^{8} \\ &=1+8(0.02)+28(0.02)^{2}+\cdot \cdot \cdot+(0.02)^{8}\end{aligned}\), $$(1.98)^{9}$$

Determine whether the statement is true or false. Justify your answer. The number of permutations of \(n\) elements can be determined by using the Fundamental Counting Principle.

A tool and die company buys a machine for \(\$ 175,000\) and it depreciates at a rate of \(30 \%\) per year. (In other words, at the end of each year the depreciated value is \(70 \%\) of what it was at the beginning of the year.) Find the depreciated value of the machine after 5 full years.