91Ó°ÊÓ

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{8}\), when \(a_{1}=12, r=\frac{1}{2}\).

Perform the indicated operations. If possible, reduce the answer to its lowest terms. \(\frac{13}{15}-\frac{2}{45}\)

Use the order of operations to find the value of each expression. \(-8(-3)-5(-6)\)

Perform the indicated operation and express each answer in decimal notation. \(\left(1.2 \times 10^{3}\right)\left(2 \times 10^{-5}\right)\)

State the associative property of multiplication and give an example.

Use the order of operations to find the value of each expression. \(6-4(-3)-5\)

Perform the indicated operations. If possible, reduce the answer to its lowest terms. \(\frac{4}{3}-\frac{3}{4}\)

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{6}\), when \(a_{1}=18, r=-\frac{1}{3}\).

The Blitzer Bonus on page 295 gives Einstein's special-relativity equation $$ R_{a}=R_{f} \sqrt{1-\left(\frac{v}{c}\right)^{2}} $$ for the aging rate of an astronaut, \(R_{a}\), relative to the aging rate of a friend on Earth, \(R_{f}\), where \(v\) is the astronaut's speed and \(c\) is the speed of light. Take a few minutes to read the essay and then solve. You are moving at \(90 \%\) of the speed of light. Substitute \(0.9 c\) in the equation shown above. What is your aging rate, correct to two decimal places, relative to a friend on Earth? If 100 weeks have passed for your friend, how long, to the nearest week, were you gone?

A prime number \(p\) such that \(2 p+1\) is also a prime number is called a Germain prime, named after the German mathematician Sophie Germain (1776-1831), who made major contributions to number theory. Determine whether or not each prime number is a Germain prime. 241