91Ó°ÊÓ

Express each repeating decimal as a fraction in lowest terms. $$0 . \overline{257}$$

In Exercises \(49-52,\) a single die is rolled twice. Find the probability of rolling a 2 the first time and a 3 the second time.

Express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. $$\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+\dots+\frac{14}{14+1}$$

Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. $$\sum_{i=1}^{100} 4 i$$

Use the Binomial Theorem to expand each expression and write the result in simplified form. $$\left(x^{3}+x^{-2}\right)^{4}$$

Use the formula for \(_{n} C_{r}\) to solve Exercises \(49-56\) An election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done?

Verify the identity: $$ \cot x+\tan x=\csc x \sec x $$

Use the Binomial Theorem to expand each expression and write the result in simplified form. $$\left(x^{2}+x^{-3}\right)^{4}$$

In Exercises \(49-52,\) a single die is rolled twice. Find the probability of rolling a 5 the first time and a 1 the second time.

Use the formula for \(_{n} C_{r}\) to solve Exercises \(49-56\) A four-person committee is to be elected from an organization's membership of 11 people. How many different committees are possible?