In Exercises 61–68, use the graphs of and to find each indicated sum.

${\sum }_{i=1}^5{a}_i^2-{\sum }_{i=3}^5{b}_i^2$

Write the first three terms in the binomial expansion, expressing the result in simplified form. (x-3)^9

Find the term indicated in the expansion. (2x-3)^6; fifth term

Evaluate the expression. *permutation notation* the number of permutations 8 things taken 3 at a time (sub 8)P(sub 3)

Evaluate the expression. *permutation notation* the number of permutations 9 things taken 5 at a time (sub 9)P(sub 5)

After a 20% reduction, a 42-inch HDTV sold for $256. What was the price before the reduction?

A club with 15 members is to choose four officers–president, vice president, secretary, and treasurer. In how many ways can these offices be filled?

How many different ways can a director select 4 actors from a group of 20 actors to attend a workshop on performing in rock musicals?

Use the Binomial Theorem to expand and then simplify the result: (x² +x+ 1)³.

In Exercises 81–85, use a calculator's factorial key to evaluate each expression.

$\frac{200!}{198!}$

Use a calculator's factorial key to evaluate each expression. (300/20)!

In the sequence 21,700, 23,172, 24,644, 26,116,... which term is 314,628?

In how many ways can five airplanes line up for departure on a runway?

Find the term in the expansion of (x² + y²)⁵ containing x⁴ as a factor.

In Exercises 81–85, use a calculator's factorial key to evaluate each expression.

$\frac{20!}{300}$

Show that the sum of the first n positive odd integers,1 +3 +5 + ··· + (2n − 1), ... is n².

Use a calculator's factorial key to evaluate each expression. 20!/(20−3)!

Write an equation in point-slope form and slope-intercept form for the line passing through (-2, -6) and perpendicular to the line whose equation is x − 3y+ 9 = 0.

In Exercises 81–85, use a calculator's factorial key to evaluate each expression.

$\frac{54!}{(54-3)!3!}$

Solve: $6\mid 1\text{–}2x\mid \text{—}7=11$.

Solve: log₂ (x+9) — log₂ x = 1.

Graph: f(x) = -2(x − 1)² (x + 3).

Exercises 88–90 will help you prepare for the material covered in the next section. Consider the sequence 1, −2, 4, −8, 16, ………. Find a2/a3, a1/a2, a4/a3 and a5/a4 What do you observe?

Evaluate n!/(n-r)! for n = 20 and r = 3

Exercises 88–90 will help you prepare for the material covered in the next section. Consider the sequence whose nth term is a_n = (3)5ⁿ Find a₂/a₃, a₁/a₂, a₄/a₃ and a₅/a₄ What do you observe?

A die is rolled. Find the probability of getting a number less than 5.

A die is rolled. Find the probability of getting a number less than 3 or greater than 4.

Exercises 88–90 will help you prepare for the material covered in the next section. Use the formula an = a₁3^(n-1) to find the seventh term of the sequence 11, 33, 99, 297,...

Evaluate n!/(n-r)!r! for n = 8 and r = 3

You are dealt one card from a 52-card deck. Find the probability of getting an ace or a king.