Question 1

Find the indicated term of the binomial expansion.
-$( x - y ) ^ { 11 } ;$ sixth term

Accepted Answer

A)  $- 462 x ^ { 6 } y ^ { 5 }$ 
B)  $- 462 x ^ { 5 } y ^ { 6 }$ 
C)  $462 x ^ { 5 } y ^ { 6 }$ 
D)  $462 x ^ { 6 } y ^ { 5 }$ 
A)  $- 462 x ^ { 6 } y ^ { 5 }$ 
B)  $- 462 x ^ { 5 } y ^ { 6 }$ 
C)  $462 x ^ { 5 } y ^ { 6 }$ 
D)  $462 x ^ { 6 } y ^ { 5 }$

Question 2

Find the nth term $a _ { n }$ of a sequence whose first four terms are given.
-$4,16,64,256 , \ldots$

Accepted Answer

A)  $a _ { n } = \mathrm { n } + 2$ 
B)  $a _ { n } = 2 ^ { n - 1 }$ 
C)  $a _ { n } = 2 ^ { n }$ 
D)  $a _ { n } = 2 n$ 
A)  $a _ { n } = \mathrm { n } + 2$ 
B)  $a _ { n } = 2 ^ { n - 1 }$ 
C)  $a _ { n } = 2 ^ { n }$ 
D)  $a _ { n } = 2 n$

Question 3

Find the nth term $a _ { n }$ of a sequence whose first four terms are given.
-$\frac { 1 \cdot 2 \cdot 3 \cdot 4 } { 2 } , \frac { 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 } { 4 } , \frac { 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 } { 6 } , \frac { 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 } { 8 } , \ldots$

Accepted Answer

A)  $a _ { n } = \frac { ( n + 4 ) ! } { 2 ^ { n } }$ 
B)  $a _ { n } = \frac { ( n + 4 ) ! } { 2 n }$ 
C)  $a _ { n } = \frac { ( n + 3 ) ! } { 2 n }$ 
D)  $a _ { n } = \frac { ( n + 3 ) ! } { 2 ^ { n } }$ 
A)  $a _ { n } = \frac { ( n + 4 ) ! } { 2 ^ { n } }$ 
B)  $a _ { n } = \frac { ( n + 4 ) ! } { 2 n }$ 
C)  $a _ { n } = \frac { ( n + 3 ) ! } { 2 n }$ 
D)  $a _ { n } = \frac { ( n + 3 ) ! } { 2 ^ { n } }$

Question 4

Find the sum.
-$$\sum _ { i = 1 } ^ { 45 } 7$$

Accepted Answer

A)  1,035 
B)  7 
C)  315 
D)  308 
A)  1,035 
B)  7 
C)  315 
D)  308

Question 5

Stirling's formula (named after Scottish mathematician, James Stirling: 1692-1770) is used to
approximate large values of n!. Stirling's formula is $n ! \approx \sqrt { 2 \pi n } \left( \frac { n } { e } \right) ^ { n }$ a. Use Stirling's formula to approximate the given expression. Round to the nearest whole unit.
b. Compute the actual value of the expression.
-$8 !$

Accepted Answer

A)  a. 39,902
b. 40,312 
B)  a. 40,111
b. 40,320 
C)  a. 40,111
b. 40,312 
D)  a. 39,902
b. 40,320 
A)  a. 39,902
b. 40,312 
B)  a. 40,111
b. 40,320 
C)  a. 40,111
b. 40,312 
D)  a. 39,902
b. 40,320

Question 6

Choose the one alternative that best completes the statement or answers the question.
Determine whether the sequence is geometric. If so, find the value of r.
-$$\sqrt { 5 } , 5,5 \sqrt { 5 } , 25$$

Accepted Answer

A)  not geometric 
B)  geometric, $r = 5 + \sqrt { 5 }$ 
C)  geometric, $r = 5$ 
D)  geometric, $r = \sqrt { 5 }$ 
A)  not geometric 
B)  geometric, $r = 5 + \sqrt { 5 }$ 
C)  geometric, $r = 5$ 
D)  geometric, $r = \sqrt { 5 }$

Question 7

Use the Binomial Theorem to find the value of the complex number raised to the given power. Recall that $i = \sqrt { - 1 }$
-$$( - 5 + 3 i ) ^ { 4 }$$

Accepted Answer

A)  $- 644 - 960 i$ 
B)  $644 + 960 i$ 
C)  $644 - 960 i$ 
D)  $- 644 + 960 i$ 
A)  $- 644 - 960 i$ 
B)  $644 + 960 i$ 
C)  $644 - 960 i$ 
D)  $- 644 + 960 i$

Question 8

Solve the problem.
-Suppose that a jury pool consists of 19 women and 20 men. 
a. What is the probability that a jury of 7 people taken at random from the pool will consist only of
Women?
b. What is the probability that the jury will consist only of men?

Accepted Answer

A)  a. $\approx 0.51282 ;$ b. $\approx 0.00504$ 
B)  $\mathbf { a } . \approx 0.00328 ;$ b. $\approx 0.00504$ 
C)  a. $\approx 0.01842 ;$ b. $\approx 0.01842$ 
D)  $\mathbf { a } . \approx 0.51282 ;$ b. $\approx 0.01842$ 
A)  a. $\approx 0.51282 ;$ b. $\approx 0.00504$ 
B)  $\mathbf { a } . \approx 0.00328 ;$ b. $\approx 0.00504$ 
C)  a. $\approx 0.01842 ;$ b. $\approx 0.01842$ 
D)  $\mathbf { a } . \approx 0.51282 ;$ b. $\approx 0.01842$

Question 9

Write the first four terms of the geometric sequence.
-$a _ { 1 } = - \frac { 1 } { 2 }$ and $r = - \frac { 1 } { 3 }$.

Accepted Answer

A)  $- \frac { 1 } { 2 } , - \frac { 1 } { 6 } , - \frac { 1 } { 18 } , - \frac { 1 } { 54 } , \ldots$ 
B)  $- \frac { 1 } { 2 } , \frac { 3 } { 2 } , - \frac { 9 } { 2 } , \frac { - 27 } { 2 } , \ldots$ 
C)  $- \frac { 1 } { 2 } , - \frac { 3 } { 2 } , - \frac { 9 } { 2 } , - \frac { - 27 } { 2 } , \ldots$ 
D)  $- \frac { 1 } { 2 } , \frac { 1 } { 6 } , - \frac { 1 } { 18 } , \frac { 1 } { 54 } , \ldots$ 
A)  $- \frac { 1 } { 2 } , - \frac { 1 } { 6 } , - \frac { 1 } { 18 } , - \frac { 1 } { 54 } , \ldots$ 
B)  $- \frac { 1 } { 2 } , \frac { 3 } { 2 } , - \frac { 9 } { 2 } , \frac { - 27 } { 2 } , \ldots$ 
C)  $- \frac { 1 } { 2 } , - \frac { 3 } { 2 } , - \frac { 9 } { 2 } , - \frac { - 27 } { 2 } , \ldots$ 
D)  $- \frac { 1 } { 2 } , \frac { 1 } { 6 } , - \frac { 1 } { 18 } , \frac { 1 } { 54 } , \ldots$

Question 10

Solve the problem.
-Airlines often overbook flights because a small percentage of passengers do not show up (perhaps due to missed connections). Past history indicates that for a certain route, the probability that an
Individual passenger will not show up is 0.03. Suppose that 66 people bought tickets for a flight that
Has 65 seats. Determine the probability that there will not be enough seats. Round to 4 decimal
Places.

Accepted Answer

A)  0.1339 
B)  0.1795 
C)  0.1741 
D)  0.1381 
A)  0.1339 
B)  0.1795 
C)  0.1741 
D)  0.1381

Find the indicated term of the binomial expansion. - $( x - y ) ^ { 11 } ;$ sixth term

Find the nth term $a _ { n }$ of a sequence whose first four terms are given. - $4,16,64,256 , \ldots$

Find the sum. - $\sum _ { i = 1 } ^ { 45 } 7$

Choose the one alternative that best completes the statement or answers the question. Determine whether the sequence is geometric. If so, find the value of r. - $\sqrt { 5 } , 5,5 \sqrt { 5 } , 25$

Use the Binomial Theorem to find the value of the complex number raised to the given power. Recall that $i = \sqrt { - 1 }$ - $( - 5 + 3 i ) ^ { 4 }$

Solve the problem. -Suppose that a jury pool consists of 19 women and 20 men. a. What is the probability that a jury of 7 people taken at random from the pool will consist only of Women? b. What is the probability that the jury will consist only of men?

Write the first four terms of the geometric sequence. - $a _ { 1 } = - \frac { 1 } { 2 }$ and $r = - \frac { 1 } { 3 }$ .

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants and Applications

Analytic Geometry

Review of Prerequisites

Filters

Exam 8: Sequences, Series, Induction, and Probability

Find the indicated term of the binomial expansion. - (x−y)11;( x - y ) ^ { 11 } ;(x−y)11; sixth term

Find the nth term ana _ { n }an​ of a sequence whose first four terms are given. - 4,16,64,256,…4,16,64,256 , \ldots4,16,64,256,…

Find the sum. - ∑i=1457\sum _ { i = 1 } ^ { 45 } 7∑i=145​7

Choose the one alternative that best completes the statement or answers the question. Determine whether the sequence is geometric. If so, find the value of r. - 5,5,55,25\sqrt { 5 } , 5,5 \sqrt { 5 } , 255​,5,55​,25

Use the Binomial Theorem to find the value of the complex number raised to the given power. Recall that i=−1i = \sqrt { - 1 }i=−1​ - (−5+3i)4( - 5 + 3 i ) ^ { 4 }(−5+3i)4