Question 1

Use the Binomial Theorem to expand and simplify the expression. $\left( x ^ { 3 / 4 } + 1 \right) ^ { 4 }$

Accepted Answer

A)  $x ^ { 3 } + 1$ 
B)  $x ^ { 3 } + 4 x ^ { 9 / 7 } + 6 x ^ { 3 / 2 } + 4 x ^ { 3 / 4 } + 1$ 
C)  $x ^ { 3 } + 4 x ^ { 9 / 4 } + 6 x ^ { 3 / 2 } + 4 x ^ { 3 / 4 } + 1$ 
D)  $- x ^ { 3 } + 4 x ^ { 9 / 4 } + 6 x ^ { 3 / 2 } + 4 x ^ { 3 / 4 } - 1$ 
E)  $x ^ { 3 } + 4 x ^ { 2 } + 6 x + 1$ 
A)  $x ^ { 3 } + 1$ 
B)  $x ^ { 3 } + 4 x ^ { 9 / 7 } + 6 x ^ { 3 / 2 } + 4 x ^ { 3 / 4 } + 1$ 
C)  $x ^ { 3 } + 4 x ^ { 9 / 4 } + 6 x ^ { 3 / 2 } + 4 x ^ { 3 / 4 } + 1$ 
D)  $- x ^ { 3 } + 4 x ^ { 9 / 4 } + 6 x ^ { 3 / 2 } + 4 x ^ { 3 / 4 } - 1$ 
E)  $x ^ { 3 } + 4 x ^ { 2 } + 6 x + 1$

Question 2

Find the sum of the finite geometric sequence   $\sum _ { n = 1 } ^ { 6 } ( - 6 ) ^ { n - 1 }$

Accepted Answer

A) -6,665 
B) -9,331 
C) -185 
D) 1,555 
E) 1,111 
A) -6,665 
B) -9,331 
C) -185 
D) 1,555 
E) 1,111

Question 3

There are six processes involved in assembling a product, and these processes can be performed in any order.The management wants to test each order to determine which is the least time-consuming.How many different orders will have to be tested? ​

Accepted Answer

A) 1,220 
B) 720 
C) 770 
D) 820 
E) 1,720 
A) 1,220 
B) 720 
C) 770 
D) 820 
E) 1,720

Question 4

In a high school graduating class of 128 students, 52 are on the honor roll.Of these, 45 are going on to college; of the other 76 students, 53 are going on to college.A student is selected at random from the class.What is the probability that the person chosen is going to college. ?

Accepted Answer

A)  $\frac { 49 } { 64 }$ 
B)  $\frac { 64 } { 49 }$ 
C)  $\frac { 53 } { 128 }$ 
D)  $\frac { 128 } { 53 }$ 
E)  $\frac { 45 } { 128 }$ 
A)  $\frac { 49 } { 64 }$ 
B)  $\frac { 64 } { 49 }$ 
C)  $\frac { 53 } { 128 }$ 
D)  $\frac { 128 } { 53 }$ 
E)  $\frac { 45 } { 128 }$

Question 5

Use the Binomial Theorem to expand and simplify the expression.   $( r + 5 s ) ^ { 6 }$

Accepted Answer

A)  $r ^ { 6 } + 30 s r ^ { 5 } + 375 s ^ { 2 } r ^ { 4 } + 2500 s ^ { 3 } r ^ { 3 } + 9375 s ^ { 4 } r ^ { 2 } + 18750 s ^ { 5 } r - 15625 s ^ { 6 }$ 
B)  $r ^ { 6 } - 30 s r ^ { 5 } + 375 s ^ { 2 } r ^ { 4 } + 2500 s ^ { 3 } r ^ { 3 } + 9375 s ^ { 4 } r ^ { 2 } + 18750 s ^ { 5 } r + 15625 s ^ { 6 }$ 
C)  $r ^ { 6 } + 30 s r ^ { 5 } + 375 s ^ { 2 } r ^ { 4 } - 2500 s ^ { 3 } r ^ { 3 } + 9375 s ^ { 4 } r ^ { 2 } + 18750 s ^ { 5 } r + 15625 s ^ { 6 }$ 
D)  $r ^ { 6 } - 30 s r ^ { 5 } - 375 s ^ { 2 } r ^ { 4 } - 2500 s ^ { 3 } r ^ { 3 } - 9375 s ^ { 4 } r ^ { 2 } - 18750 s ^ { 5 } r - 15625 s ^ { 6 }$ 
E)  $r ^ { 6 } + 30 s r ^ { 5 } + 375 s ^ { 2 } r ^ { 4 } + 2500 s ^ { 3 } r ^ { 3 } + 9375 s ^ { 4 } r ^ { 2 } + 18750 s ^ { 5 } r + 15625 s ^ { 6 }$ 
A)  $r ^ { 6 } + 30 s r ^ { 5 } + 375 s ^ { 2 } r ^ { 4 } + 2500 s ^ { 3 } r ^ { 3 } + 9375 s ^ { 4 } r ^ { 2 } + 18750 s ^ { 5 } r - 15625 s ^ { 6 }$ 
B)  $r ^ { 6 } - 30 s r ^ { 5 } + 375 s ^ { 2 } r ^ { 4 } + 2500 s ^ { 3 } r ^ { 3 } + 9375 s ^ { 4 } r ^ { 2 } + 18750 s ^ { 5 } r + 15625 s ^ { 6 }$ 
C)  $r ^ { 6 } + 30 s r ^ { 5 } + 375 s ^ { 2 } r ^ { 4 } - 2500 s ^ { 3 } r ^ { 3 } + 9375 s ^ { 4 } r ^ { 2 } + 18750 s ^ { 5 } r + 15625 s ^ { 6 }$ 
D)  $r ^ { 6 } - 30 s r ^ { 5 } - 375 s ^ { 2 } r ^ { 4 } - 2500 s ^ { 3 } r ^ { 3 } - 9375 s ^ { 4 } r ^ { 2 } - 18750 s ^ { 5 } r - 15625 s ^ { 6 }$ 
E)  $r ^ { 6 } + 30 s r ^ { 5 } + 375 s ^ { 2 } r ^ { 4 } + 2500 s ^ { 3 } r ^ { 3 } + 9375 s ^ { 4 } r ^ { 2 } + 18750 s ^ { 5 } r + 15625 s ^ { 6 }$

Use the Binomial Theorem to expand and simplify the expression. $\left( x ^ { 3 / 4 } + 1 \right) ^ { 4 }$

Find the sum of the finite geometric sequence $\sum _ { n = 1 } ^ { 6 } ( - 6 ) ^ { n - 1 }$

There are six processes involved in assembling a product, and these processes can be performed in any order.The management wants to test each order to determine which is the least time-consuming.How many different orders will have to be tested?

In a high school graduating class of 128 students, 52 are on the honor roll.Of these, 45 are going on to college; of the other 76 students, 53 are going on to college.A student is selected at random from the class.What is the probability that the person chosen is going to college. ?

Use the Binomial Theorem to expand and simplify the expression. $( r + 5 s ) ^ { 6 }$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 9: Sequences Series and Probability

Use the Binomial Theorem to expand and simplify the expression. (x3/4+1)4\left( x ^ { 3 / 4 } + 1 \right) ^ { 4 }(x3/4+1)4

Find the sum of the finite geometric sequence ∑n=16(−6)n−1\sum _ { n = 1 } ^ { 6 } ( - 6 ) ^ { n - 1 }∑n=16​(−6)n−1

There are six processes involved in assembling a product, and these processes can be performed in any order.The management wants to test each order to determine which is the least time-consuming.How many different orders will have to be tested? ​

In a high school graduating class of 128 students, 52 are on the honor roll.Of these, 45 are going on to college; of the other 76 students, 53 are going on to college.A student is selected at random from the class.What is the probability that the person chosen is going to college. ?

Use the Binomial Theorem to expand and simplify the expression. (r+5s)6( r + 5 s ) ^ { 6 }(r+5s)6

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Use the Binomial Theorem to expand and simplify the expression. $\left( x ^ { 3 / 4 } + 1 \right) ^ { 4 }$

Find the sum of the finite geometric sequence $\sum _ { n = 1 } ^ { 6 } ( - 6 ) ^ { n - 1 }$

There are six processes involved in assembling a product, and these processes can be performed in any order.The management wants to test each order to determine which is the least time-consuming.How many different orders will have to be tested?

Use the Binomial Theorem to expand and simplify the expression. $( r + 5 s ) ^ { 6 }$