Question 1

Use mathematical induction to prove that the statement is true for every positive integer n.
-The series of sketches below starts with an equilateral triangle having sides of length 1 (one). In the following steps, equilateral triangles are constructed by joining the midpoints of the sides of the preceding triangle. Develop a formula for the length of the sides of the new triangle.

Accepted Answer

The answer of Use mathematical induction to prove that the...

Question 2

Use a calculator to evaluate the expression.
-${ } _ { 29 } \mathrm { C } _ { 5 }$

Accepted Answer

A)  $14,250,600$ 
B)  237,510 
C)  $2,850,120$ 
D)  118,755

Question 3

Use mathematical induction to prove that the statement is true for every positive integer n.
-$3 ^ { n } > 1$

Accepted Answer

The answer of Use mathematical induction to prove that the...

Question 4

Find a general term an for the geometric sequence.
-$$\mathrm { a } _ { 1 } = \frac { 1 } { 2 } , \mathrm { r } = 2$$

Accepted Answer

A)  $a _ { n } = \frac { 1 } { 2 } \cdot 2 ^ { n - 1 }$ 
B)  $a _ { n } = \left( \frac { 1 } { 2 } \right) n - 1 + \frac { 1 } { 2 }$ 
C)  $\mathrm { a } _ { \mathrm { n } } = \frac { 1 } { 2 } + \frac { 1 } { 2 } ( \mathrm { n } - 1 )$ 
D)  $a _ { n } = \frac { 1 } { 2 } + 2 ( n - 1 )$

Question 5

Find the future value of the annuity.
-A sequence of yearly payments of $5000 is invested at the end of each of 9 years at an interest rate of 2.1%, compounded annually. What is the total amount of the annuity after 9 years?

Accepted Answer

A)  $48,471.18 
B)  $48,971.18 
C)  $49,971.18 
D)  $47,971.18

Question 6

Evaluate the expression.
-$\left( \begin{array} { l } 10 \ 10 \end{array} \right)$

Accepted Answer

A)  0 
B)  1 
C)  $3,628,800$ 
D)  2

Question 7

Provide an appropriate response.
-Consider the selection of officers for a club. Is this a combination, a permutation, or neither?

Accepted Answer

A)  Permutation 
B)  Neither 
C)  Combination

Question 8

Use a calculator to evaluate the expression.
-${ } _ { 32 } \mathrm { P } _ { 4 }$

Accepted Answer

A)  35,960 
B)  863,040 
C)  215,760 
D)  143,840

Question 9

Solve the problem.
-A musician plans to perform 5 selections for a concert. If he can choose from 7 different selections, how many ways can he arrange his program?

Accepted Answer

A)  16,807 
B)  21 
C)  35 
D)  2520

Question 10

Write the binomial expansion of the expression.
-$$\left( \frac { 1 } { x } - \sqrt { 15 } y \right) ^ { 3 }$$

Accepted Answer

A)  $\frac { 1 } { x ^ { 3 } } - \frac { 3 \sqrt { 15 } y } { x ^ { 2 } } + \frac { 135 y ^ { 2 } } { x } - 15 \sqrt { 15 } y ^ { 3 }$ 
B)  $\frac { 1 } { x ^ { 3 } } - \frac { 3 \sqrt { 15 } y } { x ^ { 2 } } + \frac { 45 y ^ { 2 } } { x } - 15 \sqrt { 15 } y ^ { 3 }$ 
C)  $\frac { 1 } { x ^ { 3 } } + \frac { 3 \sqrt { 15 } y } { x ^ { 2 } } + \frac { 45 y ^ { 2 } } { x } + 15 \sqrt { 15 } y ^ { 3 }$ 
D)  $\frac { 1 } { x ^ { 3 } } - \frac { 3 \sqrt { 15 } y } { x ^ { 2 } } - \frac { 45 y ^ { 2 } } { x } - 15 \sqrt { 15 } y ^ { 3 }$

Question 11

Write the indicated term of the binomial expansion.
-$( 3 x - 2 y ) ^{11 }; 9$ th term

Accepted Answer

A)  $- 570,240 x ^ { 3 } y ^ { 9 }$ 
B)  $380,160 \mathrm { x } ^ { 8 } \mathrm { y } ^ { 3 }$ 
C)  $- 570,240 x ^ { 8 } y ^ { 3 }$ 
D)  $1,140,480 \mathrm { x } ^ { 3 } \mathrm { y }^ 8$

Question 12

Evaluate the expression.
-P(12, 12)

Accepted Answer

A)  12 
B)  479,001,600 
C)  1 
D)  239,500,800

Question 13

Evaluate the sum using the given information.
-$\mathrm { x } _ { 1 } = 4 , \mathrm { x } _ { 2 } = - 1 , \mathrm { x } _ { 3 } = 2 , \mathrm { x } _ { 4 } = 1$, and $\mathrm { x } _ { 5 } = - 4$
$\sum _ { i = 1 } ^ { 5 } \left( 2 x _ { i } + x _ { i } \right)$

Accepted Answer

A)  45 
B)  19 
C)  6 
D)  8

Question 14

Evaluate the expression.
-${ } _ { 10 } \mathrm { C } _ { 8 }$

Accepted Answer

A)  90 
B)  45 
C)  $\frac { 5 } { 8 }$ 
D)  $1,814,400$

Question 15

Write the binomial expansion of the expression.
-$$( 2 x + 4 ) ^ { 5 }$$

Accepted Answer

A)  $32 x ^ { 5 } + 64 x ^ { 4 } + 128 x ^ { 3 } + 256 x ^ { 2 } + 512 x + 1024$ 
B)  $\left( 4 x ^ { 2 } + 16 x + 16 \right) ^ { 5 }$ 
C)  $32 x ^ { 5 } + 2560 x ^ { 4 } + 2560 x ^ { 3 } + 2560 x ^ { 2 } + 2560 x + 1024$ 
D)  $32 x ^ { 5 } + 320 x ^ { 4 } + 1280 x ^ { 3 } + 2560 x ^ { 2 } + 2560 x + 1024$

Question 16

Solve the problem.
-Find the sum of the first 78 positive multiples of 4.

Accepted Answer

A)  12012 
B)  12482 
C)  12168 
D)  12324

Question 17

Solve the problem.
-What are the odds in favor of spinning a D on this spinner?

Accepted Answer

A)  1 to 6 
B)  5 to 1 
C)  1 to 7 
D)  6 to 1

Question 18

Use mathematical induction to prove that the statement is true for every positive integer n.
-$$9 n > n$$

Accepted Answer

The answer of Use mathematical induction to prove that the...

Question 19

Find all natural number values for n for which the given statement is false.
-$$n ! > 10 n$$

Accepted Answer

A)  $n > 5$ 
B)  $\mathrm { n } = 1,2$ or 3 
C)  $\mathrm { n } = 1,2,3,4$, or 5 
D)  $n = 1,2,3$, or 4

Question 20

Solve the problem.
-Martin saves $5 on the first day of a 30-day period, $10 on the second day, and so on. For the next 30 days, he increases the amount saved by $10 each day (instead of $5 each day). How much will
He have saved after 60 days?

Accepted Answer

A)  $11,400 
B)  $11,700 
C)  $11,475 
D)  $11,550

Exam 11: Further Topics in Algebra

Use a calculator to evaluate the expression. - ${ } _ { 29 } \mathrm { C } _ { 5 }$

Use mathematical induction to prove that the statement is true for every positive integer n. - $3 ^ { n } > 1$

Find a general term an for the geometric sequence. - $\mathrm { a } _ { 1 } = \frac { 1 } { 2 } , \mathrm { r } = 2$

Find the future value of the annuity. -A sequence of yearly payments of $5000 is invested at the end of each of 9 years at an interest rate of 2.1%, compounded annually. What is the total amount of the annuity after 9 years?

Evaluate the expression. - $\left( \begin{array} { l } 10 \\ 10 \end{array} \right)$

Provide an appropriate response. -Consider the selection of officers for a club. Is this a combination, a permutation, or neither?

Use a calculator to evaluate the expression. - ${ } _ { 32 } \mathrm { P } _ { 4 }$

Solve the problem. -A musician plans to perform 5 selections for a concert. If he can choose from 7 different selections, how many ways can he arrange his program?

Write the binomial expansion of the expression. - $\left( \frac { 1 } { x } - \sqrt { 15 } y \right) ^ { 3 }$

Write the indicated term of the binomial expansion. - $( 3 x - 2 y ) ^{11 }; 9$ th term

Evaluate the expression. -P(12, 12)

Evaluate the sum using the given information. - $\mathrm { x } _ { 1 } = 4 , \mathrm { x } _ { 2 } = - 1 , \mathrm { x } _ { 3 } = 2 , \mathrm { x } _ { 4 } = 1$ , and $\mathrm { x } _ { 5 } = - 4$ $\sum _ { i = 1 } ^ { 5 } \left( 2 x _ { i } + x _ { i } \right)$

Evaluate the expression. - ${ } _ { 10 } \mathrm { C } _ { 8 }$

Write the binomial expansion of the expression. - $( 2 x + 4 ) ^ { 5 }$

Solve the problem. -Find the sum of the first 78 positive multiples of 4.

Solve the problem. -What are the odds in favor of spinning a D on this spinner?

Use mathematical induction to prove that the statement is true for every positive integer n. - $9 n > n$

Find all natural number values for n for which the given statement is false. - $n ! > 10 n$

Solve the problem. -Martin saves $5 on the first day of a 30-day period, $10 on the second day, and so on. For the next 30 days, he increases the amount saved by $10 each day (instead of $5 each day) . How much will He have saved after 60 days?

Exam 11: Further Topics in Algebra

Use a calculator to evaluate the expression. - 29C5{ } _ { 29 } \mathrm { C } _ { 5 }29​C5​

Use mathematical induction to prove that the statement is true for every positive integer n. - 3n>13 ^ { n } > 13n>1

Find a general term an for the geometric sequence. - a1=12,r=2\mathrm { a } _ { 1 } = \frac { 1 } { 2 } , \mathrm { r } = 2a1​=21​,r=2

Find the future value of the annuity. -A sequence of yearly payments of $5000 is invested at the end of each of 9 years at an interest rate of 2.1%, compounded annually. What is the total amount of the annuity after 9 years?

Evaluate the expression. - (1010) \left( \begin{array} { l } 10 \\ 10 \end{array} \right) (1010​)

Provide an appropriate response. -Consider the selection of officers for a club. Is this a combination, a permutation, or neither?

Use a calculator to evaluate the expression. - 32P4{ } _ { 32 } \mathrm { P } _ { 4 }32​P4​

Solve the problem. -A musician plans to perform 5 selections for a concert. If he can choose from 7 different selections, how many ways can he arrange his program?

Write the binomial expansion of the expression. - (1x−15y) 3\left( \frac { 1 } { x } - \sqrt { 15 } y \right) ^ { 3 }(x1​−15​y) 3

Write the indicated term of the binomial expansion. - (3x−2y) 11;9( 3 x - 2 y ) ^{11 }; 9(3x−2y) 11;9 th term

Evaluate the expression. -P(12, 12)

Evaluate the expression. - 10C8{ } _ { 10 } \mathrm { C } _ { 8 }10​C8​

Write the binomial expansion of the expression. - (2x+4) 5( 2 x + 4 ) ^ { 5 }(2x+4) 5

Solve the problem. -Find the sum of the first 78 positive multiples of 4.

Solve the problem. -What are the odds in favor of spinning a D on this spinner?

Use mathematical induction to prove that the statement is true for every positive integer n. - 9n>n9 n > n9n>n

Find all natural number values for n for which the given statement is false. - n!>10nn ! > 10 nn!>10n

Solve the problem. -Martin saves $5 on the first day of a 30-day period, $10 on the second day, and so on. For the next 30 days, he increases the amount saved by $10 each day (instead of $5 each day) . How much will He have saved after 60 days?

Use a calculator to evaluate the expression. - ${ } _ { 29 } \mathrm { C } _ { 5 }$

Use mathematical induction to prove that the statement is true for every positive integer n. - $3 ^ { n } > 1$

Find a general term an for the geometric sequence. - $\mathrm { a } _ { 1 } = \frac { 1 } { 2 } , \mathrm { r } = 2$

Evaluate the expression. - $\left( \begin{array} { l } 10 \\ 10 \end{array} \right)$

Use a calculator to evaluate the expression. - ${ } _ { 32 } \mathrm { P } _ { 4 }$

Write the binomial expansion of the expression. - $\left( \frac { 1 } { x } - \sqrt { 15 } y \right) ^ { 3 }$

Write the indicated term of the binomial expansion. - $( 3 x - 2 y ) ^{11 }; 9$ th term

Evaluate the expression. - ${ } _ { 10 } \mathrm { C } _ { 8 }$

Write the binomial expansion of the expression. - $( 2 x + 4 ) ^ { 5 }$

Use mathematical induction to prove that the statement is true for every positive integer n. - $9 n > n$

Find all natural number values for n for which the given statement is false. - $n ! > 10 n$