Write the statements SS1U1B1kS1U1B0 and SS1U1B1kS1U1B0+1. -\[S _ { n } : 4 + 9 + 14 + \ldots + ( 5 n - 1 ) = \frac { n ( 5 n + 3 ) } { 2 }\]

\[\begin{array} { l } \mathrm { S } _ {

Exam 9: Sequences and Series; Counting and Probability

Solve the problem. -How many different 3-letter codes are there if only the letters A, B, C, D, E, F, G, H, and I can be used and no letter can be used more than once?

(Multiple Choice)

4.8/5

(31)

Question 201

Use the Venn diagram below to determine the probability. $Use the Venn diagram below to determine the probability. - P ( A \cap C )$ - $P ( A \cap C )$

(Multiple Choice)

5.0/5

(22)

Question 202

Find the indicated term of the arithmetic sequence. -Given an arithmetic sequence with a16 = 19 and a10 = 7, find a4.

(Multiple Choice)

4.9/5

(36)

Question 203

Find the probability. -Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the die will be 6?

(Multiple Choice)

4.8/5

(29)

Question 204

Write the statements S_k and S_k+1. - $S _ { n } : 4 + 9 + 14 + \ldots + ( 5 n - 1 ) = \frac { n ( 5 n + 3 ) } { 2 }$

(Essay)

4.8/5

(31)

Question 205

Solve the problem. -Seven slips of paper marked with the numbers 1, 2, 3, 4, 5, 6, and 7 are placed in a box and mixed well. Two are drawn. What are the odds that the sum of the numbers on the two selected slips is not 5?

(Multiple Choice)

4.9/5

(39)

Question 206

Write the first five terms of the geometric sequence with the given information. -The first term is -5 and the common ratio is -4.

(Multiple Choice)

4.9/5

(37)

Question 207

Solve the problem. -A football player with a field goal kicking percentage of 60% for kicks of 40 yards or less attempts a final-minute field goal of 32 yards. What are the odds of a successful kick?

(Multiple Choice)

4.8/5

(30)

Question 208

Determine if the sequence is arithmetic. If the sequence is arithmetic, find the common difference. -3 , 9 , 27 , 81 , 243, . . .

(Multiple Choice)

4.7/5

(37)

Question 209

Find the sum of the geometric series. - $\sum _ { i = 1 } ^ { 8 } 5 \left( \frac { 1 } { 3 } \right) ^ { \mathrm { i } - 1 }$ Express the answer as a fraction.

(Multiple Choice)

4.8/5

(35)

Question 210

Find the sum of the series. - $\sum _ { j = 1 } ^ { 4 } \left( j ^ { 2 } - 4 \right)$

(Multiple Choice)

4.7/5

(30)

Question 211

Find the indicated term or coefficient of the binomial expansion. -Find the 11th term of the expansion of $( x + 2 y ) ^ { 12 }$ .

(Multiple Choice)

4.8/5

(34)

Question 212

Solve the problem. -A pendulum bob swings through an arc 50 inches long on its first swing. Each swing thereafter, it swings only 70% as far as on the previous swing. How far will it swing altogether before coming to a complete stop?

(Multiple Choice)

4.8/5

(44)

Question 213

Use Pascal's triangle to expand the binomial. - $( x - 4 ) ^ { 4 }$

(Multiple Choice)

4.9/5

(40)

Question 214

Evaluate the binomial coefficient. - $\left( \begin{array} { l } 5 \\2\end{array} \right)$

(Multiple Choice)

4.9/5

(45)

Question 215

Evaluate the binomial coefficient. - $\left( \begin{array} { l } 8 \\4\end{array} \right)$

(Multiple Choice)

4.7/5

(41)

Question 216

Find the indicated term or coefficient of the binomial expansion. -Find the 8 th term of the expansion of $( x - 2 ) ^ { 13 }$ .

(Multiple Choice)

4.9/5

(33)

Question 217

Solve the problem. -Suppose that $P ( A ) = 0.3 , P ( B ) = 0.42$ , and $P ( A \cup B ) = 0.61$ , find $P ( A \cap B )$ .

(Multiple Choice)

4.9/5

(33)

Question 218

Write the first four terms of the recursive sequence. - $a _ { 1 } = 3 , a _ { n } = 3 a _ { n } - 1 - 5$ for $n \geq 2$

(Multiple Choice)

4.9/5

(34)

Question 219

Find the indicated sum. - $\sum _ { n = 1 } ^ { 42 } ( - 3 n - 3 )$

(Multiple Choice)

4.9/5

(34)

Question 220

Solve the problem. -How many different 3-letter codes are there if only the letters A, B, C, D, E, F, G, H, and I can be used and no letter can be used more than once?

Use the Venn diagram below to determine the probability. $Use the Venn diagram below to determine the probability. - P ( A \cap C )$ - $P ( A \cap C )$

Find the indicated term of the arithmetic sequence. -Given an arithmetic sequence with a16 = 19 and a10 = 7, find a4.

Find the probability. -Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the die will be 6?

Write the statements S_k and S_k+1. - $S _ { n } : 4 + 9 + 14 + \ldots + ( 5 n - 1 ) = \frac { n ( 5 n + 3 ) } { 2 }$

Solve the problem. -Seven slips of paper marked with the numbers 1, 2, 3, 4, 5, 6, and 7 are placed in a box and mixed well. Two are drawn. What are the odds that the sum of the numbers on the two selected slips is not 5?

Write the first five terms of the geometric sequence with the given information. -The first term is -5 and the common ratio is -4.

Solve the problem. -A football player with a field goal kicking percentage of 60% for kicks of 40 yards or less attempts a final-minute field goal of 32 yards. What are the odds of a successful kick?

Determine if the sequence is arithmetic. If the sequence is arithmetic, find the common difference. -3 , 9 , 27 , 81 , 243, . . .

Find the sum of the geometric series. - $\sum _ { i = 1 } ^ { 8 } 5 \left( \frac { 1 } { 3 } \right) ^ { \mathrm { i } - 1 }$ Express the answer as a fraction.

Find the sum of the series. - $\sum _ { j = 1 } ^ { 4 } \left( j ^ { 2 } - 4 \right)$

Find the indicated term or coefficient of the binomial expansion. -Find the 11th term of the expansion of $( x + 2 y ) ^ { 12 }$ .

Solve the problem. -A pendulum bob swings through an arc 50 inches long on its first swing. Each swing thereafter, it swings only 70% as far as on the previous swing. How far will it swing altogether before coming to a complete stop?

Use Pascal's triangle to expand the binomial. - $( x - 4 ) ^ { 4 }$

Evaluate the binomial coefficient. - $\left( \begin{array} { l } 5 \\2\end{array} \right)$

Evaluate the binomial coefficient. - $\left( \begin{array} { l } 8 \\4\end{array} \right)$

Find the indicated term or coefficient of the binomial expansion. -Find the 8 th term of the expansion of $( x - 2 ) ^ { 13 }$ .

Solve the problem. -Suppose that $P ( A ) = 0.3 , P ( B ) = 0.42$ , and $P ( A \cup B ) = 0.61$ , find $P ( A \cap B )$ .

Write the first four terms of the recursive sequence. - $a _ { 1 } = 3 , a _ { n } = 3 a _ { n } - 1 - 5$ for $n \geq 2$

Find the indicated sum. - $\sum _ { n = 1 } ^ { 42 } ( - 3 n - 3 )$

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Exam 9: Sequences and Series; Counting and Probability

Solve the problem. -How many different 3-letter codes are there if only the letters A, B, C, D, E, F, G, H, and I can be used and no letter can be used more than once?

Use the Venn diagram below to determine the probability. - P(A∩C)P ( A \cap C )P(A∩C)

Find the indicated term of the arithmetic sequence. -Given an arithmetic sequence with a16 = 19 and a10 = 7, find a4.

Find the probability. -Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the die will be 6?

Write the statements Sk and Sk+1. - Sn:4+9+14+…+(5n−1)=n(5n+3)2S _ { n } : 4 + 9 + 14 + \ldots + ( 5 n - 1 ) = \frac { n ( 5 n + 3 ) } { 2 }Sn​:4+9+14+…+(5n−1)=2n(5n+3)​

Solve the problem. -Seven slips of paper marked with the numbers 1, 2, 3, 4, 5, 6, and 7 are placed in a box and mixed well. Two are drawn. What are the odds that the sum of the numbers on the two selected slips is not 5?

Write the first five terms of the geometric sequence with the given information. -The first term is -5 and the common ratio is -4.

Solve the problem. -A football player with a field goal kicking percentage of 60% for kicks of 40 yards or less attempts a final-minute field goal of 32 yards. What are the odds of a successful kick?

Determine if the sequence is arithmetic. If the sequence is arithmetic, find the common difference. -3 , 9 , 27 , 81 , 243, . . .

Find the sum of the geometric series. - ∑i=185(13)i−1\sum _ { i = 1 } ^ { 8 } 5 \left( \frac { 1 } { 3 } \right) ^ { \mathrm { i } - 1 }∑i=18​5(31​)i−1 Express the answer as a fraction.

Find the sum of the series. - ∑j=14(j2−4)\sum _ { j = 1 } ^ { 4 } \left( j ^ { 2 } - 4 \right)∑j=14​(j2−4)

Find the indicated term or coefficient of the binomial expansion. -Find the 11th term of the expansion of (x+2y)12( x + 2 y ) ^ { 12 }(x+2y)12 .

Solve the problem. -A pendulum bob swings through an arc 50 inches long on its first swing. Each swing thereafter, it swings only 70% as far as on the previous swing. How far will it swing altogether before coming to a complete stop?

Use Pascal's triangle to expand the binomial. - (x−4)4( x - 4 ) ^ { 4 }(x−4)4

Evaluate the binomial coefficient. - (52)\left( \begin{array} { l } 5 \\2\end{array} \right)(52​)

Evaluate the binomial coefficient. - (84)\left( \begin{array} { l } 8 \\4\end{array} \right)(84​)

Find the indicated term or coefficient of the binomial expansion. -Find the 8 th term of the expansion of (x−2)13( x - 2 ) ^ { 13 }(x−2)13 .

Solve the problem. -Suppose that P(A)=0.3,P(B)=0.42P ( A ) = 0.3 , P ( B ) = 0.42P(A)=0.3,P(B)=0.42 , and P(A∪B)=0.61P ( A \cup B ) = 0.61P(A∪B)=0.61 , find P(A∩B)P ( A \cap B )P(A∩B) .

Write the first four terms of the recursive sequence. - a1=3,an=3an−1−5a _ { 1 } = 3 , a _ { n } = 3 a _ { n } - 1 - 5a1​=3,an​=3an​−1−5 for n≥2n \geq 2n≥2

Find the indicated sum. - ∑n=142(−3n−3)\sum _ { n = 1 } ^ { 42 } ( - 3 n - 3 )∑n=142​(−3n−3)

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Use the Venn diagram below to determine the probability. $Use the Venn diagram below to determine the probability. - P ( A \cap C )$ - $P ( A \cap C )$

Write the statements S_k and S_k+1. - $S _ { n } : 4 + 9 + 14 + \ldots + ( 5 n - 1 ) = \frac { n ( 5 n + 3 ) } { 2 }$

Find the sum of the geometric series. - $\sum _ { i = 1 } ^ { 8 } 5 \left( \frac { 1 } { 3 } \right) ^ { \mathrm { i } - 1 }$ Express the answer as a fraction.

Find the sum of the series. - $\sum _ { j = 1 } ^ { 4 } \left( j ^ { 2 } - 4 \right)$

Find the indicated term or coefficient of the binomial expansion. -Find the 11th term of the expansion of $( x + 2 y ) ^ { 12 }$ .

Use Pascal's triangle to expand the binomial. - $( x - 4 ) ^ { 4 }$

Evaluate the binomial coefficient. - $\left( \begin{array} { l } 5 \\2\end{array} \right)$

Evaluate the binomial coefficient. - $\left( \begin{array} { l } 8 \\4\end{array} \right)$

Find the indicated term or coefficient of the binomial expansion. -Find the 8 th term of the expansion of $( x - 2 ) ^ { 13 }$ .

Solve the problem. -Suppose that $P ( A ) = 0.3 , P ( B ) = 0.42$ , and $P ( A \cup B ) = 0.61$ , find $P ( A \cap B )$ .

Write the first four terms of the recursive sequence. - $a _ { 1 } = 3 , a _ { n } = 3 a _ { n } - 1 - 5$ for $n \geq 2$

Find the indicated sum. - $\sum _ { n = 1 } ^ { 42 } ( - 3 n - 3 )$