Question 1

Which one of the following sequences is divergent?

Accepted Answer

A)  $\left\{\frac{n+200}{n}\right\}$ 
B)  $\left\{e^{-n}\right\}$ 
C)  $\{\sqrt[3]{n}\}$ 
D)  $\left\{n^{-5}\right\}$ 
E)  $\left\{\frac{100 n+1}{n}\right\}$ 
A)  $\left\{\frac{n+200}{n}\right\}$ 
B)  $\left\{e^{-n}\right\}$ 
C)  $\{\sqrt[3]{n}\}$ 
D)  $\left\{n^{-5}\right\}$ 
E)  $\left\{\frac{100 n+1}{n}\right\}$ C

Question 2

A hoagie consists of a roll, one type of meat, one type of cheese, and three different toppings. If there are 5 kinds of rolls, 5 kinds of meat, 4 kinds of cheese, and 9 toppings from which to choose, how many different hoagies can be built?

Accepted Answer

50,400

Question 3

Write the series in summation notation and find the sum, assuming the suggested pattern continues. 
$6+2+\frac{2}{3}+\frac{2}{9}+\ldots+\frac{2}{729}$

Accepted Answer

$\sum_{n=1}^{8} 6\left(\frac{1}{3}\right)^{n-1}=\frac{6560}{729}=8 \frac{728}{729} \approx 8.999$

Question 4

Write the statements  P1, Pk , and  Pk+1  for the equation $1(1 !)+2(2 !)+\cdots+n(n !)=(n+1) !-1$ as if you were writing a proof by mathematical induction. Do not write a proof.

Accepted Answer

None

Question 5

A student's grade in a particular class is determined as follows:
mean of three class exams  -45% 
final exam  -25% 
project  -30% 
If a student scored 85,88 , and 76 on the three exams, 90 on the final exam, and 86 on the project, what is the student's grade in the class? (Round your answer to the nearest whole number.)

Accepted Answer

The answer of A student's grade in a particular class...

Question 6

If the scores on a certain exam are normally distributed with a mean of 79 and a standard deviation of 7 , then  95%  of the scores will fall in which interval?

Accepted Answer

A)   [72,86] 
B)   [58,100] 
C)   [68.5,89.5] 
D)   [65,93] 
E)   [75,83] 
A)   [72,86] 
B)   [58,100] 
C)   [68.5,89.5] 
D)   [65,93] 
E)   [75,83]

Question 7

Find the standard deviation and variance of the scores on a final exam.
 65,88,83,80,78,90,92,85,74,70,95,62

Accepted Answer

Standard d

Question 8

The table below shows the tuition fee for one semester at a certain university.
$\begin{array}{|l|l|l|l|l|l|}
\hline \text { Year } & 2002 & 2003 & 2004 & 2005 & 2006 \
\hline \text { Cost } & 5500 & 5600 & 6000 & 6300 & 6700 \
\hline
\end{array}$
Complete a line graph that shows this university's tuition fee trend.

B. Calculate  r . Does the data show strong positive correlation?

Accepted Answer

The answer of  The table below shows the tuition...

Question 9

Find the mean, median, and variance. If necessary, round to the nearest hundredth.

Accepted Answer

Mean:  54.

Question 10

Make a histogram of the data, using interval widths of 10 points.
$\begin{array}{|c|c|c|c|c|c|c|c|}
\hline \text { Student } & \text { Al } & \text { Barry } & \text { Chen } & \text { Doris } & \text { Ella } & \text { Fred } & \text { Geoff } \
\hline \text { Score } & 69 & 85 & 73 & 78 & 62 & 82 & 55 \
\hline
\end{array}$

$\begin{array}{|c|c|c|c|c|c|c|c|}
\hline \text { Student } & \text { Harold } & \text { Ingrid } & \text { Jay } & \text { Kay } & \text { Leon } & \text { Matt } & \text { Nguyen } \
\hline \text { Score } & 79 & 67 & 84 & 75 & 95 & 87 & 91 \
\hline
\end{array}$

Accepted Answer

The answer of Make a histogram of the data, using...

Question 11

A computer password is 6 entries long. If the password must have 3 letters followed by 3 numbers with repetition of numbers and/or letters permitted, how many different passwords are possible?

Accepted Answer

The answer of A computer password is 6 entries long....

Question 12

The third and fifth terms of a geometric sequence are 2 and 32, respectively. Find explicit and recursive formulas for the sequence.

Accepted Answer

Explicit:

Question 13

Using the binomial theorem, expand the binomial $(3 x+y)^{4}$

Accepted Answer

The answer of Using the binomial theorem, expand the binomial...

Question 14

Find the coefficient of the $x^{3} y^{4}$ term in the expansion of $(x+y)^{7}$

Accepted Answer

A)  3 
B)  4 
C)  $7 !$ 
D)  35 
E)  210 
A)  3 
B)  4 
C)  $7 !$ 
D)  35 
E)  210

Question 15

Find the fifteenth term of $(x+2 y)^{20}$ where $x^{20}$ is labelled the zeroth term.

Accepted Answer

The answer of Find the fifteenth term of $(x+2 y)^{20}$...

Question 16

A computer randomly selects a number from 1 through 50 . Two selections are made by the computer to create an ordered pair of numbers. 2500 elements are in the sample space for this experiment
-For the experiment above , what is the probability that the computer will not select the same number in both selections?

Accepted Answer

The answer of A computer randomly selects a number from...

Question 17

There are 85 students in a college mathematics class. Five students are chosen to work on a project together. How many different groups of five students are there in this class?

Accepted Answer

The answer of There are 85 students in a college...

Question 18

How many different groups of officers  -  president, vice-president, treasurer, and secretary - can be formed from an organization with 45 members?

Accepted Answer

The answer of How many different groups of officers ...

Question 19

Write the series in summation notation and find the sum, assuming the suggested pattern continues.
$-5+2+9+16+\ldots+177$

Accepted Answer

The answer of Write the series in summation notation and...

Question 20

Two dice are rolled. Find the probability of rolling a sum greater than 6.

Accepted Answer

The answer of Two dice are rolled. Find the probability...

Which one of the following sequences is divergent?

A hoagie consists of a roll, one type of meat, one type of cheese, and three different toppings. If there are 5 kinds of rolls, 5 kinds of meat, 4 kinds of cheese, and 9 toppings from which to choose, how many different hoagies can be built?

Write the series in summation notation and find the sum, assuming the suggested pattern continues. $6+2+\frac{2}{3}+\frac{2}{9}+\ldots+\frac{2}{729}$

Write the statements P₁, P_k , and P_k+1 for the equation $1(1 !)+2(2 !)+\cdots+n(n !)=(n+1) !-1$ as if you were writing a proof by mathematical induction. Do not write a proof.

If the scores on a certain exam are normally distributed with a mean of 79 and a standard deviation of 7 , then 95% of the scores will fall in which interval?

Find the standard deviation and variance of the scores on a final exam. 65,88,83,80,78,90,92,85,74,70,95,62

The table below shows the tuition fee for one semester at a certain university. Year 2002 2003 2004 2005 2006 Cost 5500 5600 6000 6300 6700 Complete a line graph that shows this university's tuition fee trend. B. Calculate r . Does the data show strong positive correlation?

Find the mean, median, and variance. If necessary, round to the nearest hundredth.

A computer password is 6 entries long. If the password must have 3 letters followed by 3 numbers with repetition of numbers and/or letters permitted, how many different passwords are possible?

The third and fifth terms of a geometric sequence are 2 and 32, respectively. Find explicit and recursive formulas for the sequence.

Using the binomial theorem, expand the binomial $(3 x+y)^{4}$

Find the coefficient of the $x^{3} y^{4}$ term in the expansion of $(x+y)^{7}$

Find the fifteenth term of $(x+2 y)^{20}$ where $x^{20}$ is labelled the zeroth term.

There are 85 students in a college mathematics class. Five students are chosen to work on a project together. How many different groups of five students are there in this class?

How many different groups of officers - president, vice-president, treasurer, and secretary - can be formed from an organization with 45 members?

Write the series in summation notation and find the sum, assuming the suggested pattern continues. $-5+2+9+16+\ldots+177$

Two dice are rolled. Find the probability of rolling a sum greater than 6.

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

An Introduction to Calculus: Limits, Derivatives, and Integrals

P Prerequisites

Mathematical Problem Set

Filters

Exam 9: Discrete Mathematics

Which one of the following sequences is divergent?

A hoagie consists of a roll, one type of meat, one type of cheese, and three different toppings. If there are 5 kinds of rolls, 5 kinds of meat, 4 kinds of cheese, and 9 toppings from which to choose, how many different hoagies can be built?

Write the series in summation notation and find the sum, assuming the suggested pattern continues. 6+2+23+29+…+27296+2+\frac{2}{3}+\frac{2}{9}+\ldots+\frac{2}{729}6+2+32​+92​+…+7292​

Write the statements P1, Pk , and Pk+1 for the equation 1(1!)+2(2!)+⋯+n(n!)=(n+1)!−11(1 !)+2(2 !)+\cdots+n(n !)=(n+1) !-11(1!)+2(2!)+⋯+n(n!)=(n+1)!−1 as if you were writing a proof by mathematical induction. Do not write a proof.

If the scores on a certain exam are normally distributed with a mean of 79 and a standard deviation of 7 , then 95% of the scores will fall in which interval?

Find the standard deviation and variance of the scores on a final exam. 65,88,83,80,78,90,92,85,74,70,95,62

The table below shows the tuition fee for one semester at a certain university. Year 2002 2003 2004 2005 2006 Cost 5500 5600 6000 6300 6700 Complete a line graph that shows this university's tuition fee trend. B. Calculate r . Does the data show strong positive correlation?

Find the mean, median, and variance. If necessary, round to the nearest hundredth.

Make a histogram of the data, using interval widths of 10 points. Student Al Barry Chen Doris Ella Fred Geoff Score 69 85 73 78 62 82 55 Student Harold Ingrid Jay Kay Leon Matt Nguyen Score 79 67 84 75 95 87 91

A computer password is 6 entries long. If the password must have 3 letters followed by 3 numbers with repetition of numbers and/or letters permitted, how many different passwords are possible?

The third and fifth terms of a geometric sequence are 2 and 32, respectively. Find explicit and recursive formulas for the sequence.

Using the binomial theorem, expand the binomial (3x+y)4(3 x+y)^{4}(3x+y)4

Find the coefficient of the x3y4x^{3} y^{4}x3y4 term in the expansion of (x+y)7(x+y)^{7}(x+y)7

Find the fifteenth term of (x+2y)20(x+2 y)^{20}(x+2y)20 where x20x^{20}x20 is labelled the zeroth term.

There are 85 students in a college mathematics class. Five students are chosen to work on a project together. How many different groups of five students are there in this class?

How many different groups of officers - president, vice-president, treasurer, and secretary - can be formed from an organization with 45 members?

Write the series in summation notation and find the sum, assuming the suggested pattern continues. −5+2+9+16+…+177-5+2+9+16+\ldots+177−5+2+9+16+…+177

Two dice are rolled. Find the probability of rolling a sum greater than 6.

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

An Introduction to Calculus: Limits, Derivatives, and Integrals

P Prerequisites

Mathematical Problem Set

Filters

Write the series in summation notation and find the sum, assuming the suggested pattern continues. $6+2+\frac{2}{3}+\frac{2}{9}+\ldots+\frac{2}{729}$

Write the statements P₁, P_k , and P_k+1 for the equation $1(1 !)+2(2 !)+\cdots+n(n !)=(n+1) !-1$ as if you were writing a proof by mathematical induction. Do not write a proof.

Using the binomial theorem, expand the binomial $(3 x+y)^{4}$

Find the coefficient of the $x^{3} y^{4}$ term in the expansion of $(x+y)^{7}$

Find the fifteenth term of $(x+2 y)^{20}$ where $x^{20}$ is labelled the zeroth term.

Write the series in summation notation and find the sum, assuming the suggested pattern continues. $-5+2+9+16+\ldots+177$