Question 1

Sketch a boxplot for the data  . 
 $\begin{array}{l|l}
\text { Stem } & \text { Leaf } \
\hline 3 & 556 \
4 & 23368 \
5 & 235567 \
6 & 3444556 \
7 & 23455677
\end{array}$

Accepted Answer

The answer of Sketch a boxplot for the data ...

Question 2

The sequence  2,6,18,54, ....  is geometric.
(a) What is the common ratio of the sequence?
(b) What is a recursive rule for the  n th term $(n \geq 2)$ of the sequence?

Accepted Answer

The answer of The sequence  2,6,18,54, ....  is...

Question 3

Twenty-four students participated in a basketball contest. Each student took five shots. The number of baskets scored by each student is shown below. Find the mean, median, and mode for the data.
$\begin{array}{llllll}
4 & 3 & 3 & 4 & 5 & 3 \
2 & 3 & 2 & 5 & 5 & 5 \
1 & 2 & 5 & 3 & 3 & 4 \
0 & 2 & 5 & 1 & 3 & 5
\end{array}$

Accepted Answer

The answer of Twenty-four students participated in a basketball contest....

Question 4

A machine fills 16-ounce soda cans with a mean of  16.06  ounces of soda and a standard deviation of  0.03 . Approximately what percentage of the cans will actually contain less than the advertised less than the advertised 16 ounces of soda?

Accepted Answer

Using the Z-score formula, $Z = \frac{X - \mu}{\sigma}$, where $X = 16$ ounces, $\mu = 16.06$ ounces, and $\sigma = 0.03$ ounces, we find $Z = \frac{16 - 16.06}{0.03} = -2$. Looking up a Z-score of -2 in a standard normal distribution table gives us an area of approximately 2.5%, indicating that about 2.5% of the cans will contain less than 16 ounces of soda.

Question 5

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

The answer of A hoagie consists of a roll, one...

Question 6

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

The answer of Find the standard deviation and variance of...

Question 7

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 8

Use the formulas $\sum_{k=1}^{n} k=\frac{n(n+1)}{2}$  and
$\sum_{k=1}^{n} k^{2}=\frac{n(n+1)(2 n+1)}{6}$  to find the sum in terms
of $\text { n. } \sum_{k=1}^{n}\left(3 k^{2}-5 k+7\right)$

Accepted Answer

The answer of Use the formulas $\sum_{k=1}^{n} k=\frac{n(n+1)}{2}$  and
\(\sum_{k=1}^{n}...

Question 9

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

The answer of If the scores on a certain exam...

Question 10

What is the probability of obtaining exactly four heads
in eleven tosses of a fair coin?

Accepted Answer

The probability of obtaining exactly four heads in eleven tosses of a fair coin can be calculated using the binomial probability formula, which is $C(n, k) \cdot p^k \cdot (1-p)^{n-k}$, where $C(n, k)$ is the combination of n items taken k at a time, $p$ is the probability of success (getting a head in this case, which is 0.5), and $n-k$ is the number of failures. Here, $n=11$ and $k=4$, so $C(11, 4) = \frac{11!}{4!(11-4)!} = 330$, and $p=0.5$, thus the probability is $330\left(\frac{1}{2}\right)^{11}$.

Question 11

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 12

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 13

Which one of the following sequences is divergent?

Accepted Answer

The sequence $\{\sqrt[3]{n}\}$ is divergent because as $n$ approaches infinity, $\sqrt[3]{n}$ also approaches infinity, indicating that the sequence does not converge to a finite limit.

Question 14

Using the binomial theorem, expand the binomial $(2 x+y)^{5}$

Accepted Answer

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

Question 15

A magazine includes an insert in its January issue that asks readers to answer questions about the magazine's new cover design and layout and return the insert in the mail. Will this sample suffer any biases?

Accepted Answer

The answer of A magazine includes an insert in its...

Question 16

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

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

Question 17

Does correlation imply causation?

Accepted Answer

The answer of Does correlation imply causation?...

Question 18

How many different groups of officers  -  president, vice-president, treasurer, and secretary - can be formed from an organization with 35 members?

Accepted Answer

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

Question 19

Find the five-number summary and the range for the data in the stemplot below.
$\begin{array}{l|l}
\text { Stem } & \text { Leaf } \
\hline 3 & 556 \
4 & 23368 \
5 & 235567 \
6 & 3444556 \
7 & 23455677
\end{array}$

Accepted Answer

The answer of Find the five-number summary and the range...

Question 20

Determine whether the infinite geometric series converges. If it does converge, what is the sum?
$\frac{5}{4}+\frac{5}{16}+\frac{5}{64}+\ldots$

Accepted Answer

The answer of Determine whether the infinite geometric series converges....

Quiz 9: Discrete Mathematics

The sequence 2,6,18,54, .... is geometric. (a) What is the common ratio of the sequence? (b) What is a recursive rule for the n th term $(n \geq 2)$ of the sequence?

A machine fills 16-ounce soda cans with a mean of 16.06 ounces of soda and a standard deviation of 0.03 . Approximately what percentage of the cans will actually contain less than the advertised less than the advertised 16 ounces of soda?

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?

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

Use the formulas $\sum_{k=1}^{n} k=\frac{n(n+1)}{2}$ and $\sum_{k=1}^{n} k^{2}=\frac{n(n+1)(2 n+1)}{6}$ to find the sum in terms of $\text { n. } \sum_{k=1}^{n}\left(3 k^{2}-5 k+7\right)$

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?

What is the probability of obtaining exactly four heads in eleven tosses of a fair coin?

Which one of the following sequences is divergent?

Using the binomial theorem, expand the binomial $(2 x+y)^{5}$

A magazine includes an insert in its January issue that asks readers to answer questions about the magazine's new cover design and layout and return the insert in the mail. Will this sample suffer any biases?

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

Does correlation imply causation?

How many different groups of officers - president, vice-president, treasurer, and secretary - can be formed from an organization with 35 members?

Find the five-number summary and the range for the data in the stemplot below. $\begin{array}{l|l}\text { Stem } & \text { Leaf } \\\hline 3 & 556 \\4 & 23368 \\5 & 235567 \\6 & 3444556 \\7 & 23455677\end{array}$

Determine whether the infinite geometric series converges. If it does converge, what is the sum? $\frac{5}{4}+\frac{5}{16}+\frac{5}{64}+\ldots$

Quiz 9: Discrete Mathematics

Sketch a boxplot for the data . Stem Leaf 3556423368523556763444556723455677\begin{array}{l|l}\text { Stem } & \text { Leaf } \\\hline 3 & 556 \\4 & 23368 \\5 & 235567 \\6 & 3444556 \\7 & 23455677\end{array} Stem 34567​ Leaf 55623368235567344455623455677​​

The sequence 2,6,18,54, .... is geometric. (a) What is the common ratio of the sequence? (b) What is a recursive rule for the n th term (n≥2)(n \geq 2)(n≥2) of the sequence?

A machine fills 16-ounce soda cans with a mean of 16.06 ounces of soda and a standard deviation of 0.03 . Approximately what percentage of the cans will actually contain less than the advertised less than the advertised 16 ounces of soda?

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?

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

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?

What is the probability of obtaining exactly four heads in eleven tosses of a fair coin?

Which one of the following sequences is divergent?

Using the binomial theorem, expand the binomial (2x+y)5(2 x+y)^{5}(2x+y)5

A magazine includes an insert in its January issue that asks readers to answer questions about the magazine's new cover design and layout and return the insert in the mail. Will this sample suffer any biases?

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​

Does correlation imply causation?

How many different groups of officers - president, vice-president, treasurer, and secretary - can be formed from an organization with 35 members?

Determine whether the infinite geometric series converges. If it does converge, what is the sum? 54+516+564+…\frac{5}{4}+\frac{5}{16}+\frac{5}{64}+\ldots45​+165​+645​+…

The sequence 2,6,18,54, .... is geometric. (a) What is the common ratio of the sequence? (b) What is a recursive rule for the n th term $(n \geq 2)$ of the sequence?

Using the binomial theorem, expand the binomial $(2 x+y)^{5}$

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

Determine whether the infinite geometric series converges. If it does converge, what is the sum? $\frac{5}{4}+\frac{5}{16}+\frac{5}{64}+\ldots$