A shape has Symmetry if it can be folded about a line so that
its two parts match exactly. Indeed this is the definition of Symmetries of a Graph and the line is called as axis oF summetry of the graph.

Question

asked 2020-10-28

a. In how many ways can the letters in the word CARLETON be arranged so that it contains either CA or AC as sub-words?

asked 2021-01-17

American automobiles produced in 2012 and classified
as “large” had a mean fuel economy of 19.6 miles per
gallon with a standard deviation of 3.36 miles per gallon.
A particular model on this list was rated at 23 miles per
gallon, giving it a z-score of about 1.01. Which statement
is true based on this information?
A) Because the standard deviation is small compared to
the mean, a Normal model is appropriate and we can
say that about 84.4% of “large” automobiles have a
fuel economy of 23 miles per gallon or less.
B) Because a z-score was calculated, it is appropriate
to use a Normal model to say that about 84.4% of
“large” automobiles have a fuel economy of 23 miles
per gallon or less.
C) Because 23 miles per gallon is greater than the mean
of 19.6 miles per gallon, the distribution is skewed
to the right. This means the z-score cannot be used to
calculate a proportion.D) Because no information was given about the shape of
the distribution, it is not appropriate to use the z-score
to calculate the proportion of automobiles with a fuel
economy of 23 miles per gallon or less.
E) Because no information was given about the shape
of the distribution, it is not appropriate to calculate a
z-score, so the z-score has no meaning in this situation.

asked 2021-01-31

Use symbols to write the logical form of the following arguments. If valid, iden-
tify the rule of inference that guarantees its validity. Otherwise, state whether the
converse or the inverse error has been made.
If you study hard for your discrete math final you will get an A.
Jane got an A on her discrete math final.
‘Therefore, Jane must have studied hard.

asked 2020-12-15

Two disks are mounted (like a merry-go-round) on low-frictionbearings on the same axle and can be brought together so that theycouple and rotate as one unit. The first disk, withrotational inertia 3.30 about its central axis, is set spinning counterclock wise at 450 rev/min. The second disk, withrotational inertia 6.60 about its central axis, is set spinningcounterclockwise at 900 rev/min. They then couple together. (a.) What is their angular speed aftercoupling? If instead the second disk is set spinningclockwise at 900 rev/min, what are their (b.) angular speed and(c.) direction of rotation after they couple together?

asked 2021-03-11

Give an example of a poset which has exactly one maximal element but does not have a greatest element.

asked 2021-02-25

Researchers have asked whether there is a relationship between nutrition and cancer, and many studies have shown that there is. In fact, one of the conclusions of a study by B. Reddy et al., “Nutrition and Its Relationship to Cancer” (Advances in Cancer Research, Vol. 32, pp. 237-345), was that “...none of the risk factors for cancer is probably more significant than diet and nutrition.” One dietary factor that has been studied for its relationship with prostate cancer is fat consumption. On the WeissStats CD, you will find data on per capita fat consumption (in grams per day) and prostate cancer death rate (per 100,000 males) for nations of the world. The data were obtained from a graph-adapted from information in the article mentioned-in J. Robbins’s classic book Diet for a New America (Walpole, NH: Stillpoint, 1987, p. 271). For part (d), predict the prostate cancer death rate for a nation with a per capita fat consumption of 92 grams per day.
a) Construct and interpret a scatterplot for the data.
b) Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c)-(f).
c) Determine and interpret the regression equation.
d) Make the indicated predictions.
e) Compute and interpret the correlation coefficient.
f) Identify potential outliers and influential observations.

asked 2021-01-05

Let \(\displaystyle{A}_{{{2}}}{A}_{{{2}}}\) be the set of all multiples of 2 except for 2.2. Let \(\displaystyle{A}_{{{3}}}{A}_{{{3}}}\) be the set of all multiples of 3 except for 3. And so on, so that \(\displaystyle{A}_{{{n}}}{A}_{{{n}}}\) is the set of all multiples of nn except for n,n, for any \(\displaystyle{n}\geq{2}.{n}\geq{2}\). Describe (in words) the set \(\displaystyle{A}_{{{2}}}\cup{A}_{{{3}}}\cup{A}_{{{4}}}\cup\ldots\)

asked 2020-12-25

Im confused on this question for Discrete Mathematics.

Let \(\displaystyle{A}_{{{2}}}\) be the set of all multiples of 2 except for 2. Let \(\displaystyle{A}_{{{3}}}\) be the set of all multiples of 3 except for 3. And so on, so that \(\displaystyle{A}_{{{n}}}\) is the set of all multiples of n except for n, for any \(\displaystyle{n}\geq{2}\). Describe (in words) the set \(\displaystyle{A}_{{{2}}}\cup{A}_{{{3}}}\cup{A}_{{{4}}}\cup\ldots\).

Let \(\displaystyle{A}_{{{2}}}\) be the set of all multiples of 2 except for 2. Let \(\displaystyle{A}_{{{3}}}\) be the set of all multiples of 3 except for 3. And so on, so that \(\displaystyle{A}_{{{n}}}\) is the set of all multiples of n except for n, for any \(\displaystyle{n}\geq{2}\). Describe (in words) the set \(\displaystyle{A}_{{{2}}}\cup{A}_{{{3}}}\cup{A}_{{{4}}}\cup\ldots\).

asked 2020-11-10

For the following, write your list in increasing order, separated by commas.

a, List the first 10 multiples of 8.

b. LIst the first 10 multiples on 12.

c. Of the lists you produced in parts a. and b., list the multiples that 8 and 12 have in common.

d. From part c., what is the smallest multiple that 8 and 12 have in common.

a, List the first 10 multiples of 8.

b. LIst the first 10 multiples on 12.

c. Of the lists you produced in parts a. and b., list the multiples that 8 and 12 have in common.

d. From part c., what is the smallest multiple that 8 and 12 have in common.

asked 2021-02-09

Polychlorinated biphenyls (PCBs), industrial pollutants, are known to be carcinogens and a great danger to natural ecosystems. As a result of several studies, PCB production was banned in the United States in 1979 and by the Stockholm Convention on Persistent Organic Pollutants in 2001: One study, published in 1972 by R. Risebrough, is titled “Effects of Environmental Pollutants Upon Animals Other Than Man”. In that study, 50 Anacapa pelican eggs were collected and measured for their shell thickness, in millimetres (mm), and concentration of PCBs, in parts per million (ppm).
a) Obtain a scatterplot for the data.
b) Decide whether finding a regressimz line for the data is reasonable. If so, then also do parts (c)-(f).
c) Determine and interpret the regression equation for the data.
d) Identify potential outliers and influential observations.
e) In case a potential outlier is present, remove it and discuss the effect.
f) In case a potential influential observation is present, remove it and discuss the effect.