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1.(1) The claim by a weight loss Company is that on average, the client will lose 10 pounds over ...

first 2 weeks. 50 people who joined the programme are sampled, their weight loss is 9 pounds with a standard deviation of 2.8 pounds. Can we conclude at the .05 level that a person joining the programme will lose less than 10 pounds?
(2) The following is a random sample of 90-day futures prices in dollars for 1 troy oz. of silver from The Wall Street Journal issues in May and June of 1997: 4.74, 4.77, 4.87, 4.91, 4.83, 4.72, 4.92, 4.86, 4.97, 4.71, 4.90, 4.93, 4.75, 4.88, 4.79, 4.83, 4.89.
Required:
a. Calculate the mean
b. Median
c. Standard deviation of the 90-day future price of silver data
(3) A mining company needs to estimate the average amount of copper ore per ton mined. A random sample of 50 tons gives a sample mean of 146,75 pounds. The population standard deviation is assumed to be 35.2 pounds.
Required:
a. Give a 95% confidence interval for the average amount of copper in the population of tons mined.
b. Give a 90% confidence interval for the average amount of coper per ton
c. Give a 99% confidence interval for the average amount of coper per ton
(4) An e-commerce Website gets 2,385 visitors on a particular day. Among these, 1790 visitors explore the products by looking at more pages at the site. Among these 1790 visitors who explore the products, 387 make a purchase.
Required:
a. If a visitor chosen at random from all those who visited the site, what is the probability that the visitor explored the products
b. If a visitor is chosen at random from all those who visited the site, what is the probability that the visitor made a purchase.
c. If a visitor is chosen at random from all those who explored the products, what is the probability that the visitor made a purchase.
d. Which of the preceding three probabilities is relevant to the design of the home page that leads to product page.

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infants using their formula brand vs. a competitors. A sample of 40 babies using their product revealed a mean weight gain of 7.6 lbs in the first 3 months after birth. The standard deviation of the Gibbs sample is 2.3 lbs. A sample of 55 babies using the competitors brand had a mean increase of 8.1 lbs with a standard deviation of 2.9 lbs. At the 5% significance level, can we conclude that babies using Gibbs brand gained less weight?

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aw scores have a mean of 40 and a standard deviation of 5. Assuming these raw scores form a normal distribution:
a) What number represents the 55th percentile (what number separates the lower 55% of the distribution)?

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rd deviation of 3.2 hours. A sample of 35 high school seniors is selected. Find the following values, if possible. Please round your answers to four decimal places. If you should not find a probability, please write NA for your answer.
What is the probability that the sample mean studying time is between 4 and 5 hours?
What is the probability that the sample mean studying time is less than 6 hours?
What is the probability that the sample mean studying time is more than 8.5 hours?

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a mean of $321,000 and a standard deviation of $38,000. Estimate the percentage of homes in this community with selling prices
(a) between $283,000 and $359,000.
%
(b) above $359,000.
%
(c) below $207,000.
%
(d) between $207,000 and $359,000.
%

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63 and a standard deviation of 2. Estimate the percentage of scores that were
(a) between 59 and 67.
%
(b) above 69.
%
(c) below 59.
%
(d) between 57 and 67.
%

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7.A population has a standard deviation of σ = 29 and a mean of μ = 155. On average, how ...

ence should exist between the population mean and the sample mean for n = 10 scores randomly selected from the population?

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e difference between reported height and actual height was calculated.
You're testing the claim that the mean difference is greater than 0.6.
From the sample, the mean difference was 0.7, with a standard deviation of 0.74.
Calculate the test statistic, rounded to two decimal places
Incorrect

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2 ounces of fluid. if the standard deviation of fill is 2.1 ounces, what should the mean setting of the machines be if the fills are normally distributed? What percentage of the bottles then filled contain greater than 60 ounces?

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illion dollars. If the mean revenue was 50 million dollars and the data has a standard deviation of 15 million, find the percentage. Assume that the distribution is normal. Round your answer to the nearest hundredth.

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ard deviation of 18 million. Find the percentage of companies with revenue greater than 95 million dollars. Assume that the distribution is normal. Round your answer to the nearest hundredth.

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n of μ= 160.4 and a standard deviation of σ = 9.0760. If all possible samples of size 13 are drawn from this population, find the percentage of them that would have means between 154 centimeters and 156 centimeters?

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n of μ= 160.4 and a standard deviation of σ=9.0760. If all possible samples of size 13 are drawn from this population, find the percentage of them that would have means between 154 centimeters and 156 centimeters?

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than 7.33 is 0.6738, then what is the mean of x?

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dard deviation of 0.02cm and a mean of 8.4cm. the factory rejects pistons that have a diamter less than 8.38 and more than 8.42. In a production of 500 pistons, how many would be expected to be unacceptable

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dard deviation of 0.02cm and a mean of 8.4cm. the factory rejects pistons that have a diamter less than 8.38 and more than 8.42. In a production of 500 pistons, how many would be expected to be unacceptable

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mpirical rule to answer the following question.
A quantitative data set of size 100 has mean 40 and standard deviation 6 . Approximately how many observations lie between 22 and 58?

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rt. Extensive data collection has shown that the noise level (measured from a specific point on the ground) is a variable following a normal distribution with a mean of 95 decibels, and a standard deviation of 10 decibels. The noise levels from jet to jet can be considered to be independent.
What percent of jets have noise levels between 80 and 100 decibels ?

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ime of bulbs follows a normal distribution.
(a) Calculate the mean and standard deviation of the distribution.

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and a standard deviation of 0.55 kg.
If researchers take random samples of 25 newborn babies, the sample means will have a mean of _____kg, and a standard deviation of _____kg.

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nd standard deviation 6 inches.
A button hyperlink to the SALT program that reads: Use SALT.
(a) What is the probability that an 18-year-old man selected at random is between 64 and 66 inches tall? (Round your answer to four decimal places.)
Correct: Your answer is correct.
(b) If a random sample of seven 18-year-old men is selected, what is the probability that the mean height x is between 64 and 66 inches? (Round your answer to four decimal places.)
Incorrect: Your answer is incorrect.
(c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?
The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.
The probability in part (b) is much higher because the standard deviation is larger for the x distribution.
The probability in part (b) is much higher because the mean is smaller for the x distribution.
The probability in part (b) is much higher because the mean is larger for the x distribution.
The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.

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time a bag of chips remains fresh on the grocery shelf. A random sample of potato chips with the old design of the bag was compared to a random sample of potato chips with the new bag. Summary statistics pertaining to the number of days the chips remained fresh are given below. At a 95% level of confidence (α = .05), the company wishes to investigate if the new bag has an increased freshness time over the old bag.
Summary Statistics
New Bag Old Bag
(Sample #1) (Sample #2)
Sample Mean 21.2 days 20.8 days
Sample Standard Deviation 2.5 days 2.8 days
Sample Size 45 50
What is the correct Null and Alternate Hypothesis?
Select one:
a. H_0: \mu_d>0\;\; H_1: \mu_d < 0
b. H_0: \mu_1>\mu_2 \;\;H_1:\mu_1 \leq \mu_2
c. H_0: \mu_d =0\;\; H_1: \mu_d < 0
d. H_0: \mu_1\leq\mu_2 \;\;H_1:\mu_1 > \mu_2

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ches and standard deviation 5.6 inches. What percentage of years will have an annual rainfall of less than 44 inches? What percentage of years will have an annual rainfall of more than 38 inches? What percentage of years will have an annual rainfall of between 37 inches and 42 inches?

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Construct a confidence level of 95% for the population mean. In your solution, show all steps as discussed in our class notes.

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with a mean life of 3000 hours and a standard deviation of 400 hours.
What is the probability that a randomly selected light bulb last for more than 4000 hours?

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d deviation of 18. What is the minimum score needed to be in the top 10% of the scores on the test? Carry your intermediate computations to at least four decimal places, and round your answer to one decimal place.

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ehalf of their customers, portfolio managers give a questionnaire to new customers to measure their desire to take financial risks. The scores on the questionnaire are approximately normally distributed with a mean of 49 and a standard deviation of 14 The customers with scores in the bottom 10% are described as "risk averse." What is the questionnaire score that separates customers who are considered risk averse from those who are not? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.

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Since he became the president, did President Trump act with the transparency and the integrity
that you expect from a president?” 675 voters responded the poll and 351 responded “YES.”
Assume that 40% of the U.S. population supports Trump.
a. Define a binary random variable, Y, for supporting Trump (Y=1) vs. not (Y=0).
Calculate the population mean (????????) and variance (????????
2
) for supporting Trump.
b. Calculate the sample mean ????̅ and the sample standard deviation of ????̅ (????????̅ ) for the poll.
c. Calculate the standard error of ????̅ and construct a 95% confidence interval from the
poll using ????̅ and its sample standard error.
d. Conduct a two-sided hypothesis test at 5% significance level to determine whether
40% of the U.S. population supports Trump. State the null and the alternative
hypotheses, calculate the test statistics and the associated p-value, and conclude. Is
the Fox News survey reliable? Why? Why Not?
e. Suppose that you wanted to design a survey that had a margin of error of at most 1%.
That is: the difference between the upper bound and the lower bound of the
confidence interval should be a maximum of 2 percentage points. For example, for
????̅ = 0.52 you are aiming for the 95 % CI to be [0.51 0.53].
How large should n be if the survey uses simple random sampling?

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on with mean 81 and standard deviation 22. I have been asked to find the probability that X (bar) is greater than 86 and to find the 85th percentile of this data set

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30.It has a mean score of 100 with a standard deviation of 20 points. if the test scores are normally ...

istributed, what percentage of scores would be expected to fall between 60 and 130?

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ution with a mean of 267 days and a standard deviation of 9 days.
(a) What is the minimum pregnancy length that can be in the top 8% of pregnancy lengths?
(b) What is the maximum pregnancy length that can be in the bottom 6% of pregnancy lengths?

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32.A data set is normally distributed with a mean of 42 and a standard deviation of 9. What percent of ...

the data values lie between 15 and 60?

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standard deviation $100. Approximately what percentage of the painting have value between $800 and $1000?

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.Assume that the hourly operating cost for the airplane is normally distributed. If 11% of the hourly operating costs are 1800$ or less , what is the standard deviation of hourly operating cost ?

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rd deviation of 20. Determine the value of x such that 5% of the values are less than x.

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37.A data set has a mean of 85 and a standard deviation of 4 and is distributed normally. What is ...

robability that a randomly selected data value is less than 72?

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he National Center for Health Statistics reports that
the mean systolic blood pressure for males 35 to 44 years of age is 128 and
the standard deviation in this population is 15. The medical director of a
company looks at the medical records of 72 company executives in this age
group and finds that the mean systolic blood pressure in this sample is X =
126.07. Is this evidence that executive blood pressures differ from the national
average? Conduct a hypothesis test to answer this question using α = 0.05.

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nt
City is $125. A random sample of 25 Quant City households yielded a mean of $133 and a standard
deviation of $22. Assume that weekly household expenditures on groceries in Quant City are normally
distributed. What is the conclusion of testing the analyst’s belief at the .05 level of significance?

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40.Vanessa found that the average for all students who feel that good manners are necessary to ...

75 with a sample standard deviation of 15; (this data is normally
distributed). If she took a random sample of 64 students that shared this
view
Find:
a) The probability that the average number of students that share this view is more than 78 students.
b) The probability that the mean number of students that share this view is
between 65 and 72

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of 45 inches and a standard deviation of 8 inches. What is the probability
a randomly-selected student is taller than 50 inches?

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ple mean is found to be x bar =61 and the sample standard deviation is found to be s = 16. construct a 90% confidence interval about the pop mean. what is the upper and lower bounds?

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100 and a standard deviation of 15.
a. What is the probability that a given applicant will score over 100?
b. Determine the probability that a random applicant scores over 135.
c. Determine the probability that an applicant scores between 85 and 135.

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, a standard deviation of $1 would be considered large if it is describing the variability from store to store in the price of an ice cube tray. On the other hand, a standard deviation of $1 would be considered small if it is describing store-to-store variability in the price of a particular brand of freezer. A quantity designed to give a relative measure of variability is the coefficient of variation. Denoted by CV, the coefficient of variation expresses the standard deviation as a percentage of the mean. It is defined by the formula CV = 100(s/ x ). Consider two samples. Sample 1 gives the actual weight (in ounces) of the contents of cans of pet food labeled as having a net weight of 8 oz. Sample 2 gives the actual weight (in pounds) of the contents of bags of dry pet food labeled as having a net weight of 50 lb. There are weights for the two samples.
Sample 1 7.7 6.8 6.5 7.2 6.5
7.7 7.3 6.6 6.6 6.1
Sample 2 50.7 50.9 50.5 50.3 51.5
47 50.4 50.3 48.7 48.2
(a) For each of the given samples, calculate the mean and the standard deviation. (Round all intermediate calculations and answers to five decimal places.)
For sample 1
Mean
Standard deviation
For sample 2
Mean
Standard deviation
(b) Compute the coefficient of variation for each sample. (Round all answers to two decimal places.)
CV1
CV2

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consumes each year is 196 with a standard deviation of
22 pounds (Source: American Dietetic Association). If a sample of 50 individuals is randomly selected, find
the probability that the mean of the sample will be less than 200 pounds.

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10,4,10,0 = 24/4 = 6 average return
Don’t add up because it 0
Square the number:
10-6=4^2= 16
4-6 = -2^2= 4
10-6=4^2 = 16
0-6 = -6^2 = 36
=72 sum of square of diff of mean
/3=24
Square root 24 = 4.9
24= variance
4.9= standard deviation
20,2,2,0 = 24/4= 6 average return
20-6 = 14 = 196
2-6 = -4 =16
2-6 = -4 = 16
0-6 = -6 = 36
= 256 – variance
Square root 256 = 14.6 = standard deviation

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ulation standard deviation is 4. Conduct the following test of hypothesis using the 0.05 significance level.
H0: μ = 43
H1: μ ≠ 43
find the p value (round z value to 2 decimals and final answer 4 decimal place)

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d a standard deviation of 43.
What percentage of the students scored between 418 and 504 on the exam? (Give your answer to 3 significant figures.)

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d balls for all players is normally distributed with a mean of 87 mph and a standard deviation of 2.5 mph. For any sample of individual batted balls hit by one player, the standard deviation of exit velocity of those batted balls around this particular player's true-talent AEV is 9 mph. At this point in the season, Marco Masher has a total of 10 batted balls with an average exit velocity of 96 mph. Given only this information, the best estimate for his "true talent" exit velocity is closest to which whole number?

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de the printout below. Use these values as estimates of the mean and standard deviation found in the population of all low prices. Suppose that the low prices were normally distributed (regardless of what your data may indicate). Find the proportion of all low prices that would be between $20 and $50 in the population. I want you to show your work. To receive full credit, you should include pictures of the normal curve (labeled with both x and z-values) with the pertinent probabilities shaded in the picture

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e effect of lowering the heart rate. For a sample of 50 medical students whose pulse was measured after 6 weeks of taking the drug, the mean heart rate was 70 beats per minute (bpm). If the mean heart rate for a population was 72 bpm with a standard deviation of 12, can the psychiatrist conclude that the new drug lowers heart rate significantly? (Set the alpha level at .05)
Complete all steps of the hypothesis test to test the null hypothesis.

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survey of all their employees found that employees were required to respond to an average of 50 work-related emails per week with a standard deviation of 1.5 emails per week. However, an employee advocacy group believes the average number of work-related emails Indigo Insurance Company employees are now required to respond to is more than 50 emails per week.
To investigate this further, the employee advocacy group took a random sample of 20 staff employed by Indigo Insurance Company during the second week of March 2018,and asked these employees to record the number of work-related emails to which they were required to respond.
(b). What does the highlighted section of the distribution in Figure 1 represent?
(c). The random sample of 20 employees of Indigo Insurance Company taken by the employee advocacy group turned out to have a mean of 50.8 work-related emails to respond to in that week. Does this sample look like it belongs to the sampling distribution displayed in Figure 1? Justify your answer.
(d). Given the sample was randomly selected and that the number of work-related emails each employee was required to respond to was recorded accurately, what conclusion can we reach from part (c)?
To answer questions (b) to (d), consider the sampling distribution shown in Figure 1.

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ion of 129.1 cm cubed. Use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such data, would a brain volume of 1373.5 cm cubed be significantly high?
1. Significantly low values are
____ cm cubed or lower.
2. Significantly high values are
_________ cm cubed or higher.
3.

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weighing between 140 lb and 191 lb. The new population of pilots has normally distributed weights with a mean of 145 lb and a standard deviation of 29.9 lb.
a. If a pilot is randomly selected, find the probability that his weight is between 140 lb and 191 lb.

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viduals differ from people in general in remembering threatening information. The memory performance of an individual for negative words was measured and was found to have a score of 48. The population average is 34 with a standard deviation of 9. At the 5% level of significance what should you conclude about whether clinically anxious individuals have a tendency to remember threatening words?
(a) Clearly state null and research hypotheses in terms of the mean scores on the memory performance on negative words, μ, of anxious individuals.
(b) What is the comparison distribution for the sample’s Z score?
(c) What are the cut-off values for a test with significance level 0.05?
(d) What is the observed Z score?
(e) What is your conclusion?
An educational psychologist was interested in whether children who grow up in bilingual settings have an advantage of distraction resistance compared with children in general. The distraction resistance test was administered to a randomly chosen child with bilingual upbringing background who was found to have a score of 69. The population average is 60 with a standard deviation of 3. Do children with bilingual upbringing background score higher on distraction resistance test than children in general? Use the 1% level of significance.
(a) Clearly state null and research hypotheses in terms of the mean scores on distraction resistance, μ, of children with bilingual upbringing.
(b) What is the comparison distribution for the sample’s Z score?
(c) What are the cut-off values for a test with significance level 0.01?
(d) What is the observed Z score?
(e) What is your conclusion?

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with a mean of 25 gm and a standard deviation of 5 gm.
(a) If the machine is used 500 times, approximately how many times will it be expected to dispense 30 gm or more of chilli sauce?
(b) How can you decrease this number to half? Give a numerical answer.
2. StarTech manufactures re sensors. They use a protective screen for their sensors to protect it from dust. The sensor becomes useless if the thickness of the screen exceeds 0.5 mm. They outsource the production of the screen to a di erent company that claims to manufacture screens with a mean thickness of 0.3 mm and a standard deviation of 0.1 mm.
(a) If 10000 screens are manufactured how many will be discarded because they are too thick?
(b) If screens less than 0.2 mm are too thin to be used, what is the probability that screens manufactured by the above company will be discarded because they are too thick or too thin? Show the result on a graph.
3. The amount of time that Sam spends playing the guitar is normally distributed with a mean of 15 hours and a standard deviation of 3 hours.
(a) Find the probability that he spends between 15 and 18 hours playing the guitar during a given week.
(b) What is the probability that he spends less than 3 hours playing the guitar during a given week?
4. Soon after he took oce in 1963, President Johnson was approved by 160 out of a sample of 200 Americans. With growing disillusionment over his Vietnam policy, by 1968 he was approved by only 70 out of a sample of 200 Americans.
(a) What is the 90% con dence interval for the percentage of all Americans who approved of Johnson in 1963? In 1968?
(b) What is the 90% con dence interval for the change?

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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics