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3 years ago

What is the solution to the following system of equations? -5x-4y=-4 25x+20y=20

1 answer:

5 0

Simplify
2nd one divide both sides by 5
5x+4y=4
hmm, seems familliar
times it by -1
-5x-4y=-4
same as other one

they are the same line
therefor the solution set is all the points on the line -5x-4y=-4 or y=(-5/4)x+1

solution set is alll points on y=(-5/4)x+1 or 5x+4y=4

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Consumer complaints are frequently reported to the Better Business Bureau. Industries with the most complaints to the Better Bus

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Answer:

Let the complaints by Industry be CbI

CbI Frequency

Bank 26

Cable 44

Car 42

Cell 60

Collection 28

b) Percentages

CbI percentage (%)

Bank 13

Cable 22

Car 21

Cell 30

Collection 14

c) The industry with the highest number of complaints is the Cell Industry.

d) The Bar Chart is attached to this solution. It was constructed in the Ms Excel suite.

Step-by-step explanation:

a) The frequencies are simply the number of times each industry sector sent in a complaint. So, it's straight forward to present.

b) The percentage for each industry is done in comparison to the the total amount of complaints received.

Percentage for each industry = 100% × (Number of complaints from that industry)/(Total number of complaints)

Total amount of complaints received = 200

For Bank industry,

Percentage = 100% × (26/200) = 13%

For the Cable Industry,

Percentage = 100% × (44/200) = 22%

For Car industry,

Percentage = 100% × (42/200) = 21%

For Cell industry,

Percentage = 100% × (60/200) = 30%

For Collection industry,

Percentage = 100% × (28/200) = 14%

c) The industry with the highest number of complaints is the one with the highest frequency and percentage, and that is the Cell Industry.

d) The Bar Chart is attached to this solution. It was constructed in the Ms Excel suite.

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3 years ago

The sodium content of a popular sports drink is listed as 200 mg in a 32-oz bottle. Analysis of 20 bottles indicates a sample me

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Answer:

The sample does not contradicts the manufacturer's claim.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 200 mg

Sample mean, $\bar{x}$ = 211.5 mg

Sample size, n = 20

Alpha, α = 0.05

Sample standard deviation, s = 18.5 mg

a) First, we design the null and the alternate hypothesis for a two tailed test

$H_{0}: \mu = 200\\H_A: \mu \neq 200$

We use Two-tailed t test to perform this hypothesis.

b) Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$ Putting all the values, we have

$t_{stat} = \displaystyle\frac{211.5 - 200}{\frac{18.5}{\sqrt{20}} } = 2.7799$

c) Now,

$t_{critical} \text{ at 0.05 level of significance, 19 degree of freedom } = \pm 2.0930$

Since, the calculated t-statistic does not lie in the range of the acceptance region(-2.0930,2.0930), we reject the null hypothesis.

Thus, the sample does not contradicts the manufacturer's claim.

d) P-value = 0.011934

Since the p-value is less than the significance level, we reject the null hypothesis and accept the alternate hypothesis.

Yes, both approach the critical value and the p-value approach gave the same results.

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