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kenny6666 [7]
2 years ago
9

the sum of 3 times a number and twice the same number is less than 45.a. 3n + 2n < 45b. 3n + 2 > 45c. 3(n + 2) < 45d. 2

(n + 3) < 45
Mathematics
1 answer:
ludmilkaskok [199]2 years ago
4 0

Let be "n" the number mentioned in the exercise.

You need to remember that:

1. In Math word problems:

- The word "times" means multiplication.

- The word "twice" indicates that something is multiplied by 2.

- "Sum" is the result of an Addition.

2. In inequalities, "Less than" is represented with the following symbol:

Then, based on the above, you know that "3 times a number" can be expressed as:

3n

And "Twice the same number":

2n

Therefore, "The sum of 3 times a number and twice the same number is less than 45" can be represented with the following inequality:

3n+2n

The answer is: Option a.

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Answer:

Check the explanation

Step-by-step explanation:

(a)

H0: Population mean = 8.46

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The test statistic (t) is given by the following expression -

{t=\frac{\overline{x}-\mu_0}{s/\sqrt{n}}}

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The left-sided critical value from t-distribution (two-tailed) is -2.01. Thus the test statistic falls in the rejection region and we reject the null hypothesis at 95% confidence level and conclude that the population mean is different from 8.46 inches.

(b)

There are the following four assumptions for a single sample t-test.

The observations are in ratio scale.

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There should not be any significant outliers in the sample observations.

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(c)

The first assumption is true as the data is in inches. The second assumption cannot be tested now. It will depend upon the situation and study design which we assume as correct in this case. The third assumption is checked by plotting a box plot and finding the outliers. The final assumption can be checked using the Anderson-Darling normality test.

Kindly check the graphical table in the attached images below.

(d)

The data is normal (the p-value of Anderson-Darling test in > 0.05). However, two points in the Box plot are outliers though not grossly different from the entire sample data set. So, we conclude that the assumptions are valid in this case for conducting the t-test.

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