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snow_lady [41]
3 years ago
7

10. Find the range of possible values for the variable.

Mathematics
1 answer:
Lapatulllka [165]3 years ago
4 0

The range of possible values for the variable is x < 12

From the given figure, we can see that the side facing angle 30 degrees, is greater than the side facing angle 3x -6. Therefore the inequality expression is true based on the figure.

30 > 3x - 6

Swap sides

3x - 6 < 30

Add 6 to both sides

3x - 6 + 6 < 30 + 6

3x < 36

Divide both sides by 3

3x/3 < 36/3

x < 12

Hence the range of possible values for the variable is x < 12

Learn more on inequality expression here: brainly.com/question/24372553

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if it makes it easier for u, x/4 is the same as (1/4)x and y/3 is the same as (1/3)y

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The Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that the sales
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Answer:

We conclude that the mean number of calls per salesperson per week is more than 37.

Step-by-step explanation:

We are given that the Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that the sales representatives make an average of 37 sales calls per week on professors.

To investigate, a random sample of 41 sales representatives reveals that the mean number of calls made last week was 40. The standard deviation of the sample is 5.6 calls.

<em><u>Let </u></em>\mu<em><u> = true mean number of calls per salesperson per week.</u></em>

SO, <u>Null Hypothesis</u>, H_0 : \mu \leq 37   {means that the mean number of calls per salesperson per week is less than or equal to 37}

<u>Alternate Hypothesis,</u> H_A : \mu > 37   {means that the mean number of calls per salesperson per week is more than 37}

The test statistics that will be used here is <u>One-sample t test statistics</u> as we don't know about the population standard deviation;

                        T.S.  = \frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample mean number of calls made last week = 40

             s = sample standard deviation = 5.6 calls

             n = sample of sale representatives = 41

So, <em><u>test statistics</u></em>  =   \frac{40-37}{\frac{5.6}{\sqrt{41} } }  ~ t_4_0

                               =  3.43

Hence, the value of test statistics is 3.43.

<em>Now at 0.025 significance level, the t table gives critical value of 2.021 at 40 degree of freedom for right-tailed test. Since our test statistics is more than the critical value of t as 3.43 > 2.021, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.</em>

Therefore, we conclude that the mean number of calls per salesperson per week is more than 37.

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3 years ago
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