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snow_lady [41]
2 years ago
8

Janet an experienced shipping clerk can fill a certain order in 5 hours . Tom a new clerk needs 8 hours to do the same job. work

ing together how long will it take them to fill the order
Mathematics
1 answer:
aksik [14]2 years ago
7 0

Janet can fill a certain order in 5 hours, therefore she performs 1/5 of the order within 1 hour.

Tom needs 8 hours to do the same job, therefore he performs 1/8 of the order within 1 hour.

Working together, they make 1/5 + 1/8 orders within 1 hour.

Let <em>t</em> mean the number of hours they need. Then we have equation:

\left(\dfrac{1}{5}+\dfrac{1}{8}\right)t=1\\\\_{\text{use}\ \frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}}\\\\\dfrac{(1)(8)+(1)(5)}{(5)(8)}t=1\\\\\dfrac{8+5}{40}t=1\\\\\dfrac{13}{40}t=1\ \ \ \ |\text{multiply both sides by 40}\\\\13t=40\ \ \ \ |\text{divide both sides by 13}\\\\t=\dfrac{40}{13}\\\\t=3\dfrac{1}{13}\\\\Answer:\ 3\dfrac{1}{13}h=3h\ \dfrac{60}{13}min\approx3h\ 5min

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Step-by-step explanation:

1) Data given and notation  

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X=63 represent the lawyers had used some form of advertising for their business

\hat p=\frac{63}{200}=0.315 estimated proportion of lawyers had used some form of advertising for their business

p_o=0.25 is the value that we want to test

\alpha=0.05 represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

2) Concepts and formulas to use  

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Null hypothesis:p\leq 0.25  

Alternative hypothesis:p > 0.25  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.315 -0.25}{\sqrt{\frac{0.25(1-0.25)}{200}}}=2.123  

4) Statistical decision  

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The significance level provided \alpha=0.05. The next step would be calculate the p value for this test.  

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