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Mumz [18]
2 years ago
7

Need assistance with the question attached

Mathematics
1 answer:
natulia [17]2 years ago
6 0

Answer:

x = \frac{4\pi }{9},\frac{10\pi }{9}

Step-by-step explanation:

Given equation is,

\sqrt{3}\text{tan}(\frac{2x}{3})+1=0

By solving this equation,

\text{tan}(\frac{2x}{3})=-\frac{1}{\sqrt{3}}

x=\frac{2}{3}\times \text{tan}^{-1}(-\frac{1}{\sqrt{3}}) [tangent of any angle is negative in IInd and IVth quadrants]

x = \frac{2}{3}\times (\frac{2\pi }{3}), \frac{2}{3}\times (\frac{5\pi}{3})

x = \frac{4\pi }{9},\frac{10\pi }{9}

Therefore, value of x in the interval of [0, 2π] are \frac{4\pi }{9},\frac{10\pi }{9}.

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A lathe is set to cut bars of steel into lengths of 6 cm. The lathe is considered to be in perfect adjustment if the average len
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Answer:

t=\frac{5.97-6}{\frac{0.4}{\sqrt{93}}}=-0.723    

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Step-by-step explanation:

Information provided

\bar X=5.97 represent the sample mean for the length

s=0.4 represent the sample standard deviation

n=93 sample size  

\mu_o =6 represent the value that we want to test

\alpha=0.05 represent the significance level

t would represent the statistic  

p_v represent the p value for the test

System of hypothesis

We need to conduct a hypothesis in order to check if the lathe is in perfect adjustment (6cm), then the system of hypothesis would be:  

Null hypothesis:\mu = 6  

Alternative hypothesis:\mu \neq 6  

since we don't know the population deviation the statistic is:

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

Replacing in formula (1) we got:

t=\frac{5.97-6}{\frac{0.4}{\sqrt{93}}}=-0.723    

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P value

The degrees of freedom are given by:

df=n-1=93-1=92  

Since is a two tailed test the p value would be:  

p_v =2*P(t_{(92)}  

Since the p value is very high we don't have enough evidence to conclude that the true mean for the lengths is different from 6 cm.

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