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pogonyaev
2 years ago
6

Math help please Let f(x)=x2+5 and g (x)=3x+4; find (g o f)(7); (g o f)(7)=; help me solve!! Please!

Mathematics
1 answer:
lorasvet [3.4K]2 years ago
5 0

f(x) = 2x

g(x) = x + 3

First let us find (fog)(x)

<span />

(fog)(x) = f(g(x)

             = f(x+3)

               = 2(x+3)

               = 2x + 6

==> (fog)(x) = 2x + 6

Now let us find (gof)(x):

(gof)(x) = g(f(x)

            = g(2x)

           = 2x + 3

==> <span>(gof)(x) = 2x + 3</span>

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Data given

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   1                 330               33                      8

   2                310                31                       7

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\bar X_{2}=31 represent the mean for sample 2  

\sigma_{1}=8 represent the population standard deviation for 1  

\sigma_{2}=7 represent the population standard deviation for 2  

n_{1}=330 sample size for the group 1  

n_{2}=310 sample size for the group 2  

\alpha Significance level provided  

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Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the mean for Campus 1 is higher than the mean for Campus 2, the system of hypothesis would be:

Null hypothesis:\mu_{1}-\mu_{2}\leq 0  

Alternative hypothesis:\mu_{1} - \mu_{2}> 0  

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z=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}} (1)  

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With the info given we can replace in formula (1) like this:  

z=\frac{(33-31)-0}{\sqrt{\frac{8^2}{330}+\frac{7^2}{310}}}}=3.37  

P value  

Since is a one right tailed test the p value would be:  

p_v =P(Z>3.37)=1-P(Z  

Comparing the p value with a significance level for example \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that the mean for the Campus 1 is significantly higher than the mean for the group 2.  

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