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dusya [7]
3 years ago
10

Someone please help me !!!

Mathematics
1 answer:
djverab [1.8K]3 years ago
5 0

Answer:

a.\ \ \ A=684\ m^2

b.\ \ \ A=130.2 \ km^2

Step-by-step explanation:

a. Area is calculated by summing the areas of the prism's individual surfaces.

#First, calculate the areas of the right-angled surfaces:

Area=2(\frac{1}{2}bh), b=9, h=12\\\\=2\times \frac{1}{2}\times 9\times 12\\\\=108\ m^2

#We then find the areas of the rectangular surfaces:

A=lw\\\\=15\times 16+9\times 16+16\times 12\\\\=576\ m^2

#We sum the areas to find the total surface areas:

A=\sum{Areas_i}\\\\=108+576\\\\=684\ m^2

Hence, the prism's surface area is 684\ m^2

b.Area is calculated by summing the areas of the prism's individual surfaces.

#First, calculate the areas of the right-angled surfaces:

A=2\times \frac{1}{2}bh,\ b=12, h=4.1\\\\=2\times 0.5\times 12\times 4.1\\\\=49.2 \ km^2

#We then find the areas of the rectangular surfaces:

A=lw\\\\=5\times 3+3\times 10+12\times 3\\\\=81\ km^2

#We sum the areas to find the total surface areas:

A=A_r+A_t\\\\=81+49.2\\\\=130.2 \ km^2

Hence, the prism's surface area is  130.2 \ km^2

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Answer:

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Step-by-step explanation:

Previous concepts  

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

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And replacing we got:

\bar X= 47.917, s= 2.811

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The confidence interval for the mean is given by the following formula:  

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)  

The degrees of freedom are given:

df= n-1= 12-1=11

Since the Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.05, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,11)".And we see that t_{\alpha/2}=1.796

Now we have everything in order to replace into formula (1):

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Part b

For this case the system of hypothesis are:

Null hypothesis: \mu =50

Alternative hypothesis: \mu \neq 50

And after analyze the interval obtained the upper limit not contains the value of 50, so then we can conclude that the claim is not satisfied for this case, and the population mean seems to be lower than 50 at 10% of significance.

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