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White raven [17]
3 years ago
6

8. Multiply the following numbers using scientific notation: (2 x 10^3)(2 x 10^4).

Mathematics
1 answer:
Fiesta28 [93]3 years ago
4 0

Answer:

<h2><u>Question 8 </u></h2>

Multiply the following numbers using scientific notation: (2 x 10^3)(2 x 10^4).

(2 x 10^3) = 2*10*10*10 = 2000

(2 x 10^4) = 2*10*10*10*10 = 20000

2000*20000

=40 000 000

= 4 * 10^{7}

<h2><u>Question 9 </u></h2>

Divide the following numbers using scientific notation: (4 x 10^2)/(1 x 10^3)

(4 x 10^2) = 4*10*10 = 400

(1 x 10^3) = 1*10*10*10= 1000

400/1000 = 0.4

=4*10^{-1}

<h2><u>Question 10</u></h2>

Perform the following calculation: (1 x 10^2)(2 x 10^3)/(1 x 10^2)

(1 x 10^2) = 1*10*10= 100

(2 x 10^3) = 2*10*10*10 =2000

100*2000 = 200 000

(1 x 10^2) = 1*10*10 = 100

200 000/100 = 2000

=2*10^{3}

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The mean calculated for this case is \bar X=584

And the 95% confidence interval is given by:

584-2.776\frac{86.776}{\sqrt{5}}=476.271    

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So on this case the 95% confidence interval would be given by (476.271;691.729)    

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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\bar X represent the sample mean for the sample  

\mu population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

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

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

In order to calculate the mean and the sample deviation we can use the following formulas:  

\bar X= \sum_{i=1}^n \frac{x_i}{n} (2)  

s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}} (3)  

The mean calculated for this case is \bar X=584

The sample deviation calculated s=86.776

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=5-1=4

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,4)".And we see that t_{\alpha/2}=2.776

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

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584+2.776\frac{86.776}{\sqrt{5}}=691.729    

So on this case the 95% confidence interval would be given by (476.271;691.729)    

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