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3 years ago

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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3 years ago

Scores on the SAT Mathematics test are believed to be normally distributed. The scores of a simple random sample of five student

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

And the 95% confidence interval is given by:

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

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

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

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.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ 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):

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

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

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

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