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3 years ago

Which expression is equivalent to 3x/5 a: 15x/20 b: 12x/20 c: 12x/5

Mathematics

1 answer:

ivann1987 [24]3 years ago

3 0

Answer: 12x/20

Step-by-step explanation:

Looking at 3x/5

The expression equivalent is 12x/20

The reason is this

12x/20

If you divide the 12x by 4

It will give you 3x

If you divide 20 by 4

It will give you 5

Therefore, you will still have 3x/5

Another way to look at it is this

3x/5= 0.6x

12x/20= 0.6x

Therefore, the final answer is b which is 12x/20

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a) The 99% confidence interval would be given by (24.409;24.979)

b) n=464

Step-by-step explanation:

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".

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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)

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

$df=n-1=47-1=46$

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 table to find the critical value. The excel command would be: "=-T.INV(0.025,46)".And we see that $t_{\alpha/2}=2.01$

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

$525-2.01\frac{75}{\sqrt{47}}=503.01$

$525+2.01\frac{75}{\sqrt{47}}=546.99$

So on this case the 95% confidence interval would be given by (503.01;546.99)

Part b

The margin of error is given by this formula:

$ME=t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And on this case we have that ME =7 msec, we are interested in order to find the value of n, if we solve n from equation (1) we got:

$n=(\frac{t_{\alpha/2} s}{ME})^2$ (2)

The critical value for 95% of confidence interval is provided, $t_{\alpha/2}=2.01$ from part a, replacing into formula (2) we got:

$n=(\frac{2.01(75)}{7})^2 =463.79 \approx 464$

So the answer for this case would be n=464 rounded up to the nearest integer

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$\begin{gathered} (h,k),\text{ which is } \\ (0,0) \end{gathered}$

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Substituting the values of a, b, h and k, we have

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$\frac{x^2}{1}-\frac{y^2}{3}=1$

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Step-by-step explanation:

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