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ser-zykov [4K]
3 years ago
10

What is twice 2 to the 30 power ? Write using exponents. Explain your reasoning

Mathematics
2 answers:
andrey2020 [161]3 years ago
7 0

Answer:

Step-by-step explanation:

We are to find out twice 2 to the 30 power.

Let us write this 2 to the 30 power as

2^{30}

Twice this value would be 2 multiplied by this

=2(2^{30})\\2^{31}

Hence answer is 2^{31}

Rus_ich [418]3 years ago
4 0

2 times 2^30 simple means that = (2^1) x (2^30)

<span>In multiplying numbers of the same base (in this case 2), the exponents are just added, therefore giving us:

</span>

(2^1) x (2^30) = (2^31)

 

Answer:

<span>2 to the 31 power</span>

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So the answer for this case would be n=65 rounded up to the nearest integer

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1) 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  

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s represent the sample standard deviation

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

2) Solution to the problem

Since the new 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: "=-NORM.INV(0.05,0,1)".And we see that z_{\alpha/2}=1.64

Assuming that the deviation is known we can express the margin of error is given by this formula:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}    (a)

And on this case we have that ME =\pm 3 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (b)

Replacing into formula (b) we got:

n=(\frac{1.64(14.7)}{3})^2 =64.57 \approx 65

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