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Vedmedyk [2.9K]
3 years ago
14

Write the prime factorization of 500 using exponents

Mathematics
1 answer:
murzikaleks [220]3 years ago
6 0

Answer :Ex.: 2, 3, 4, 11, 10225, etc

Step-by-step explanation:

The number 500 is a composite number so, it is possible to factorize it. In other words, 500 can be divided by 1, by itself and at least by 2 and 5. A composite number is a positive integer that has at least one positive divisor other than one or the number itself. In other words, a composite number is any integer greater than one that is not a prime number.

The prime factorization of 500 = 22•53.

The prime factors of 500 are 2 and 5.

Factor tree or prime decomposition for 500

As 500 is a composite number, we can draw its factor tree:

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bearing in mind that an explicit form is simply the sequence written as a function of some variables, so we simply simplify and add like-terms.

\bf a_n=(-1)+(n-7)(-4)\implies a_n=-1+(-4n+28)\implies a_n=27-4n

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Which variable is most important to the following problem? At 9:45 a.m. a patient’s temperature was 101.5 degrees at 10:41, the
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Answer:

Option A is the important variable.

Step-by-step explanation:

Given is - At 9:45 a.m. a patient’s temperature was 101.5 degrees at 10:41, the nurse took the patients temperature again and found it was 105.8 degrees, the highest ever recorded.

The variable that is most important here is A: the number of minutes it took for the to reach its peak.

Firstly it is not mentioned if 10:41 is am or pm.

If its am, then such a temperature rise in less than an hour is very dangerous.

So, the important variable is option A.

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12. If a manufacturer conducted a survey among randomly selected target market households and wanted to be 95% confident that th
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Answer:

n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11  

And rounded up we have that n=1068

Step-by-step explanation:

We have the following info given:

Confidence= 0.95 the confidence level desired

ME =0.03 represent the margin of error desired

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

The confidence level is 95% or 0.95, the significance is \alpha=0.05 and the critical value for this case using the normal standard distribution would be z_{\alpha/2}=1.96

Since we don't have prior information we can use \hat p= 0.5 as an unbiased estimator

Also we know that ME =\pm 0.03 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11  

And rounded up we have that n=1068

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