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3 years ago

The prime factorization of a number is 2x2x3x7x7. Is the number a perfect square? how do you know ?

Mathematics

1 answer:

Naya [18.7K]3 years ago

5 0

Answer:

No,the number isn't a perfect square

Step-by-step explanation:

Taking the prime factor of the number, each factor can be raised to the power of 2 except 3

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adelina 88 [10]

Answer:

A sample of 11352 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is given by:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

For this problem, we have that:

400 cards, 120 cases were correct. So

$p = \frac{120}{400} = 0.3$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

How large a sample n would you need to estimate p with margin of error 0.01 and 95% confidence

We would need a sample of size n, and n is found when $M = 0.01$ . So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.01 = 2.325\sqrt{\frac{0.3*0.7}{n}}$

$0.01\sqrt{n} = 2.325\sqrt{0.3*0.7}$

$\sqrt{n} = \frac{2.325\sqrt{0.3*0.7}}{0.01}$

$(\sqrt{n})^2 = (\frac{2.325\sqrt{0.3*0.7}}{0.01})^2$

$n = 11351.8$

Rounding up

A sample of 11352 is needed.

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3 years ago

The prime factorization of a number is 2x2x3x7x7. Is the number a perfect square? how do you know ?​

The prime factorization of a number is 2x2x3x7x7. Is the number a perfect square? how do you know ?