Use powers of 2 to perform each calculation without a calculator or other technology

Mathematics

1 answer:

aleksley [76]2 years ago

6 0

Answer:

$\frac{2^{7} . 2^{5} }{16}$ = 256

Step-by-step explanation:

The given expression is $\frac{2^{7} . 2^{5} }{16}$

Now, the Laws of Exponents state that

1. $a^{x}.a^{y} = a^{(x+ y)}$

2. $\frac{a^{x} }{a^{y} } = a^{(x-y)}$

Now, simplifying the expression using the two laws, we get

$\frac{2^{7} . 2^{5} }{16}$ = $\frac{2^{7 + 5} }{16}$

Now, $16 = 2^{4}$

So, substituting 16 with it, we get

$\frac{2^{7 + 5} }{16}$ = $\frac{2^{12} }{2^{4}}$

= $2^{12 - 4} = 2^{8}$

Simplyimng this further, we get

$2^{8} = 256$

⇒ $\frac{2^{7} . 2^{5} }{16}$ = 256

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Marizza181 [45]

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.04}{1.64})^2}=420.25$

And rounded up we have that n=421

Step-by-step explanation:

We know that the sample proportion have the following distribution:

$\hat p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64$

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)

And on this case we have that $ME =\pm 0.04$ 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)

We assume that a prior estimation for p would be $\hat p =0.5$ since we don't have any other info provided. And replacing into equation (b) the values from part a we got: