35 Points !

Mathematics

1 answer:

antoniya [11.8K]3 years ago

6 0

For this case we have to:

x: It is the variable that represents the quantity of paint bottles

y: It is the variable that represents the number of boxes of colored pencils

So, we have:

$2x + 3.50y$

If you can not spend more than $ 42 then we have:

$2x + 3.50y\leq42$

Then you can buy 10 boxes of colored pencils and 3 of paint bottles at a cost of $ 41

$2 (3) +3.50 (10)\\6 + 35 = 41$

You can buy 5 boxes of colored pencils and 12 of paint bottles at a cost of $

$2 (12) +3.50 (5)\\24 + 17.5 = 41.5$

You can buy 7 boxes of colored pencils and 8 of paint bottles at a cost of $

$2 (8) +3.50 (7)\\16 + 24.5 = 40.5$

Answer:

$2x + 3.50y\leq42$

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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: