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3 years ago

15

In a fruit cocktail, for every 28 ml of orange juice you need 14 ml of apple juice and 56 ml of coconut milk. What is the ratio

of apple juice to coconut milk to orange juice expressed in its simplest form?

1 answer:

ludmilkaskok [199]3 years ago

5 0

Answer:

1 : 4 : 2.

Step-by-step explanation:

Ratio is 14:56:528

Divide each number by 14 to get the answer:-

1 : 4 : 2.

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Of 1000 randomly selected cases of lung cancer, 823 resulted in death within 10 years.

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a) $0.823 - 1.96\sqrt{\frac{0.823(1-0.823)}{1000}}=0.799$

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

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Step-by-step explanation:

Part a

$\hat p=\frac{823}{1000}=0.823$

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 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

If we replace the values obtained we got:

$0.823 - 1.96\sqrt{\frac{0.823(1-0.823)}{1000}}=0.799$

$0.823 + 1.96\sqrt{\frac{0.823(1-0.823)}{1000}}=0.847$

The 95% confidence interval would be given by (0.799;0.847)

Part b

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 $ME =\pm 0.03$ 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:

$n=\frac{0.823(1-0.823)}{(\frac{0.03}{1.96})^2}=621.79$

And rounded up we have that n=622

Part c

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

And rounded up we have that n=1068

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