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3 years ago

To make lemonade, Andy adds

Mathematics

1 answer:

JulsSmile [24]3 years ago

3 0

Answer:

64/3 tablespoons of sugar for 32 ounces of water

Step-by-step explanation:

In these kinds of questions it is nice to find how muc of 1 thing there is for every ONE of another. so 8 tablespoons of sugar for 12 ouncesof water you can divide both sides by 8 or 12.

Dividing it by 8 gets 8/8 = 1 tablespoon of sugar for 12/8 = 1.5 ounces of water.

Dividing by 12 gets 8/12 = 2/3 tablespoon of sugar for 12/12 = 1 ounce of water.

Now you can take one or the other and multiply it to fit whichever you want to fit a ratio.

It asks what happens if you use 32 ounces of water, so lets use the ratio where we hae 1 ounce, then multiply everything by 32.

2/3 tablespoon of sugar for 1 ounce of water

Multiply by 32 and you get 32*(2/3) = 64/3 tablespoons of sugar for 32 ounces of water

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Step-by-step explanation:

We have to calculate a 99%CI for the difference of means for the vegan and the omnivore.

First, we have to estimate the standard deviation

$s_{Md}=\sqrt{\frac{2MSE}{n_h}}$

The MSE can be calculated as

$MSE=\frac{(SSE_1+SSE_2)}{df} =\frac{(n_1s_1)^2+(n_2*s_2)^2}{n_1+n_2-2}\\\\MSE=\frac{(85*1.05)^2+(96*1.20)^2}{85+96-2}=\frac{7965.56+13272.04}{179} =118.65$

The weighted sample size nh can be calculated as

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The standard deviation then becomes

$s_{Md}=\sqrt{\frac{2MSE}{n_h}}=\sqrt{\frac{2*118.65}{90.16}}=\sqrt{2.632} =1.623$

The z-value for a 99% confidence interval is z=2.58.

The difference between means is

$\Delta M=M_v-M_o=5.10-5.55=-0.45$

Then the confidence interval can be constructed as

$\Delta M-z*s_{Md}\leq\mu_v-\mu_o\leq \Delta M+z*s_{Md}\\\\ -0.45-2.58*1.623\leq\mu_v-\mu_o\leq -0.450+2.58*1.623\\\\-0.450-4.187\leq\mu_v-\mu_o\leq-0.450+4.187\\\\-4.637\leq\mu_v-\mu_o\leq 3.737$