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3 years ago

Leon is using the recipe shown.

Mathematics

1 answer:

stira [4]3 years ago

3 0

He will use 11 and half cups of olive oil to use with 1 teaspoon of cinnamon.

Step-by-step explanation:

Given,

Olive oil used in recipe = 23 cups

Cinnamon used in recipe = 2 teaspoons

Ratio of cinnamon to olive oil in recipe = 2:23

Cinnamon Leon has = 1 teaspoon

Let x be the olive oil.

Ratio of available cinnamon to olive oil = 1:x

Using proportion;

Ratio of cinnamon to olive oil in recipe :: Ratio of available cinnamon to olive oil

$2:23::1:x$

Product of extreme = Product of mean

$2*x=23*1\\2x=23$

Dividing both sides by 2;

$\frac{2x}{2}=\frac{23}{2}\\x=11.5$

11.5 can also be written as $11\frac{1}{2}$

He will use 11 and half cups of olive oil to use with 1 teaspoon of cinnamon.

Keywords: ratio, proportion

Learn more about ratios at:

#LearnwithBrainly

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From what I gather from your latest comments, the PDF is given to be

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and in particular, f(x, y) = cxy over the unit square [0, 1]², meaning for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. (As opposed to the unbounded domain, x ≤ 0 *and* y ≤ 1.)

(a) Find c such that f is a proper density function. This would require

$\displaystyle\int_0^1\int_0^1 cxy\,\mathrm dx\,\mathrm dy=c\left(\int_0^1x\,\mathrm dx\right)\left(\int_0^1y\,\mathrm dy\right)=\frac c{2^2}=1\implies \boxed{c=4}$

(b) Get the marginal density of X by integrating the joint density with respect to y :

$f_X(x)=\displaystyle\int_0^1 4xy\,\mathrm dy=(2xy^2)\bigg|_{y=0}^{y=1}=\begin{cases}2x&\text{for }0\le x\le 1\\0&\text{otherwise}\end{cases}$

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(d) The conditional distribution of X given Y can obtained by dividing the joint density by the marginal density of Y (which follows directly from the definition of conditional probability):

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