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2 years ago

6

J3.

1 answer:

alisha [4.7K]2 years ago

3 0

By using the given table, we can see that the expected value is 20.97 AED.

<h3>How to find the expected value?</h3>

The expected value is given by the sum between the products between the value of each outcome and the probability of said outcome.

Then, by using the table, we can write the expected value as:

$12*0.8 + 18*0.15 + 20*0.31 + 22*0.08 + 24*0.15 + 25*0.23 = 20.97$

Then we can see that the correct option is C, the expected value is 20.97 AED.

If you want to learn more about expected value:

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Step-by-step explanation:

Given

The shape above

Required

Determine PQ

Determine dimension of the garden

Calculating Length PQ

Represent the length of the inner rectangle as L

Represent the width of the inner rectangle as W

$W = x$

$L = x + 9$

The distance between the inner rectangle and the outer triangle is 4ft

This implies that;

$PQ = L + 4$

Substitute $x + 9$ for $L$

$PQ = x + 9 + 4$

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Also;

$QR = W + 4$

Substitute $x$ for $W$

$QR = x + 4$

Calculating The Dimension of The Garden

First, we need to determine the Area of the inner rectangle

$Area_1 = L * W$

Recall that $W = x$ and $L = x + 9$

So;

$Area_1 = x * (x + 9)$

For the bigger rectangle

$Area_2 = PQ * QR$

Recall that $PQ = x + 13$ and $QR = x + 4$

So;

$Area_2 = (x + 13)(x + 4)$

Given that the Area of the walkway is $400ft^2$

This implies that

$Area_2 = Area_1 + 400$

Substitute $Area_1 = x * (x + 9)$ and $Area_2 = (x + 13)(x + 4)$

$(x + 13)(x + 4) = x * (x + 9) + 400$

Open All Brackets

$x^2 + 13x + 4x + 52 = x^2 + 9x + 400$

$x^2 + 17x + 52 = x^2 + 9x + 400$

Collect Like Terms

$x^2 - x^2 + 17x - 9x = 400- 52$

$8x = 348$

Divide both sides by 8

$\frac{8x}{8} = \frac{348}{8}$

$x = \frac{348}{8}$

$x =43.5$

Since the dimensions of the garden is $W = x$ and $L = x + 9$

<em>Substitute 43.5 for x in both cases</em>

$L = 43.5 + 9 = 52.5$

$W = 43.5$

<em>Hence, the dimension of the garden is 52.5ft by 43.5ft</em>

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2 years ago