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3 years ago

The figure below shows a triangular wooden frame ABC. The side AD of the frame has rotted and needs to be replaced:

Mathematics

1 answer:

rodikova [14]3 years ago

6 0

Answer:

The question has missing figure, the figure is in the attachment.

The length of wood needed to replace AD is $5.01\ in$ .

Step-by-step explanation:

Given;

ABC is a triangle in which AB is of 12 inches in length.

∠DCB = 30° ∠ACD = 15°

Solution,

In ΔABC, BC=12 in

∠ACB = ∠DCB + ∠ACD = $30\°+15\°=45\°$

tan∠ACB = $\frac{AB}{BC}$

$tan45\°=\frac{AB}{BC}\\ 1=\frac{AB}{12} \\AB=12\ in$

Now in ΔDCB,

∠DCB = 30° and BC=12 in

tan∠DCB = $\frac{DB}{BC}$

$tan30\°=\frac{DB}{12}\\\frac{1}{\sqrt{3} } =\frac{DB}{12} \\DB=\frac{12}{\sqrt{3} } =\frac{12\times\sqrt{3} }{3}=4\sqrt{3}$

$DB = 4\times1.732=6.928\ in$

Length of AD = Length of AB - Length of DB

Length of AD= $12-6.928=5.072\approx5.01\ in$

Thus the length of wood needed to replace AD is $5.01\ in$ .

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Consider a discrete random variable x with pmf px (1) = c 3 ; px (2) = c 6 ; px (5) = c 3 and 0 otherwise, where c is a positive

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Looks like the PMF is supposed to be

$\mathbb P(X=x)=\begin{cases}\dfrac c3&\text{for }x\in\{1,5\}\\\\\dfrac c6&\text{for }x=2\\\\0&\text{otherwise}\end{cases}$

which is kinda weird, but it's not entirely clear what you meant...

Anyway, assuming the PMF above, for this to be a valid PMF, we need the probabilities of all events to sum to 1:

$\displaystyle\sum_{x\in\{1,2,5\}}\mathbb P(X=x)=\dfrac c3+\dfrac c6+\dfrac c3=\dfrac{5c}6=1\implies c=\dfrac65$

Next,

$\mathbb P(X>2)=\mathbb P(X=5)=\dfrac c3=\dfrac25$

$\mathbb E(X)=\displaystyle\sum_{x\in\{1,2,5\}}x\,\mathbb P(X=x)=\dfrac c3+\dfrac{2c}6+\dfrac{5c}3=\dfrac{7c}3=\dfrac{14}5$

$\mathbb V(X)=\mathbb E\bigg((X-\mathbb E(X))^2\bigg)=\mathbb E(X^2)-\mathbb E(X)^2$
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$\mathbb P(Y=y)=\begin{cases}\dfrac c3&\text{for }y=2\\\\\dfrac c6&\text{for }y=5\\\\\dfrac c3&\text{for }y=26\\\\0&\text{otherwise}\end{cases}$

Part (5) is incomplete, so I'll stop here.

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Answer:

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3 years ago

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RoseWind [281]

The distance travelled by an object is 50 m.

<h3>What is Distance?</h3>

The distance between two points is the length of the path connecting them.

Here, given equation of distance

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t in seconds.

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Learn more about Distance from:

brainly.com/question/15172156

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