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satela [25.4K]
3 years ago
5

A bag of marbles contains 6 blue marbles, 2 yellow marbles, 4 red marbles, and 1 green marble. What is the probability of reachi

ng into the bag and selecting a yellow marble? StartFraction 1 over 13 EndFraction StartFraction 2 over 13 EndFraction StartFraction 1 over 6 EndFraction StartFraction 2 over 6 EndFraction
Mathematics
1 answer:
Mashutka [201]3 years ago
6 0

Answer:StartFraction 2 over 13 End fraction

Step-by-step explanation:

Probability = number of possible outcomes/ total number of outcomes

P (Yellow marble) = 2/ 13

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A 51-foot wire running from the top of a tent pole to the ground makes an angle of 58° with the ground. If the length of the ten
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Answer:

<em>35.11 ft</em>

<em></em>

Step-by-step explanation:

This given situation can be thought of as triangle \triangle PQR where PQ is the length of pole.

PR is the length of rope.

and QR is the distance of bottom of pole to the point of fastening of rope to the ground.

And \angle Q \neq 90^\circ

Given that:

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To find:

Side QR = ?

Solution:

We can apply Sine Rule here to find the unknown side.

Sine Rule:

\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}

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b is the side opposite to \angle B

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\dfrac{PR}{sinQ}=\dfrac{PQ}{sinR}\\\Rightarrow sin Q =\dfrac{PR}{PQ}\times sinR\\\Rightarrow sin Q =\dfrac{51}{44}\times sin58^\circ\\\Rightarrow \angle Q =79.41^\circ

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\angle P +\angle Q +\angle R =180^\circ\\\Rightarrow \angle P +58^\circ+79.41^\circ=180^\circ\\\Rightarrow \angle P = 42.59^\circ

Let us use the Sine rule again:

\dfrac{QR}{sinP}=\dfrac{PQ}{sinR}\\\Rightarrow QR =\dfrac{sinP}{sinR}\times PQ\\\Rightarrow QR =\dfrac{sin42.59}{sin58}\times 44\\\Rightarrow QR = 35.11\ ft

So, the answer is <em>35.11 ft</em>.

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