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luda_lava [24]
3 years ago
5

In ΔRST, the measure of ∠T=90°, the measure of ∠S=21°, and ST = 7.7 feet. Find the length of TR to the nearest tenth of a foot.

Mathematics
1 answer:
Natali [406]3 years ago
3 0

Answer:

TR = 3 ft

Step-by-step explanation:

<h3>tan x = \frac{o}{a}</h3><h3>tan (21) = \frac{o}{7.7}</h3><h3>7.7( tan 21) = o</h3><h3>2.9 = o</h3><h3>round up and you get;</h3><h3>3.0=o</h3>
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Thomas wants to invite Madeline to a party. He has an 80% chance of bumping into her at school. Otherwise, he'll call her on the
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Answer:

The probability of Thomas inviting Madeline to the party over the phone is 0.143.

Step-by-step explanation:

Consider the tree diagram below.

The events are denoted as follows:

<em>A</em> = Thomas bumps into Madeline at school

<em>B</em> = Thomas call Madeline on the phone

<em>X</em> = Thomas asks Madeline to the party

The information provided is:

P (A) = 0.80

P (B) = 1 - P (A) = 1 - 0.80 = 0.20

P (X|A) = 0.90

⇒ P (X'|A) = 1 - P (X|A) = 1 - 0.90 = 0.10

P (X|B) = 0.60

⇒ P (X'|B) = 1 - P (X|B) = 1 - 0.60 = 0.40

The conditional probability of event <em>U</em> given that another events <em>V</em> has already occurred is:

P(U|V)=\frac{P(V|U)P(U)}{P(V)}

The law of total probability states that:

P(V)=P(V|U)P(U)+P(V|U')P(U')

In this case we need to determine the probability that Thomas invites Madeline to the party over the phone, i.e. P (B|X).

Use the law of total probability to determine the value of P (X) as follows:

P(X) = P(X|A)P(A)+P(X|B)P(B)

         =(0.90\times 0.80)+(0.60\times 0.20)\\=0.72+0.12\\=0.84

Compute the value of P (B|X) as follows:

P(B|X)=\frac{P(X|B)P(B)}{P(X)}

             =\farc{0.60\times 0.20}{0.84}\\\\=0.14286\\\\\approx 0.143

Thus, the probability of Thomas inviting Madeline to the party over the phone is 0.143.

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