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3 years ago

What information would allow you to identify angle BFA and angle AFE as complementary angles?

Mathematics

1 answer:

timama [110]3 years ago

7 0

Two angles are complementary if they add up to 90 degrees so we would need to know angle BFE is 90 degrees to identify it as complementary.

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Pollution of the rivers in the United States has been a problem for many years. Consider the following events: a: the river is p

vampirchik [111]

Answer:

The answer is below

Step-by-step explanation:

P(A') = 1 - P(A) = 1 - 0.3 = 0.7

P(B'/A) = 1 - P(B/A) = 1 - 0.75 - 0.25

P(B/A') = 0.2, P(B'/A') = 1 - 0.2 = 0/8

P(C|A∩B) = 0.20,

P(C|A'∩B) = 0.15,

P(C|A∩B') = 0.80, and

P(C|A'∩B') = 0.90.

A) From conditional probability;

P(B/A) = P(B ∩ A) / P(A)

P(B∩A) = P(B/A) × P(A) = 0.75 × 0.3 = 0.225

P(C/A∩B) = P(A∩B∩C)/P(A∩B)

P(A∩B∩C) = P(C/A∩B) × P(A∩B)

P(A∩B∩C) = 0.2 ×0.225 = 0.045

B) P(A∩B∩C) = P(A) × P(B/A) × P(C/A∩B)

P(B'∩C) = P(A∩(B'∩C)) + P((A'∩B')∩C)

P(B'∩C) = P(A) × P(B'/A) × P(C/A∩B') + P(A') × P(B'/A') × P(C/A'∩B')

P(B'∩C) = 0.3 × 0.25 × 0.8 + (0.7 × 0.8 × 0.9) = 0.06 + 0.504 = 0.564

C) P(C) = P(A∩B∩C) + P(A'∩B∩C) + P(A∩B'∩C) + P(A'∩B'∩C)

P(A'∩B∩C) = P(A') × P(B/A') × P(C/A'∩B) = 0.7 × 0.2 × 0.15 = 0.021

P(A∩B'∩C) = P(A) × P(B'/A) × P(C/A∩B') = 0.3 × 0.25 × 0.8 = 0.06

P(A'∩B'∩C) = P(A') × P(B'/A') × P(C/A'∩B') = 0.7 × 0.8 × 0.9 = 0.504

P(C) = P(A∩B∩C) + P(A'∩B∩C) + P(A∩B'∩C) + P(A'∩B'∩C) = 0.045 + 0.021 + 0.06 + 0.504 = 0.63

D) P(A/B'∩C) = P(A∩B'∩C)/P(B'∩C)

P(A/B'∩C) = 0.06 / 0.564 = 0.106

6 0

4 years ago

Sound travels through sea water at a speed of about 1500 meters per second. At this rate, how far will sound travel in 2 minutes

Mariulka [41]

Answer:

180,000 m

Step-by-step explanation:

There are 60 seconds in a minute, so:

2 min × 60 s/min = 120 s

Distance = rate × time

d = 1500 m/s × 120 s

d = 180,000 m

8 0

4 years ago

Enrique left the study group traveling 20 mph. Then, 2 hours later, Tevin left traveling the same direction at 28 mph. How long

nadya68 [22]

Answer:

After 7 hours Tevin will catch Enrique

Step-by-step explanation:

We have given speed of Enrique is 20 mph

Tevin left traveling after 2 hours of Enrique

Speed of Tevin is 28 mph

When Tevin catches Enrique will cover same distance

Let Enrique is traveling for t hours

Then Tevin will travel for t-2 hours

We know that distance = speed × time

So $20\times t=28\times (t-2)$

$20t=28t-56$

$8t=56$

t = 7 hours

So after 7 hours Tevin will catch Enrique

4 0

4 years ago

Car thieves steal one automobile out of 400 of a certain type every year in a certain city.What annual net premium should an own

bixtya [17]

Without including other expenses and the benefit of the insurance company, the premium has to meet this proportion:

1/400 = premim / value of the car

=> 1/400 = premum / $16,000

=> premium = $16,000 * (1/400) = $ 40

As already said this is witout taking into consideration the other expenses of the insurance company and their margin.

Answer: option B. $40.

3 0

4 years ago

Read 2 more answers

4 1/3 Divided by 1/2

romanna [79]

Answer: 26/3

Explanation: Convert 4 1/3 which is 13/3

13/3 divided by 1/2

13/3 * 2

13/3 * 2= 26/3

8 0

3 years ago