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3 years ago

PLEASE ANSWER ONLY IF RIGHT.

Mathematics

1 answer:

Colt1911 [192]3 years ago

8 0

Answer:

• Second step → Division property of equality.

• Third step → Simplifying.

• Fourth step → Subtraction property of equality.

• last step → Simplifying [ answer ]

$.$

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Waiting on the platform, a commuter hears an announcement that the train is running five minutes late. He assumes the arrival ti

natima [27]

Answer:

D. 91%

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Less than 15 minutes.

Event B: Less than 10 minutes.

We are given the following probability distribution:

$f(T = t) = \frac{3}{5}(\frac{5}{t})^4, t \geq 5$

Simplifying:

$f(T = t) = \frac{3*5^4}{5t^4} = \frac{375}{t^4}$

Probability of arriving in less than 15 minutes:

Integral of the distribution from 5 to 15. So

$P(A) = \int_{5}^{15} = \frac{375}{t^4}$

Integral of $\frac{1}{t^4} = t^{-4}$ is $\frac{t^{-3}}{-3} = -\frac{1}{3t^3}$

Then

$\int \frac{375}{t^4} dt = -\frac{125}{t^3}$

Applying the limits, by the Fundamental Theorem of Calculus:

At $t = 15$ , $f(15) = -\frac{125}{15^3} = -\frac{1}{27}$

At $t = 5$ , $f(5) = -\frac{125}{5^3} = -1$

Then

$P(A) = -\frac{1}{27} + 1 = -\frac{1}{27} + \frac{27}{27} = \frac{26}{27}$

Probability of arriving in less than 15 minutes and less than 10 minutes.

The intersection of these events is less than 10 minutes, so:

$P(B) = \int_{5}^{10} = \frac{375}{t^4}$

We already have the integral, so just apply the limits:

At $t = 10$ , $f(10) = -\frac{125}{10^3} = -\frac{1}{8}$

At $t = 5$ , $f(5) = -\frac{125}{5^3} = -1$

Then

$P(A \cap B) = -\frac{1}{8} + 1 = -\frac{1}{8} + \frac{8}{8} = \frac{7}{8}$

If given the train arrived in less than 15 minutes, what is the probability it arrived in less than 10 minutes?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{7}{8}}{\frac{26}{27}} = 0.9087$

Thus 90.87%, approximately 91%, and the correct answer is given by option D.

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3 years ago

a rectangular room is 2meters longer than it is wide, and it's perimeter is 24 meters. find the dimension of the room

asambeis [7]

$2l + 2(l+2)=24 \\2l +2l+4=24 \\4l=20 \\\boxed{l=5}$

Length of the room is 5 m and width is 5 + 2 = 7 m.

Hope this helps.

r3t40

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4 years ago

Read 2 more answers

A rectangle room is 15 feet long and 12 feet wide. What is the area?

vaieri [72.5K]

There is an area of 180 square ft. Hope this helps (:

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What is m∠B to the nearest tenth?

Tcecarenko [31]

Answer:

18.044

Step-by-step explanation:

hope it helps you good day if I'm wrong tell me right away I'll try it out again.

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3 years ago

Find the equation of the graphed line.

VikaD [51]

The last one hope this helps
Y=Mx+b b is always on the y intercept so that canceled out c and b is canceled out Bc the Mx is negative and it can’t just be 6 Bc there is no point on where it clear like right on the point if u can understand that so that just leaves u with d y=-7/6x-7

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3 years ago