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3 years ago

Round off the decimal 55.345 to 2 decimal places.

Mathematics

2 answers:

barxatty [35]3 years ago

7 0

Answer:

55.35

Step-by-step explanation:

please mark brainliest

zalisa [80]3 years ago

7 0

Answer:

Step-by-step explanation:

round off the decimal 55.345 to 2 places: 55.35

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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.

3 0

3 years ago

What is the product of 16(cos(47°) + i sin(47°)) and 4(cos(12degrees)+ i sin(12"))?

Scorpion4ik [409]

Answer:

64(cos(59°)+ i sin(59°))

just took the test

6 0

3 years ago

Read 2 more answers

Please help and show workings

Scorpion4ik [409]

Given:

In an isosceles triangle,

One base angle = (4x-15)°

Vertex angle = 95°

To find:

The value of x.

Solution:

Let the triangle be ABC.

We have,

$m\angle A=95^\circ$

$m\angle C=(4x-15)^\circ$

Since ABC is an isosceles triangle and AB=AC, therefore, the base angles are equal.

$m\angle B=m\angle C=(4x-15)^\circ$

Using angle sum property of triangles, we get

$m\angle A+m\angle B+\angle C=180^\circ$

$95^\circ+(4x-15)^\circ+(4x-15)^\circ=180^\circ$

$(8x+65)^\circ=180^\circ$

$(8x+65)=180$

On further simplification, we get

$8x=180-65$

$8x=115$

$x=\dfrac{115}{8}$

$x=14.375$

Therefore, the value of x is 14.375.

8 0

3 years ago

1) An underlying principle of statistical inference is that one uses sample statistics to learn something about population param

crimeas [40]

Answer:

Average of amount of time students spend trying to find an eatery spot on campus.

The sample would be a pool of 100 students to survey from.

Population would be all the students attending Harvard university.

Statistic would be the average amount of time spend looking for eatery spot in campus.

The parameter would be the mean used to find the average amount of time spent looking for eatery spot in campus.

It was a convenient sample.

Step-by-step explanation:

A population is the entire pool from which a statistical sample is drawn. In this case our population is the entire students that attend Harvard University.

A sample is usually drawn from a population. In this case, the 100 students that were drawn from the population is the sample.

The sample was a convenient sample as the sample can be easily drawn from the population population, it doesn't depend on any probability.

6 0

3 years ago

The length of each side of a square was increased by 6 inches, so the

marusya05 [52]

Each side was 28 inches

4 0

3 years ago

Round off the decimal 55.345 to 2 decimal places.​

Round off the decimal 55.345 to 2 decimal places.