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2 years ago

What is the rule that describes the following number pattern 0,25;2,5;25;250

Mathematics

1 answer:

Marianna [84]2 years ago

6 0

Answer:

aₙ=0.25*10ⁿ.

Step-by-step explanation:

0.25*10=2.5; 2.5*10=25; 25*10=250.., then it can be written as aₙ=0.25*10ⁿ

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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

Ryan and Marie had some marbles. if Ryan lost `15 marbles, he would have 4 times as many marbles as Marie. If Ryan lost 75 marbl

vaieri [72.5K]

Ryan's marbles = x
Marie has 4 times less marbles then Ryan would have if he lost 15 marbles (it means he would have x-15)
So, Marie marbles = (x-15):4
If Ryan lost 75 marbles (it means he would have x-75), he would have 1 1/2 times as many marbles as Marie.

We got an equation: $x-75=1\frac{1}2\cdot\frac{x-15}{4}$

          $x-75=\frac{3}2\cdot\frac{x-15}{4}$

Multiply both sides by 8:     $8x-8\cdot75=3\cdot(x-15)$

      $8x-600=3x-45$

Add 600 and subtract 3x on both sides:    $5x=555$

Divide both sides by 5:    $x=111$

Answer: Ryan have 111 marbles.

5 0

3 years ago

What type of triangle is shown here? equilateral isosceles scalene right

polet [3.4K]

Answer:

i think the given triangle is equilateral triangle because all side are equal.

7 0

2 years ago

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What is the area of Shape A and Shape B?

sashaice [31]

Answer: