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____ [38]
3 years ago
9

Square root of 24x^6y^9​

Mathematics
1 answer:
nikklg [1K]3 years ago
8 0

Answer:

Step-by-step explanation:

Break the expression into individual pieces

24 can be written as (4)(6)

x^6 can be written as (x^3)^2

y^9 can be written as (y^4)^2(y)

Notice in the variables the focus on writing to the power of 2.

Square root and power of 2 are essentially inverse operations of each other, so they cancel each other out.

The square root of 4 is 2

The square root of (x^3)^2 is x^3

The square root of (y^4)^2 is y^4

The remaining 6 and y stay underneath the square root.

The final answer is then (2x^3y^4)(square root 6y)

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Each day, Robin commutes to work by bike with probability 0.4 and by walking with probability 0.6. When biking to work injuries
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64.65% probability of at least one injury commuting to work in the next 20 years

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}


In which

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e = 2.71828 is the Euler number

\mu is the mean in the given interval.

Each day:

Bikes to work with probability 0.4.

If he bikes to work, 0.1 injuries per year.

Walks to work with probability 0.6.

If he walks to work, 0.02 injuries per year.

20 years.

So

\mu = 20*(0.4*0.1 + 0.6*0.02) = 1.04

Either he suffers no injuries, or he suffer at least one injury. The sum of the probabilities of these events is decimal 1. So

P(X = 0) + P(X \geq 1) = 1

We want P(X \geq 1). Then

P(X \geq 1) = 1 - P(X = 0)

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P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}


P(X = 0) = \frac{e^{-1.04}*1.04^{0}}{(0)!} = 0.3535


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64.65% probability of at least one injury commuting to work in the next 20 years

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