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Ad libitum [116K]

4 years ago

15

Assume that the number of customers who arrive at a water ice stand follows the Poisson distribution with an average rate of 6.4

per 30 minutes. What is the probability that three or four customers will arrive during the next 30 minutes?

1 answer:

Nady [450]4 years ago

4 0

Answer:

18.88% probability that three or four customers will arrive during the next 30 minutes

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

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval.

Average rate of 6.4 per 30 minutes.

This means that $\mu = 6.4$

What is the probability that three or four customers will arrive during the next 30 minutes?

$P = P(X = 3) + P(X = 4)$

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

$P(X = 3) = \frac{e^{-6.4}*(6.4)^{3}}{(3)!} = 0.0726$

$P(X = 4) = \frac{e^{-6.4}*(6.4)^{4}}{(4)!} = 0.1162$

$P = P(X = 3) + P(X = 4) = 0.0726 + 0.1162 = 0.1888$

18.88% probability that three or four customers will arrive during the next 30 minutes

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4 years ago

David wants to rent a bicycle for a couple of hours to explore the city. The price of the bike rental, (P)(P)left parenthesis, P

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Answer:

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Step-by-step explanation:

The slope of the graph corresponds to the hourly rate for the bike rental.

During the first three hours of the bike rental, the price increases by $4 each hour.

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4 years ago

The initial size of the population is 300. After 1 day the population has grown to 800. Estimate the population after 6 days. (R

Cloud [144]

Solution :

Given initial population = 300

Final population after 1 day = 800

Number of days = 6

∴ $\frac{dP}{dt} =kt^{1/2}$

P(0) = 300 P(1) = 300

We need to find P(8).

$dP = kt^{1/2} dt$

$\int 1 dP = \int kt^{1/2} dt$

$P(t) = k \left(\frac{t^{3/2}}{3/2}\right)+c$

$P(t)= \frac{2k}{3}t^{3/2} + c$

When P(0) = 300

$300 = \frac{2k}{3} (0)^{3/2} + c$

∴ c = 300

∴ $P(t)= \frac{2k}{3}t^{3/2} + 300$

When P(1) = 800

$800 = \frac{2k}{3} (1)^{3/2} + 300$

$500 = \frac{2k}{3}$

∴ k = 750

$P(t)= 500t^{3/2} + 300$

So, P(8) is

$P(t)= 500(8)^{3/2} + 300$

= 11,614

So the population becomes 11,614 after 8 days.

8 0

3 years ago

Write a function that models the distance D from a point on the line y = 9 x - 8 to the point (0,0) (as a function of x).

lakkis [162]

The function that models the distance D from a point on the line y = 9 x - 8 to the point (0,0) (as a function of x) is y = 9x

Given the equation of a line in standard form as y = 9x - 8

Get the slope of the line

mx = 9x

m = 9

Since the line passes through the origin (0, 0), substitute the slope and the point in the point-slope form of the equation as shown below:

$y-y_0=m(x-x_0)$

$y-0=9(x-0)\\y =9x$

Hence the function that models the distance D from a point on the line y = 9 x - 8 to the point (0,0) (as a function of x) is y = 9x

Learn more here: brainly.com/question/15816805

4 0

3 years ago

Given the parent function f(x) = x^2 describe the translation of the function y=(.2x)^2?

Bad White [126]

Answer:

Option C.

Step-by-step explanation:

Let $f(x) = x ^ 2$ be a quadratic function

Then we do the function $y = f(bx) = (bx) ^ 2$

Where b is a real number.

If $b> 1$ then the function $y = (bx) ^ 2$ represents a horizontal compression of the function $y = x ^ 2$

If $0$ Then the function $y = (bx) ^ 2$ represents a horizontal expansion compression of the function $y = x ^ 2$ by a factor of $\frac{1}{b}$

In this case, the equation is:

$y = (0.2x) ^ 2$ Then:

$b = 0.2$

$0$

Thus

$y = (0.2x) ^ 2$ is a horizontal expansion of the function $y = x ^ 2$ by a factor of $\frac{1}{0.2} = 5$ .

The correct option is: Option C

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3 years ago