Find the distance between (-8, -1) and (0, 5). Give your answer in simplest radical form.

Mathematics

1 answer:

dolphi86 [110]3 years ago

5 0

Answer:

D (10)

Step-by-step explanation:

The difference in the x-values is 8 and the difference in y-values is 6; if we draw a line for each difference and connect the points, we get a right triangle. Use pythagorean's theorem of a^2 + b^2 = c^2; 36 (6^2) + 64 (8^2) = 100 (10^2). Square root 100 to get 10

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The number of phone calls that Actuary Ben receives each day has a Poisson distribution with mean 0.1 during each weekday and me

Dovator [93]

Answer:

There is a 0.73% probability that Ben receives a total of 2 phone calls in a week.

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.

The problem states that:

The number of phone calls that Actuary Ben receives each day has a Poisson distribution with mean 0.1 during each weekday and mean 0.2 each day during the weekend.

To find the mean during the time interval, we have to find the weighed mean of calls he receives per day.

There are 5 weekdays, with a mean of 0.1 calls per day.

The weekend is 2 days long, with a mean of 0.2 calls per day.

So:

$\mu = \frac{5(0.1) + 2(0.2)}{7} = 0.1286$