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3 years ago

Please help me with the following questions. Thanks in advance!!

Mathematics

1 answer:

Orlov [11]3 years ago

4 0

Answer:

Step-by-step explanation:

Eight

590 = 1800 e^(-0.4t) Divide by 1800

0.32778 = e^(-0.4t) Put the value for e in the denominator.

0.32778 = 1 / e^(0.4t) Notice the sign's gone. Multiply both sides by e^(0.4t)

0.32778 *e^(0.4t) = 1 Divide by 0.32778

e^(0.4t) = 3.0508 Take the natural log of both sides.

0.4t = 1.11542 Divide both sides by 0.4

t = 2.78855

You should put this in the original equation to see if it checks. It does.

=============================

Nine

3^(3 - 3x) + 6 = 42 Subtract 6 from both sides

3^(3 - 3x) = 36 Take the log of both sides.

(3 - 3x) ln(3) = ln 36

(3 - 3x) *1.098612 = 3.58352 Divide by 1.098612

3 - 3x = 3.26186 Subtract 3 from both sides

- 3x = 0.26186 Divide by - 3

x = - 0.087287

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Answer:

The two given numbers are 10.5 units apart.

Step-by-step explanation:

Subtract the smaller from the larger. The larger number here is 6.2. Then we have

6.2 - (-4.3) = 6.2 + 4.3 = 10.5

The two given numbers are 10.5 units apart.

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2 years ago

F(x) = x2 + 4x − 6

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Since

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3 years ago

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:

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

If today is Monday, what is the probability that Ben receives a total of 2 phone calls in a week?

This is $P(X = 2)$ . So:

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

$P(X = 2) = \frac{e^{-0.1286}*0.1286^{2}}{(2)!} = 0.0073$

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

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2 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

Read 2 more answers

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