For this item, answers should be rounded to the nearest cent.

A new phone-answering system installed by a certain utility company is capable of handling twelve calls every 5 minutes. Prior

SVEN [57.7K]

Answer:

A. P(x>12 in 5 minutes)=0.0201

Step-by-step explanation:

Because we are working with a Poisson Distribution of probability, we need to get all the data needed. In a Poisson distribution is needed a constant called λ that symbolizes the mean data (6 calls) per unit of time (5 minutes), for this distribution λ=6/5.

Poisson probabilities work like this:

$P(x=y\ 'in\ z\ unit\ of\ time')= \frac{e^{-z\lambda}(z\lambda)^{y}}{y!}$

Remember y has to be an integer and the units of z must be the same unit of time used in λ. Now we are ready to solve this problem

A. The question is asking for the probability that in 5 minutes appear more calls than the phone-answering machine could answer (i.e P(x>12 in 5 minutes)). Because there are infinite numbers greater than 12, we are using this property of probabilities that´ll help us simplify the problem:

P(x>12 in 5 minutes)= 1 - P(x≤12 in 5 minutes)

Now we can use the following:

$P(x\geq12\ in\ 5\ minutes)=P(x=0\ in\ 5\ min)+P(x=1\ in\ 5\ min)+...P(x=12\ in\ 5\ min)$

$P(x\geq12\ in\ 5\ minutes)=\sum_{n=0}^{\infty}P(x=n\ in\ 5\min)$

$P(x\geq12\ in\ 5\ minutes)=\sum_{n=0}^{\infty}\frac{e^{-6}6^{n}}{n!}$

And you can find P(x=n in 5 minutes) for every n using a calculator or a computer, and finally add them to get

P(x≤12 in 5 minutes)= 0.9799

P(x>12 in 5 minutes)= 1-0.9799

This will be our answer

P(x>12 in 5 minutes)= 0.0201

8 0

3 years ago

Factor the following trinomial. (Hint: Solve the equations first.)<br><br> x²-2x-2

Alex_Xolod [135]

Answer:

$(x-(1+\sqrt{3}))(x-(1-\sqrt{3}))$

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$x^{2} -2x-2=0$

so

$a=1\\b=-2\\c=-2$

substitute in the formula

$x=\frac{-(-2)(+/-)\sqrt{-2^{2}-4(1)(-2)}} {2(1)}$

$x=\frac{2(+/-)\sqrt{12}} {2}$

$x=\frac{2(+/-)2\sqrt{3}} {2}$

$x_1=\frac{2(+)2\sqrt{3}} {2}=1+\sqrt{3}$

$x_2=\frac{2(-)2\sqrt{3}} {2}=1-\sqrt{3}$

therefore

$x^{2} -2x-2=(x-(1+\sqrt{3}))(x-(1-\sqrt{3}))$

5 0

3 years ago

List the domain and range of (5,12)(3,-3),(-2,7)(2,12)(5,1)

Sliva [168]

Answer:

Domain={-2,2,3,5}

Range={-3,1,7,12}

Step-by-step explanation:

The given ordered pairs are (5,12)(3,-3),(-2,7)(2,12)(5,1).

The domain refers to the set of all the first coordinates(x-values).

Domain={-2,2,3,5}

The range refers to the set of all the second coordinates (y-values).

Range={-3,1,7,12}

Note that, we do not repeat elements in a set.

Do not list the 5 in the domain twice.

The same applies to the 12 in the range

8 0

4 years ago

Need help with full explanation first to answer extra points!!!

blsea [12.9K]

Answers:

Step-by-step explanation:

Those brackets indicate absolute value. Absolute value is the distance of a number from 0 on the number line. In other words, negatives don't matter. There is also no such thing as a negative absolute value.

-2 -1 0 1 2

Both -2 and 2 are the same distance from 0, just in the opposite direction. Both numbers have the same absolute value, which is 2.

Hope This helps. If it did, then....

<em>PLEASE MARK BRAINLIEST</em>

7 0

4 years ago

Keisha is investing her money in an IRA. Initially she will be putting in $775. Using C as the additional amount invested each m

Mars2501 [29]

Initial investment = $775
Monthly investments = $C
Period of investment = 1 year = 12 months

Total monthly investments = Monthly amount*12 = C*12 = 12C

Total investment after 12 months = Initial investment + Total monthly investments = 775 + 12C

6 0

3 years ago