Find the slope of (-1,-2) and (1,0)

The number of years a radio functions is exponentially distributed with parameter λ = 1 8 . If Jones buys a used radio, what is

blsea [12.9K]

Answer:

$P(X>8)=e^{-1}$

Step-by-step explanation:

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

$P(X=x)=\lambda e^{-\lambda x}, x>0$

And 0 for other case. Let X the random variable that represent "The number of years a radio functions" and we know that the distribution is given by:

$X \sim Exp(\lambda=\frac{1}{8})$

We can assume that the random variable t represent the number of years that the radio is already here. So the interest is find this probability:

$P(X>8|X>t)$

We have an important property on the exponential distribution called "Memoryless" property and says this:

$P(X>a+t| X>t)=P(X>a)$

Where a represent a shift and t the time of interest.

On this case then $P(X>8|X>t)=P(X>8+t|X>t)=P(X>8)$

We can use the definition of the density function and find this probability:

$P(X>8)=\int_{8}^{\infty} \frac{1}{8}e^{-\frac{1}{8}x}dx$

$=\frac{1}{8} \int_{8}^{\infty} e^{-\frac{1}{8}x}dx$

$=[lim_{x\to\infty} (-e^{-\frac{1}{8}x})+e^{-1}]=0+e^{-1}=e^{-1}$

8 0

2 years ago

R 3. The mean of 4 numbers is 8. Three of the numbers add up to 22. What is the last number?

statuscvo [17]

<h2><em><u>Solution</u></em> : </h2>

let the last number be x

we know,

$\boxed{mean = \frac{sum \: \: of \: \: all \: \: observations}{number \: \: of \: \: observations} }$

So,

$\hookrightarrow \: 8 = \dfrac{22 + x}{4}$

$\hookrightarrow \: 8 \times 4 = 22 + x$

$\hookrightarrow \: 32 = 22 + x$

$\hookrightarrow \: x = 32 - 22$

$\hookrightarrow \: x = 10$

therefore, the last number is 10.

7 0

2 years ago

What is the slope-intercept form of the equation of the line that passes through the point (–6, 1) and is perpendicular to the g

Morgarella [4.7K]

Answer:

Step-by-step explanation:

3y = -2x - 5

y = -2/3x - 5/3

perp: 3/2

y - 1 = 3/2(x + 6)

y - 1 = 3/2x + 9

y = 3/2x + 10

7 0

2 years ago

company x has 50 employees and company y has 60 employees. both companies have the same number of full-time employees, but compa

Sloan [31]

Using the simplification, company y has 17 number of part-time employees.

In the given question we have to find how many part-time employees does company y have.

From the question, company x has 50 employees and company y has 60 employees.

Both companies have the same number of full-time employees, but company y has 3 more than twice the number of part-time employees that company x has.

Let company x has A number of part-time employees.

According the given statement

Company y has number of part-time employees = 2A+3

Let company X and Y have B number of full-time employees.

So the total number of employees in company x;

A+B = 50....................(1)

The total number of employees in company x;

2A+3+B = 60

Subtract 3 on both side we get

2A+B=57....................(2)

Subtract Equation 2 and 1

2A+B-(A+B)=57-50

2A+B-A-B=57-50

A=7

Now putting the value of A in equation 1

7+B=50

Subtract 7 on both side we get

B=43

As, Company y has number of part-time employees = 2A+3

Company y has number of part-time employees = 2×7+3

Company y has number of part-time employees = 14+3

Company y has number of part-time employees = 17

Hence, company y has 17 number of part-time employees.

To learn more about simplification link is here

brainly.com/question/2804192

#SPJ4

8 0

1 year ago

A die is rolled once what is the probability of rolling not a 4

snow_lady [41]

Answer:

I think 1/6

Step-by-step explanation:

A die has 6 sides so every side has 1/6 chance to land on

8 0

3 years ago