Rent for a 3-bedroom apartment is regularly 936 per month. Apartment management is now offering one month free for 12- month lea

Answer:

a) 0.019

b) 0.563

c) x = 1.966 hours

Detailed explanation:

E(X) = 1

The probability function for an exponential random variable can be expressed as

P(X=x) = λ e^(-λ.x)

The cumulative distribution function is defined as

P(X ≤ x) = 1 - e^(-λ.x)

a) This refers to the time gaps between the arrivals of smaller aircraft at a county airport, which follows an exponential distribution.

To find the number of planes landing every hour, the Poisson distribution formula is used as it is more suited for discrete systems.

The Poisson formula is defined as

P(X = x) = (e^-λ)(λˣ)/x!

For this case, λ = 1 aircraft per hour.

The likelihood of having more than three aircraft arrivals in one hour is expressed as P(X > 3)

P(X > 3) = 1 - P(X ≤ 3) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]

P(X > 3) = 1 - 0.98101 = 0.01899 = 0.019 rounded to three decimal places

b) For 30 separate one-hour intervals selected, what is the probability that none of the intervals contain more than three arrivals?

The possibility that a single 1-hour interval has three or fewer arrivals equals 1 - P(X > 3)

= 1 - 0.01899 = 0.98101

The likelihood that none of the thirty 1-hour intervals exceed three arrivals is (0.98101)³⁰ = 0.5626 = 0.563 rounded to three decimal places

c) Calculate the duration of an interval (in hours) where the chance of no arrivals is 0.14

To solve this, we will apply the cumulative distribution function for an exponential random variable

P(X ≤ x) = 1 - e^(-λ.x)

P(X > x) = 1 - P(X ≤ x)

P(X > x) = e^(-λ.x)

Here, λ = 1, x =?,

0.14 = e⁻ˣ

e⁻ˣ = 0.14

Taking the natural logarithm: In e⁻ˣ = In 0.14 = -1.966

-x = -1.966

x = 1.966 hours

Hope this Helps!!!

Let

t--------> the time measured in hours

d-------> the distance in miles

we understand that

this represents a linear equation corresponding to the situation

where time t is the independent variable and distance d is the dependent variable

The distance in function notation can be expressed as

Using a graphical tool

refer to the attached image

The function's domain extends over the interval----------> [0,∞)

The range of this function is defined by the interval------->  [0,∞)

Statements

a) The independent variable, the input, is the variable d, which signifies distance

This statement is incorrect

Because the independent variable is actually t

b) The distance covered is contingent on the duration of time Marlene spends riding her bike

This statement is correct

Because the equation for distance in function notation is equal to

c) The initial speed relevant to the scenario is 16 miles per hour

This statement is incorrect

Because indicates the slope or rate of the linear equation

d) The equation t = d + 16 relates to the scenario

This statement is incorrect

Because the situation is represented by the function

e) The function f(t) = 16t relates to the scenario

This statement is correct

Answer:

What is the variation for each successive input?

✔ 1

What is the variation for each successive output?

✔ 0.35

What is the rate of variation for the correlation?

✔ 0.35

Step-by-step explanation:

The change per input is 1 since the inputs are 10,11,12,13.

The change for each successive output is 0.35 because we must subtract 4.1 from 3.75.

Thus, the rate of variation for the correlation is likewise 0.35.

Answer:

El valor de x es 4.

Explicación paso a paso:

Se indica que el triángulo MRN surge al doblar un triángulo equilátero por la mitad.

Esto sugiere que el triángulo equilátero original es MNO y que NR actúa como bisectriz perpendicular (una línea que divide un segmento en dos partes iguales formando un ángulo recto).

La longitud del lado del triángulo es

NO = NS + SM = 6 + 2 = 8

Dado que un triángulo equilátero tiene todos sus lados iguales y NR es la bisectriz perpendicular, se tiene que

RM = MO/2 = 8/2 = 4

El valor de x es 4.