The radius of a circle is 10 inches. What is the area of a sector bounded by a

The exponential distribution applies to lifetimes of a certain component. Its failure rate is unknown. Find the probability that

wlad13 [49]

Answer:

a) 0.0821

b) 0.0111

c) 0.0041

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \lambda e^{-\lambda x}$

In which $\lambda$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\lambda x}$

Either it lasts more 5 years or less, or it survives more than 5 years. The sum of the probabilities of these events is decimal 1. So

$P(X \leq 5) + P(X > 5) = 1$

In all 3 cases, we want P(X > 5). So

$P(X > 5) = 1 - P(X \leq 5)$

In which

$P(X \leq 5) = 1 - e^{-5\lambda}$

(a) lambda=.5

$P(X \leq 5) = 1 - e^{-5*0.5} = 0.9179$

$P(X > 5) = 1 - P(X \leq 5) = 1 - 0.9179 = 0.0821$

(b) lambda=0.9

$P(X \leq 5) = 1 - e^{-5*0.9} = 0.9889$

$P(X > 5) = 1 - P(X \leq 5) = 1 - 0.9889 = 0.0111$

(c) lambda=1.1

$P(X \leq 5) = 1 - e^{-5*1.1} = 0.9959$

$P(X > 5) = 1 - P(X \leq 5) = 1 - 0.9959 = 0.0041$

7 0

3 years ago

The equation having null set as its solution set is

KIM [24]

Answer:

B) x = e^x

Step-by-step explanation:

The graphs of y = e^x and y = x never intersect, so the solution set will be the empty (null) set for ...

x = e^x

_____

There is one intersection of y=x with cos(x) and with sin(x). There are an infinite number of solutions for x = tan(x).

4 0

3 years ago

What the closest volume of a cylinder with a height of 10 and a circumference of 8

jenyasd209 [6]

In order to calculate the volume of a cylinder, we can use the following formula:

$V=\pi r^2h$

Where r is the base radius and h is the height.

If the circumference is 8, we have:

$\begin{gathered} C=2\pi r \\ 8=2\pi r \\ r=\frac{4}{\pi} \end{gathered}$

Now, calculating the volume, we have:

$\begin{gathered} V=\pi(\frac{4}{\pi})^2\cdot10 \\ V=\frac{160}{\pi} \\ V=50.93 \end{gathered}$

So the correct option is the second one.

3 0

1 year ago

At a hotdog eating contest, Chris ate 3 more than twice as many hotdogs as the

fenix001 [56]

Answer:

The runner-up ate 5 hotdogs

Step-by-step explanation:

15/3 = 5

6 0

2 years ago

Based on Charles Waddell Chestnutt's "The Wife Of His Yout. Which of the following statements about Mr. Ryder is true? Choose al

Serjik [45]

I'm pretty sure that there are two statements which are true: b. At the conclusion of the story, Charles Waddell Chesnutt wants readers to see the redeeming qualities in Mr. Ryder. and c. The wife of Mr. Ryder's youth could never be a member of his exclusive society.

3 0

3 years ago