1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sveticcg [70]
3 years ago
5

A hole is drilled in a sheet-metal component, and then a shaft is inserted through the hole. The shaft clearance is equal to dif

ference between the radius of the hole and the radius of the shaft. Let the random variable X denote the clearance, in millimeters. The probability density function of X is
F(x) =1.25(1 - x4) if 0 < x < 1
F(x) = 0 otherwise

A. Components with clearances larger than 0.8 mm must be scrapped. What proportion of components are scraped?
B. Find the cumulative distribution function F(x) and plot it.
C. Use the cumulative distribution to find the probability that the shaft clearance is less than 0.5 mm.
D. Find the mean clearance and the variance of the clearance.
Mathematics
1 answer:
VashaNatasha [74]3 years ago
5 0

Answer:

(A)

P(X \geq 0.8) = \int\limits_{0.8}^{\infty} f(x) \, dx  = \int\limits_{0.8}^{1} 1.25(1-x^4) \, dx = 0.08192

(B)

Then the cumulative function would be

CF(x) = 1.25x - 0.25x^5       if   0<x<1

0 otherwise.

Step-by-step explanation:

(A)

We are looking for the probability that the random variable X is greater than 0.8.

P(X \geq 0.8) = \int\limits_{0.8}^{\infty} f(x) \, dx  = \int\limits_{0.8}^{1} 1.25(1-x^4) \, dx = 0.08192

(B)

For any  x you are looking for the probability P(X \geq x)  which is

P(X \geq x)  = \int\limits_{-\infty}^{x}  1.25(1-t^4) dt = \int\limits_{0}^{x}  1.25(1-t^4) dt = 1.25x - 0.25x^2

Then the cumulative function would be

CF(x) = 1.25x - 0.25x^5       if   0<x<1

0 otherwise.

You might be interested in
Suppose f(x) = x^2 and
SpyIntel [72]

Given:

The two functions are:

f(x)=x^2

g(x)=\left(\dfrac{1}{3}x\right)^2

To find:

The statement that best compares the graph of g(x) with the graph of f(x).

Solution:

The horizontal stretch is defined as:

g(x)=f(kx)            ...(i)

If 0, the function f(x) is horizontally stretched by factor \dfrac{1}{k}.

If k>1, the function f(x) is horizontally compressed by factor \dfrac{1}{k}.

We have,

f(x)=x^2

g(x)=\left(\dfrac{1}{3}x\right)^2

Using these functions, we get

g(x)=f\left(\dfrac{1}{3}x\right)         ...(ii)

On comparing (i) and (ii), we get

k=\dfrac{1}{3}

Since 0, the function f(x) is horizontally stretched by factor \dfrac{1}{\frac{1}{3}}=3.

Hence, the correct option is D.

5 0
3 years ago
BRAINLIEST TO CORRECT HURRY
dlinn [17]

Answer:

-5 5/10, -32/40,5

whenever a number has a negative sign,the larger the number the smaller.

i.e (-55/10= -5.5) is smaller than -32/40=-0.8 and then the greatest is 5 since it is a positive number and positive numbers are greater than negative numbers.

4 0
3 years ago
Juan got a new helicopter for Christmas and the time it takes to ascend to certain heights is shown above. His sister, Marla, be
Greeley [361]
Well for the first one, 
You have to find out if it is at 25 ft at one second, but since you can't you find the next best thing, find 25 feet then see how many seconds it is at.

For the second one you would have to find where they directly meet, I chose 40 and 20
40 April Sales = 20 March Sales
So this means that for every March sale you would have 2 April sales. 40/20 = 2 
7 0
3 years ago
Find the volume of the cone.
8_murik_8 [283]

Answer:

V=471\ \text{units}^3

Step-by-step explanation:

Given that,

Radius of the cone, r = 5 units

Height of the cone, h = 6 units

We need to find the volume of the cone. The formula for the volume of the cone is given by :

V=\pi r^2 h

Substitute all the values,

V=3.14\times 5^2\times 6\\\\V=471\ \text{units}^3

So, the volume of the cone is 471\ \text{units}^3.

4 0
2 years ago
24. a rate in which the second quantity. In the comparison is one unit.
natima [27]
24. unit rate
25. ?
26. surface area
27. trial
28. supplementary angles
29. variable
30. unit conversion ?
3 0
3 years ago
Read 2 more answers
Other questions:
  • The difference between longitude and altitude
    7·1 answer
  • A car corporation produced 1300 fewer cars this month than last. Write a signed number to represent this month's change in produ
    13·1 answer
  • The area of a square field is 2500 m2. Explain how you know the dimensions of the field are 50 m by 50 m.
    14·1 answer
  • I am having some trouble with finding out the two problems for this question, can you please help me?
    14·1 answer
  • Blank % of 50 shirts is 35 shirts
    7·1 answer
  • Solve for x: 8x - 2 = -9 + 7x<br> I need to show my work
    14·2 answers
  • What is the answer 2(x - 5) ≤ - 16
    5·1 answer
  • <img src="https://tex.z-dn.net/?f=%5Cpi%20-%201" id="TexFormula1" title="\pi - 1" alt="\pi - 1" align="absmiddle" class="latex-f
    14·2 answers
  • If B =1-6w2 and A = 1+ w, find an expression that equals 2B – A in<br> standard form.
    15·1 answer
  • 2.4 divided by 0.24 pllss help
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!