A machine produces parts that are either defect free (90%), slightly defective (3%), or obviously defective (7%). Prior to shipment produced parts are passed through an automatic inspection machine, which is supposed to be able to detect any part that is obviously defective and discard it. However, the inspection machine is not perfect. A part is incorrectly identified as defective and discarded 2% of the time that a defect free part is input. Slightly defective parts are marked as defective and discarded 40% of the time, and obviously defective parts are correctly identified and discarded 98% of the time.

Required:
a. What is the total probability that a part is marked as defective and discarded by the automatic inspection machine?
b. What is the probability that a part is 'good' (either defect free or slightly defective) given that it makes it through the inspection machine and gets shipped?
c. What is the probability that a part is 'bad' (obviously defective) given that it makes it through the inspection machine and gets shipped?

Answers

Answer 1

Answer:

(a) 0.0686

(b) 0.9984

(c) 0.0016

Step-by-step explanation:

Given that a machine produces parts that are either defect free (90%), slightly defective (3%), or obviously defective (7%).

Let A, B, and C be the events of defect-free, slightly defective, and the defective parts produced by the machine.

So, from the given data:

P(A)=0.90, P(B)=0.03, and P(C)=0.07.

Let E be the event that the part is disregarded by the inspection machine.

As a part is incorrectly identified as defective and discarded 2% of the time that a defect free part is input.

So, [tex]P\left(\frac{E}{A}\right)=0.02[/tex]

Now, from the conditional probability,

[tex]P\left(\frac{E}{A}\right)=\frac{P(E\cap A)}{P(A)}[/tex]

[tex]\Rightarrow P(E\cap A)=P\left(\frac{E}{A}\right)\times P(A)[/tex]

[tex]\Rightarrow P(E\cap A)=0.02\times 0.90=0.018\cdots(i)[/tex]

This is the probability of disregarding the defect-free parts by inspection machine.

Similarly,

[tex]P\left(\frac{E}{A}\right)=0.40[/tex]

and [tex]\Rightarrow P(E\cap B)=0.40\times 0.03=0.012\cdots(ii)[/tex]

This is the probability of disregarding the partially defective parts by inspection machine.

[tex]P\left(\frac{E}{A}\right)=0.98[/tex]

and [tex]\Rightarrow P(E\cap C)=0.98\times 0.07=0.0686\cdots(iii)[/tex]

This is the probability of disregarding the defective parts by inspection machine.

(a) The total probability that a part is marked as defective and discarded by the automatic inspection machine

[tex]=P(E\cap C)[/tex]

[tex]= 0.0686[/tex] [from equation (iii)]

(b) The total probability that the parts produced get disregarded by the inspection machine,

[tex]P(E)=P(E\cap A)+P(E\cap B)+P(E\cap C)[/tex]

[tex]\Rightarrow P(E)=0.018+0.012+0.0686[/tex]

[tex]\Rightarrow P(E)=0.0986[/tex]

So, the total probability that the part produced get shipped

[tex]=1-P(E)=1-0.0986=0.9014[/tex]

The probability that the part is good (either defect free or slightly defective)

[tex]=\left(P(A)-P(E\cap A)\right)+\left(P(B)-P(E\cap B)\right)[/tex]

[tex]=(0.9-0.018)+(0.03-0.012)[/tex]

[tex]=0.9[/tex]

So, the probability that a part is 'good' (either defect free or slightly defective) given that it makes it through the inspection machine and gets shipped

[tex]=\frac{\text{Probabilily that shipped part is 'good'}}{\text{Probability of total shipped parts}}[/tex]

[tex]=\frac{0.9}{0.9014}[/tex]

[tex]=0.9984[/tex]

(c) The probability that the 'bad' (defective} parts get shipped

=1- the probability that the 'good' parts get shipped

=1-0.9984

=0.0016


Related Questions

how many values of x will satisfy the equation -2|3x-5|=0

Answers

Answer:

1 value

Step-by-step explanation:

spicifically 5/3

The x satisfy only 1 value and x is  [tex]\frac{5}{3}[/tex]   .

What is modulus?

The modulus function, which is also called the absolute value function gives the magnitude or absolute value of a number irrespective of the number being positive or negative. It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.

According to the question

-2|3x-5|=0  

Step1: Dividing -2 both side

|3x-5|=0  

Step 2: Open modulus

3x-5=0      and        - 3x+5=0

3x=5         and         - 3x = - 5

x = [tex]\frac{5}{3}[/tex]    

Hence, the x satisfy only 1 value and x is  [tex]\frac{5}{3}[/tex]   .

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Evaluate functions from their graph .

Answers

hopefully this helps :)

f(-1) = 3
F(-1)=3 is the answer.

The ratio of dogs to cats at the veterinarian's office on Saturday. was 6 to 5. If there were 15 cats at the office, how many dogs and cats were there altogether? ​

Answers

Answer:

33 total cats and dogs

Step-by-step explanation:

15/5=3

3*6=18

18+15=33

hope this helps

Answer:

Dogs: 18Cats: 15In total: 33

Step-by-step explanation:

Set up a proportion: [tex]\frac{6}{5} = \frac{x}{15}[/tex]  Cross multiply, then divide: 15 × 6 = 90, 90 ÷ 5 = 18So, there are 18 dogs in total.Add the dogs and cats together: 18 + 15 = 33

I hope this helps!

100points please help
Image attached
Find x

Answers

The answer is x=180
180 -190
The answer is: X=180

What are m and b in the linear equation 15 + 9x + 3 + 7x = y?

Answers

Collect like terms
15 + 3 + 9x + 7x = y

18 + 16x = y

Recall
b + mx = y

m = 16
b = 18

The standard deviation for u(90, 230)

Answers

Answer:

Standard deviation is 70

Step-by-step explanation:

square root of 4,900= 70 (solved using standard deviation formula)

Please help ASAP marking brainly

Answers

Answer:

y = 2

Step-by-step explanation:

We are given the value of x (second equation). Let's substitute the value of x into the first equation to find y.

[tex]\rightarrow \dfrac{x}{y} = 6[/tex]

[tex]\rightarrow \dfrac{4(y + 1)}{y} = 6 \ \ \ \ \ \ \ \ \ \ \ \ \ \text{\large{[}x = 4(y + 1)]}[/tex]

Use cross multiplication.

[tex]\rightarrow 4(y + 1) = 6 \times y[/tex]

[tex]\rightarrow 4(y + 1) = 6 y[/tex]

Simplify the distributive property.

[tex]\rightarrow 4(y + 1) = 6 y[/tex]

[tex]\rightarrow 4y + 4 = 6 y[/tex]

Subtract 4y both sides.

[tex]\rightarrow 4y - 4y + 4 = 6 y - 4y[/tex]

[tex]\rightarrow 4 = 2y[/tex]

Divide both sides by 2.

[tex]\rightarrow \dfrac{4}{2} = \dfrac{2y}{2}[/tex]

[tex]\rightarrow 2 = y[/tex]

Thus, the value of y is 2.

find f(343) & f(-64) .

Answers

f(343) = ?

[tex] \sqrt[3]{343} = 7[/tex]

7 + 4 = 11

f(-64) = ?

[tex] \sqrt[3]{ - 64} = - 4[/tex]

-4 + 4 = 0

What are the coordinates of the vertex for f(x) = x2 + 4x + 10?

A- (−2, 2)
B- (2, 2)
C- (−2, 6)
D- (2, 6)

Answers

Answer:

I believe the answer is C (-2,6)

[tex]\\ \rm\rightarrowtail y=x^2+4x+10[/tex]

Add and subtract 4

[tex]\\ \rm\rightarrowtail y=x^2+4x+4+10-4[/tex]

[tex]\\ \rm\rightarrowtail y=x^2+4x+2^2+6[/tex]

[tex]\\ \rm\rightarrowtail y=(x+2)^2+6[/tex]

Vertex form

y=a(x-h)^2+k

Vertex:-

(h,k)=(-2,6)

X + 14 = 21 what should be done to solve this equation

Answers

Answer:

x+14=21 Add 14 to both sides of the equation. Subtract 14 from the left side of the equation. Add 14 to the left side and subtract 14 from the right side of the equation.

Step-by-step explanation:

Answer: x = 7

Step-by-step explanation:

U first subtract 14 from both sides

x + 14 - 14 = 21 - 14

And then u simplify

and get 7

Practice Translate Expressions

Write an algebraic expression that models the given word phrase.
1) 15 divided by d ________________________
2) seven fewer than a number n ________________________
3) two times the sum of a and b ________________________
4) nine less than 5 multiplied by the number p ________________________
5) the product of 15 and x ________________________
6) quotient of 4 more than the number z and the number y decreased by _________

Answers

1) 15/d
2) n - 7
3) (a + b) x 2
4) 5p - 9
5) 15x
6) 4 + z / y

Find the real-number root.

√1.44

1.2

no real roots

2.07

0.72

Answers

Answer: A. 1.2

Step-by-step explanation:

The principal, real, root of:

2^√1.44

=1.2

All roots:

1.2

−1.2

1.44 is not a perfect square

Which set of ordered pairs represents a function?
{(2, –2), (1, 5), (-2, 2), (1, –3), (8, –1)}

{(-3, –1), (-7, 1), (–6, –1), (-8, 1), (2, –1)}

{(1, 8), (5, 2), (2, –5), (1, –3), (–2, 9)}

{(–3, 1), (6, 3), (4, 2), (6, –3), (1, –1)}

Answers

Answer:

A

Step-by-step explanation:

A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.

what is the initial number of views?

A.0
B.100
C.110
D.11​

Answers

Answer:

A

Step-by-step explanation:

O because that is the number that you always start off.

It is 100.
It is 100 because the graph starts there it doesn’t start on (0,0)it starts on (0,100)

71.6 less then or greater then 71.63

Answers

Answer:

less

Step-by-step explanation: 71.6 can also be seen as 71.60 therefore 71.63 is greater

Answer:

Less than.

Think of .6 as the tenths place to tens place.

.63 is 6 tenths and 3 hundredths, so 63.

Now ask yourself, "Is 63 greater than 60?"

And your answer is yes.

AHIJ has coordinates H(0, 0), I(-3, -1), and J-1, -2). Graph the triangle and its translation 3 units to the right and 2 units down. What are the coordinates of J'

Answers

The coordinates of the triangle is plotted on the graph and the translated triangle is H' ( 3 , -2 ) , I' ( 0 , -3 ) and J' ( 2 , -4 )

Given data ,

Let the triangle be represented as ΔHIJ

Let the coordinates of the triangle be  H(0, 0), I(-3, -1), and J(-1, -2)

Now , the translation rule is

The triangle is translated 3 units to the right and 2 units down

So , add 3 to the x-coordinates and subtract 2 from the y-coordinates of each point

So , the translated triangle is H' ( 3 , -2 ) , I' ( 0 , -3 ) and J' ( 2 , -4 )

Hence , the translated triangle is H' ( 3 , -2 ) , I' ( 0 , -3 ) and J' ( 2 , -4 )

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I need help please due in a hour

Answers

Answer:

so easy ....dude

Step-by-step explanation:

you can do it..

I need help doing this I don't pay attention in class now I'm lost

Answers

Answer:

i think the answer is 6498

Step-by-step explanation:

Answer:

6498

Step-by-step explanation:

Pay attention in class :)

Okay, so basically, you just need to replace x and y with the corresponding numbers.

So our equation would be:

9 * 2(5 * 7 - 8 * 2) squared

Now we solve with PEMDAS:

9 * 2(35 - 16)squared

9 * 2(19)squared

9 * 2(361)

18 * 361

6498

Let me know if I did something wrong!

Ivan said that if a number ends in 0 both 2 and 5 are factors of the number. Is he correct? Why of why not?

Answers

Answer:

yes he is correct bc the number will always be divisive by 2 and 5

PLEASE HELP


Write a story problem to go with the multiplication problem 5 x 3/4 . Then solve the problem.

Answers

Story:

John is baking a cake. He need to feed 5 people with the cake but the recipe is only designed for 1 serving. In the regular recipe, it required 3/4 cups of sugar. How much sugar does he need for the new recipe?


Answer:
3.75 or 3 3/4


Answer:

A store has 5 oranges then a customer buys 3/4 of them. How many is left

Step-by-step explanation:

5x3/4=3.75 if it was in decimal but in fraction it is 23/4
5x3/4=3.75

3/4 is 0.75
0.75 x 5=3.75

Solve the following equations for x (5 points each). (a) -3x+10=34 and (b) 13x-4=11x+10-8

please show work

Answers

Answer:

A)x=-8 B)x=3

Step-by-step explanation:

A)-3x+10=34   -3x+10-10=34-10   -3x/-3=24/-3 x=-8

B) 13x-4=11x+10-8   13x-4+4=11x+10-8+4  13x-11x=11x-11x+6  2x/2=6/2   x=3

Emma measured a line to be 16 inches long. If the actual length of the line is 15.3 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?

Answers

Answer:

4.6% (nearest tenth)

Step-by-step explanation:

percent error = (|approx - actual| ÷ actual) × 100

percent error = (|16 - 15.3| ÷ 15.3) × 100

                      = 4.6% (nearest tenth)

[tex] \sf\% \: error = \frac{ |approx - actual| }{actual} \times 100[/tex]

Approx = 16Actual = 15.3

[tex] \tt\% \: error = \frac{ |16 - 15.3| }{15.3} \times 100[/tex]

[tex] \tt\% \: error = \frac{ |0.7| }{15.3} \times 100[/tex]

[tex] \tt\% \: error = \frac{ |0.7| }{ \frac{153}{10} } \times 100[/tex]

[tex] \tt\% \: error = \frac{0.7}{ \frac{153}{10} } \times 100[/tex]

[tex] \tt\% \: error = \frac{ \frac{7}{10} }{ \frac{153}{10} } \times 100[/tex]

[tex] \tt\% \: error = \frac{7 }{ 153 } \times 100[/tex]

[tex] \tt\% \: error = \frac{7 00}{ 153 } [/tex]

[tex] \tt\% \: error =4.57\%[/tex]

Thus, The % error is 4.6% when rounded off to the nearest tenth!!~

find the rate of change from the equation x=1 will mark brainiest ​

Answers

Answer:

undefined

Step-by-step explanation:

when graphed, x=1 goes up and down which makes it's slope undefined

Answer:

(infinity)

Step-by-step explanation:

rate of change for the equation x = 1

use the formula: y = mx + b

where:

y = how far up the line goes

m = slope

x = how far along

b = Y-intercept

the equation is a vertical line,

so the slope = ∞ (infinity)

27 3/10 - 12 5/9 write in old style math

Answers

Answer:

273/10 - 113/9

Step-by-step explanation:

Answer:

- 15 [tex]\frac{23}{50}[/tex]

Step-by-step explanation:

We need to make [tex]\frac{3}{10}[/tex] and [tex]\frac{5}{9}[/tex] have the same denominator, or bottom half, before we can subtract them.In order to do this, we need to find a number that both 10 and 9 (the bottom numbers) both go into. (Hint! Multiplying them together usually helps!)This number is 90. (See? 10 • 9 = 90!)Since we multiplied 10 by 9 to get 90, we need to multiply the top (3) by 9 too, to get us [tex]\frac{27}{90}[/tex].We multiply [tex]\frac{5}{9}[/tex] by 10 to get us [tex]\frac{50}{90}[/tex].Now we can subtract 27 [tex]\frac{27}{90}[/tex] and 12 [tex]\frac{50}{90}[/tex].27 - 12 = 15 (big numbers)27 - 50 = -23 (fractions)Now we have - 15 [tex]\frac{23}{50}[/tex]

If I am incorrect in my reasoning, please let me know so that I can plan better for my future answers. Have an amazing day.

Given: 7x/2 < 5.
Choose the solution set.
• {xlx > 10/7}
• {x|x < 35/2}
• {x|x > 35/2}
• {x|x < 10/7}
I have no idea lol.

Answers

Answer:

x < 10/7

Step-by-step explanation:

7x/2 < 5

multiply eech side by the reciprocal(2/7)

x < 10/7

Determine the solution to the equation given 4(m-2)=18

Answers

Answer:

m=13/2 hope this helped:)

Step-by-step explanation:

The rod is made of A-36 steel and has a diameter of 0.22 in . If the rod is 4 ft long when the springs are compressed 0.7 in . and the temperature of the rod is T= 30 ∘F , determine the force in the rod when its temperature is T= 150 ∘F .

Answers

The force in the rod when the temperature is 150 °F is 718.72 pounds-force.

How to determine the resulting the resulting force due to mechanical and thermal deformation

Let suppose that rod experiments a quasi-static deformation and that both springs have a linear behavior, that is, force ([tex]F[/tex]), in pounds-force, is directly proportional to deformation. Then, the elongation of the rod due to temperature increase creates a spring deformation additional to that associated with mechanical contact.

Given simmetry considerations, we derive an expression for the spring force ([tex]F[/tex]), in pounds-force,  as a sum of mechanical and thermal effects by principle of superposition:

[tex]F = k\cdot (\Delta x + 0.5\cdot \Delta l)[/tex]   (1)

Where:

[tex]k[/tex] - Spring constant, in pounds-force per inch.[tex]\Delta x[/tex] - Spring deformation, in inches.[tex]\Delta l[/tex] - Rod elongation, in inches.

The rod elongation is described by the following thermal dilatation formula:

[tex]\Delta l = \alpha \cdot L_{o}\cdot (T_{f}-T_{o})[/tex]   (2)

Where:

[tex]\alpha[/tex] - Coefficient of linear expansion, in [tex]\frac{1}{^{\circ}F}[/tex].[tex]L_{o}[/tex] - Initial length of the rod, in inches. [tex]T_{o}[/tex] - Initial temperature, in degrees Fahrenheit.[tex]T_{f}[/tex] - Final temperature, in degrees Fahrenheit.

If we know [tex]k = 1000\,\frac{lb}{in}[/tex], [tex]\Delta x = 0.7\,in[/tex], [tex]\alpha = 6.5\times 10^{-6}\,\frac{1}{^{\circ}F}[/tex], [tex]L_{o} = 48\,in[/tex], [tex]T_{o} = 30\,^{\circ}F[/tex] and [tex]T_{f} = 150\,^{\circ}F[/tex], then the force in the rod at final temperature is:

[tex]F = \left(1000\,\frac{lb}{in} \right)\cdot \left[0.7\,in + 0.5\cdot\left(6.5\times 10^{-6}\,\frac{1}{^{\circ}F} \right)\cdot (48\,in)\cdot (150\,^{\circ}F-30\,^{\circ}F)\right][/tex]

[tex]F = 718.72\,lbf[/tex]

The force in the rod when the temperature is 150 °F is 718.72 pounds-force. [tex]\blacksquare[/tex]

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In this image, what is the value of C? Round your answer to the nearest tenth.

Answers

Answer:

C = 7.2

Step-by-step explanation:

What's Pythagorean Theorem?

Pythagorean Theorem is a theorem in which it states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse. This can be represented as an equation of a² + b² = c².

To find the value of C, we're going to use Pythagorean Theorem! We're given the legs as 4 and 6.

Step 1: Simplify.

[tex]4^2+6^2=c^2[/tex][tex]16+36=c^2[/tex] [tex]52=c^2[/tex]

Step 2: Take square root of both sides.

[tex]\sqrt{c^2}=\sqrt{52}[/tex] C ≈ 7.2

Therefore, the value of C is 7.2.

I need help please ASAP !!

Answers

Answer:

Step-by-step explanation:

5) ∠1

6)  ∠2 and ∠3

7)  ∠1

What is a savings goal? PLS I NEED HELP QICK PLSSS ​ nvm

Answers

Answer:

A goal for the amount of money being saved.

Step-by-step explanation:

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