A complex electronic system is built with a certain number of backup components in its subsystems. One subsystem has four identical components, each with a probability of .2 of failing in less than 1000 hours. The subsystem will operate if any two of the four components are operating. Assume that the components operate independently. Find the probability that a exactly two of the four components last longer than 1000 hours. b the subsystem operates longer than 1000 hours.

Answers

Answer 1

Answer:

a. 0.1536

b. 0.9728

Step-by-step explanation:

The probability that a component fails, P(Y) = 0.2

The number of components in the system = 4

The number of components required for the subsystem to operate = 2

a. By binomial theorem, we have;

The probability that exactly 2 last longer than 1,000 hours, P(Y = 2) is given as follows;

P(Y = 2) = [tex]\dbinom{4}{2}[/tex] × 0.2² × 0.8² = 0.1536

The probability that exactly 2 last longer than 1,000 hours, P(Y = 2) = 0.1536

b. The probability that the system last longer than 1,000 hours, P(O) = The probability that no component fails + The probability that only one component fails + The probability that two component fails leaving two working

Therefore, we have;

P(O) = P(Y = 0) + P(Y = 1) + P(Y = 2)

P(Y = 0) = [tex]\dbinom{4}{0}[/tex] × 0.2⁰ × 0.8⁴ = 0.4096

P(Y = 1) = [tex]\dbinom{4}{1}[/tex] × 0.2¹ × 0.8³ = 0.4096

P(Y = 2) = [tex]\dbinom{4}{2}[/tex] × 0.2² × 0.8² = 0.1536

∴ P(O) = 0.4096 + 0.4096 + 0.1536 = 0.9728

The probability that the subsystem operates longer than 1,000 hours = 0.9728


Related Questions

If ABCD is a parallelogram,what is the value of x?
answers
a.) 46
b.) 82
c.) 38
d.) 44
e.) 69
f.) 37

Answers

Answer:

D.44

Step-by-step explanation:

i hope its help for you po

what is the answer to 15y − 1 = 11/2y + 2

Answers

Answer:

y= 6/19

hope it helps

i need help with this

Answers

Answer:

[tex]y = - \frac{1}{2} x + 4[/tex]

Step-by-step explanation:

Let us consider two points through which the line passes through

[tex](x_1 , y _ 1 ) = ( 0 , 4 ) \ and \ (x_ 2 , y _ 2 ) = ( 4, 2 )[/tex]

Step 1 : Find slope of the line

[tex]Slope, m_1 = \frac{rise}{run} \\\\That \ is \ m_1 \ = \frac{y_2 - y _ 1}{x_2 - x_1}[/tex]

                  [tex]= \frac{2 - 4}{4-0} \\\\=-\frac{2}{4}\\\\= - \frac{1}{2}[/tex]

Step 2 : Find equation of the line.

[tex](y - y _ 1) = m_ 1 (x - x_1)\\\\( y - 4) = - \frac{1}{2}(x - 0)\\\\y = -\frac{1}{2}x + 4[/tex]

Saw a board 5 ft 1 in. Long into six equal pieces. If the loss per cut is 1/5 in., how long will each piece be?

Answers

Answer:

The length of each piece is 0.833 ft.

Step-by-step explanation:

Length of board, L = 5 ft 1 inch

loss per cut = 1/5 inch

The board should be cut by 5 times to get the 6 pieces.

The loss in 5 cuts = 5 x 1/5 = 1 inch

So, the length of each piece is

[tex]L' =\frac{5 ft 1 in - 1in }{6}\\\\L' =\frac{5}{6}\\\\L' = 0.833 ft[/tex]

The length of each piece is 9 13/15 inches.

What is the length of each piece?

The first step is to determine the length of the board in inches. In order to do this, feet should be converted to inches.

1 feet = 12 inches

(12 x 5) + 1 = 61 inches

Total losses of the 6 cuts = 1/5 x 6 = 6/5 = 1 1/5 inches

Total length left = 61 inches - 1 1/5 inches = 59 1/5 inches

Length of each board = 59 1/5 ÷ 6

296 / 5 x 1/6 = 296 /30 = 9 26/30 = 9 13/15 inches

To learn more about multiplication of fractions, please check: https://brainly.com/question/1114498

Violet bought 2 yards of fabric. She will use it to make new pillow covers. How many inches of fabric did Violet get?

Answers

Answer:

24 inches

Step-by-step explanation:

2 yards to inches :

2 x 12 = 24

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

72 inches

Step-by-step explanation:

1 yard = 3 feet

1 foot = 12 inches

1 yard = 3(12) inches or 36"

∴ 2 yards = 72 inches

PLEASE HELP IF YOU KNOW GEOMETRY THIS SHOULD BE EASY

Answers

Answer:

Growth

Step-by-step explanation:

When x value increase, y value also increase, So growth.

When x = 1   ;f(1) = 2

When x = 2  ; f(2) = 2² = 4

When x = 3  ; f(3) = 2³ = 8

Answer:

Exponential Growth

Step-by-step explanation:

I found this photo that helps differentiate both growth and decay :)

I hope this helps! :)

no links please, i cant find the answer for q b) ii)

Answers

Answer:

-k

Step-by-step explanation:

Cos(140)=cos(180-40)=-cos(40)=-k

Answer:

Step-by-step explanation:

Sin (90 - A)  = Cos A

Cos (90 + A) =   -Sin A

Sin 50 = Sin (90 - 40)

          = Cos 40

         = k

Cos 140 = Cos (90 + 50)

             = - Sin 50

            = (- k)

Quadrilateral MNOP below is a trapezoid. Use the figure to select the best answer from the choices provided

If HG = 6 and PO = 8, what is the length of MN?

A. 4
B. 7
C. 10
D. 14

Answers

Answer:

A. 4

Step-by-step explanation:

HG = 6,

PO = 8

HG = ½(PO + MN) => Trapezoid Mid-segment Theorem

Plug in the values into the equation

6 = ½(8 + MN)

Multiply both sides by 2

2*6 = 8 + MN

12 = 8 + MN

12 - 8 = 8 + MN - 8 => Subtraction Property of Equality

4 = MN

MN = 4

Answer:

i think it is 4 because it is lowering by 2 from  po-8 to  hg-6. my answer: mn-4

Step-by-step explanation:

Please help and thank u

Answers

Answer:

The answer to this question is C.

Here's a little something that will tease your brain. I doubt someone will answer this​

Answers

Answer:

500ml orange juice is the most cost effective

500 ml is the answer

The tables represent the functions f(x) and g(x).

A table with 2 columns and 7 rows. The first row, x, has the entries, negative 3, negative 2, negative 1, 0, 1, 2. The second row, f(x), has the entries, negative 5, negative 3, negative 1, 1, 3, 5. A table with 2 columns and 7 rows. The first row, x, has the entries, negative 3, negative 2, negative 1, 0, 1, 2. The second row, g(x), has the entries, negative 13, negative 9, negative 5, negative 1, 3, 7.
Which input value produces the same output value for the two functions?

Answers

Answer:

rtyujn

Step-by-step explanation:

er456y7ujm

The diagram shows a rectangle PQRS.
PQ = 14 cm and QR = 9 cm.
The point A lies on PS so that PA = 5 cm.
The point Blies on SR so that BR = 8 cm.

Answers

Answer:

a) The area of the triangle AQB is 43 square centimeters.

b) The length of the line segment AQ is approximately 14.866 centimeters.

Step-by-step explanation:

a) The procedure consist in subtracting the areas of triangles APQ, ASB and BRQ of the area the rectangle, that is to say:

[tex]A = (9\,cm)\cdot (14\,cm) - \frac{1}{2}\cdot (5\,cm)\cdot (14\,cm) - \frac{1}{2}\cdot (8\,cm)\cdot (9\,cm) -\frac{1}{2}\cdot (4\,cm) \cdot (6\,cm)[/tex]

[tex]A = 43\,cm^{2}[/tex]

The area of the triangle AQB is 43 square centimeters.

b) The length of the line segment AQ is determined by Pythagorean Theorem:

[tex]AQ = \sqrt{AP^{2}+PQ^{2}}[/tex] (1)

[tex]AQ = \sqrt{(5\,cm)^{2}+(14\,cm)^{2}}[/tex]

[tex]AQ \approx 14.866\,cm[/tex]

The length of the line segment AQ is approximately 14.866 centimeters.

Explain in your own words why it takes more to prove quadrilaterals congruent. Include examples demonstrating how ""just angles"" or ""just sides"" is not enough.

Answers

Proving that quadrilaterals are congruent takes more because all quadrilaterals are polygons of four sides and they all have a sum angle of 360°

Meaning of Congruent quadrilaterals

A quadrilateral can be defined as a polygon shape that possesses four sides.

Congruent quadrilaterals are those quadrilaterals that are similar in sides and angles.

For example, a parallelogram needs to be proved by both the sides and the angles

In conclusion, Proving that quadrilaterals are congruent takes more because all quadrilaterals are polygons of four sides and they all have a sum angle of 360°

Learn more about Congruent quadrilaterals: https://brainly.com/question/224113

#SPJ1

PLEASE HELP!!!! i need this done tonight and i dont know how to do it

Answers

Answer:

x=-2/3

Step-by-step explanation:

So let's start off with adding 4x on both sides, we add them to cancel out the -4x on the right hand side.

4x+-9x=-5x

Now, as for the fractions all we really gotta do here is add and subtract them. Let's subtract 5/6 on both sides. once we do that we get:

2/3+7/2-5/6=-5x

A quick trick for adding and subtract fractions is to cross multiply.

2/3+7/2

Multiply 3 times 7 and 2 times 2, then we'll multiply 3 times 2 to get a denominator.

3*2=6 (our denominator)

3*7=21

21/6

2*2=4/6

21/6+4/6=

25/6

Awesome! Now we have two like denominators so we don't have to do any additional cross multiplying. So, we can subtract 25/6-5/6=20/6.

Now, all we're left with is:

20/6=-5x

We can multiply 6 on both sides to isolate the 20.

20=-30x

Divide -30 on both sides!

x=-2/3

Hope this helps!

HELP pls help me with this problem.

Answers

Answer:

8units

Step-by-step explanation:

area of a triangle=1/2base x height

1/2×4×4

2×4

8units

The answer is 8 unit I hope it helps

Find the area of the circle if the square has an area of 900in^2. Give your answer in terms of 3.14 or pi

Answers

Answer:

450in^2

Step-by-step explanation:

square root of 900 is 30.

Each side of square is 30.

Each side of a triangle formed by drawing a radi in the square is 15 in.

The hypotenuse is 15[tex]\sqrt{2}[/tex] that is also the radius of the circle.

A= (15[tex]\sqrt{2}[/tex])^2 times pi = 450 in^2

A newborn baby weighed 133 ounces.
What is the baby's weight in pounds and
ounces? (1 pound = 16 ounces)

Answers

Answer: UHHHHH i shall halp ya

Step-by-step explanation:

if its 133 in ounces its 293.215 in pounds

Answer: 8 pounds and 5 ounces

Step-by-step explanation: Do 16 ounces divided by 2 and it will give you 8 or do 8 times 2 which will give you sixteen. I prefer you do the other way and then do 10 dividedy2to get 5 ounces. The cop is 2.

what are the steps to this?

Answers

Answer:

Start at the positive

x

-axis, then rotate left by the desired angle.

Explanation:

Standard position means the first arm of the angle is the positive

x

-axis, and the other arm is placed by rotating counter-clockwise from there, by the amount of the angle.

As a basic example, the symbol

is about a 45° angle in standard position.

To get a feel for where the second arm (called the "terminal arm") will go, remind yourself that the axes themselves meet each other at 90°.

If our angle was 90°, the terminal arm would be on the positive

y

-axis.

If our angle was 180°, it would be on the negative

x

-axis.

Wait! 180° is more than 150°, so our angle is somewhere in quadrant 2. In fact, 150° is 2/3 of the way between 90° and 180°, so our terminal arm will be 2/3 of the way into quadrant 2.

graph{(y+tan(pi/6)x)(y^2-.00001x)=0 [-10, 10, -5, 5]}

(ignore the part of the line in quadrant 4)

Step-by-step explanation:

Mark 4/9 and -7/9 on a number line.​

Answers

where’s the mf number line

Answer:

Step-by-step explanation:

4/9 on the number line would be 0.44.

-7/9 on the number line would be -0.77

Please help me I really need help

Answers

hi! the first one is -2+6 i & the second one is parallelogram!

Answer:

-2 + 6i

Parallelogram

Step-by-step explanation:

( 5 - 2i ) + ( - 7 + 8i )

remove parenthesis

5 - 2i + ( -7 ) + 8i

combine like terms

5 + (-7) = -2

-2i + 8i = 6i

-2 + 6i

The arrows on the opposite sides indicate that the sides are parallel

A shape with two sets of parallel sides is known as a parallelogram

Which statement is true regarding the graphed functions?

Answers

Answer:

f(2) = 0 and g(2) = 0

f(2) = g(2) TRUE

b) f(0) = 2 and g(0) = -2

f(0) = g(0) FALSE

c) f(2) = 0 and g(0) = -2

f(2) = g(0) FALSE

d) f(0) = 2 and g(2) = 0

f(0) = g(2) FALSE

There is 28 kg 750 g of sugar in a sack. How many tins of 500 g sugar can be filled using the sugar in the sack?

Answers

Answer:

Step-by-step explanation:

28 kg + 750 g = 28*1000 + 750

                          28000 + 750

                       = 28750 g

Number of sack = Total quantity of sugar ÷ quantity of sugar in a sack

                           = 28750 ÷ 500

                           =  57 sacks

Answer:

57 sacks

Step-by-step explanation:

28750 ÷ 500 =

57 sacks

Glad to help! :)

Use the explicit formula an = a1 + (n-1)•d to find the 500th term of the sequence below.
24, 31, 38, 45, 52, ...

Answers

Step-by-step explanation:

the answer is in the image above

Answer:

a₅₀₀ = 3517

Step-by-step explanation:

a₁ represents the first term and d the common difference

Here a₁ = 24 and d = 31 - 24 = 7 , then

a₅₀₀ = 24 + (499 × 7) = 24 + 3493 = 3517

someone help!!!!!!!!

Answers

Answer:

Top right

Step-by-step explanation:

First, we have "h is increasing on the interval (3, +∞)." This means that h must be increasing for all values 3 and higher. This is shown on the top left, top right, and bottom right graphs because when x goes up on each of them, the function increases as well. However, for the bottom left graph, this is not shown because as x goes from 3 to 4, the function decreases.

Next, the statement given is "h(4)=2". This means that when the x value is 4, the y value is equal to 2. This is true for the top left and top right pictures. However, for the bottom right, as the x value is 4 on the x axis, the corresponding y value is 1, not 2.

This leaves us with the top left and top right. The final characteristic given is "The domain of h is [3, +∞). This means that the x values of said function only go from 3 to infinity. As the top left graph has values of x below 3, this leaves the top right graph as h

Solve -2x + 6 = -20. -7 -13 7 13

Answers

Answer:

13

Step-by-step explanation:

-2x + 6 = -20

Step 1 subtract 6 from both sides

6 - 6 cancels out

-20 - 6 = -26

We now have -2x = -26

Step 2 divide both sides by -2

-2x/-2 = x

-26/-2 = 13

We're left with x = 13

The equation of the circle having center (5, 4) and touching y-axis is

A. x 2 + y2 – 10x – 8y + 25 = 0

B. x 2 + y2 – 5x + 4y + 8 = 0

C. x 2 + y2 – 5x + 4y + 8 = 0

D. x 2 + y2 – 42 – 5y + 10 = 0

Answers

Answer:

None Of the Above.

Step-by-step explanation:

As we know that the general equation of circle is

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

putting h=5 and k= 4 and r= 5

x² + 25 - 10x + y² +16 - 8y = 25

x² + y² - 10x - 8y + 16 = 0 is the answer.

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Evaluate F(x) = x^2 + 1 for f(-1)

Answers

Answer:

2

Step-by-step explanation:

f(x) = x^2 + 1

f(-1) = (-1)^2 + 1

f(-1) = 2

Answer:

f(x)=x^2+1

f(-1)=(-1)^2+1

f(-1)=1+1

f(-1)=2

What are biofertilisiers​

Answers

Answer:

Step-by-step explanation:

biofertilizers are fertilizers consist of micro-organisms that will help plant growth. they are different from traditional fertilizers which consist of chemicals

Answer:

Any fertilizers involving living organisms, or the products obtained from living organisms can be referred to as biofertilizer, although nowadays, the term is generally used for living organisms used for fertilizer purpose.

Step-by-step explanation:

Hope this helps

what is the value of k in which the expression k-22=13-61​

Answers

Trust me this is the answer 18.666666

120 to 150 find the percentage of increase

Answers

Answer:

25%

Step-by-step explanation:

increase by = 150 - 120

=30

increase percent = 30/120 * 100%

=3000/120

=25 %

Answer:

25%

Step-by-step explanation:

Percentage increase=(new value-original value)/(original value) x 100%

Percentage increase=(150-120)/120 x 100%

Percentage increase=30/120 x 100%

Percentage increase=1/4 x 100%

Percentage increase=25%

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