Verify and name the property - 5 by 9 +2 by 13=2 by 13+-5 by 9

A complex electronic system is built with a certain number of backup components in its subsystems. One subsystem has eight ident

Fudgin [204]

Answer:

a) 0.0486 = 4.86% probability that exactly two of the four components last longer than 1000 hours.

b) 0.9996 = 99.96% probability that the subsystem operates longer than 1000 hours.

Step-by-step explanation:

For each component, there are only two possible outcomes. Either they last more than 1,000 hours, or they do not. Components operate independently, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

One subsystem has eight identical components, each with a probability of 0.1 of failing in less than 1,000 hours.

So 1 - 0.1 = 0.9 probability of working for more, which means that $p = 0.9$

a. exactly two of the four components last longer than 1000 hours.

This is P(X = 2) when $n = 4$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{4,2}.(0.9)^{2}.(0.1)^{2} = 0.0486$

0.0486 = 4.86% probability that exactly two of the four components last longer than 1000 hours.

b. the subsystem operates longer than 1000 hours.

The subsystem has 8 components, which means that $n = 8$

It will operate if at least 4 components are working correctly, so we want:

$P(X \geq 4) = 1 - P(X < 4)$

In which

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{8,0}.(0.9)^{0}.(0.1)^{8} \approx 0$

$P(X = 1) = C_{8,1}.(0.9)^{1}.(0.1)^{7} \approx 0tex][tex]P(X = 2) = C_{8,2}.(0.9)^{2}.(0.1)^{6} \approx 0$

$P(X = 3) = C_{8,3}.(0.9)^{3}.(0.1)^{5} = 0.0004$

Then

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0 + 0 + 0 + 0.0004 = 0.0004$

$P(X \geq 4) = 1 - P(X < 4) = 1 - 0.0004 = 0.9996$

0.9996 = 99.96% probability that the subsystem operates longer than 1000 hours.

5 0

3 years ago

Which shape will result from taking a cross section of the cuboid through the points shown?

givi [52]

Answer:

hexagon

Step-by-step explanation:

cross section of the cuboid

7 0

2 years ago

Alec pours the same amount of soup into three balls he used 4 cups of soup how much soup is in each bowl

Ugo [173]

For this question you would need to do 4 divided by 3. The answer would be 1.3 cup(s) would be in each bowl.

Hope that helps!!

7 0

3 years ago

When salt and water are combined, they form a salt or saline solution. How much ml of water must be added to 150 mL of an 80% sa

Vinvika [58]

Answer:

We must add 400 ml of water.

Step-by-step explanation:

We can use the following equation:

$C_{i}V_{i}=C_{f}V_{f}$

Where:

C(i) is the initial concentration of the solution (80%)
C(f) is the final concentration of the solution (30%)
V(i) is the initial volume (150 ml)
V(f) is the final volume

Now, we just need to solve the equation for V(f).

$V_{f}=\frac{C_{i}V_{i}}{C_{f}}$

$V_{f}=\frac{80*150}{30}$

$V_{f}=400\: ml$

Therefore, we must add 400 ml of water.

I hope it helps you!

3 0

2 years ago

Differentiate y=x⁴(1-2x⁵)⁶(5-8x³)².

Liula [17]

Step-by-step explanation:

Let $y(x)=f(x)g(x)h(x)$ where

$f(x) = x^4$

$g(x)= (1 -2x^5)^6$

$h(x)= (5 - 8x^3)^2$

so that

$y(x) = x^4(1 -2x^5)^6(5 - 8x^3)^2$

Recall that the derivative of the product of functions is

$y'(x)=f'(x)g(x)h(x)+f(x)g'(x)h(x)+f(x)g(x)h'(x)$

so taking the derivatives of the individual functions, we get

$f'(x) = 4x^3$

$g'(x) = 6(1 - 2x^5)^5(-10x^4)$

$h'(x) = 2(5 - 8x^3)(-24x^2)$

So the derivative of y(x) is given by

$y'(x) = 4x^3(1 -2x^5)^6(5 - 8x^3)^2 + x^4 6(1 -2x^5)^5(-10x^4)(5 - 8x^3)^2 + x^4(1 -2x^5)^6 2(5 - 8x^3)(-24x^2)$

or

$y'(x) = 4x^3(1 -2x^5)^6(5 - 8x^3)^2$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:- 60x^8(1 -2x^5)^5(5 - 8x^3)^2$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:- 48x^6(1 -2x^5)^6 2(5 - 8x^3)$

3 0

2 years ago

Verify and name the property - 5 by 9 +2 by 13=2 by 13+-5 by 9​

Verify and name the property - 5 by 9 +2 by 13=2 by 13+-5 by 9