Ratio 11 to 6 in perimeter

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

Write the equation of the circle with center (3, 2) and (−6, −4) a point on the circle.

yulyashka [42]

The equation for a circle is as followed:

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

where the center of the circle is at (h,k) and the radius of the circle is r.

We are given (h,k) and need to find the radius. To do so, we can use the distance formula to find the distance from the center to the point on the circle:

$d= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

Plug in the two points:

$d= \sqrt{(3-(-6))^2+(2-(-4))^2}$

$d= \sqrt{(9)^2+(6)^2}$

$d= \sqrt{117}$

If the distance from the center to the edge of the circle is the square root of 117, then r^2 = 117.

The answer is:

$(x-3)^2+(y-2)^2=117$

6 0

2 years ago

4^4= pls i need some help

Alenkasestr [34]

Hey there!

4^4

= 4 • 4 • 4 • 4

= 4 • 4 ➡️ 16

= 16 • 16

= 256

Answer: 256 ☑️

Good luck on your assignment and enjoy your day!

~ Amphitrite1040:)

7 0

2 years ago

Read 2 more answers

PLEASE HELP ASAP

Svetradugi [14.3K]

The area ratio is 1:16 meaning that the old area is 1 while the new area is 16. So this is another way of saying "the area is multiplied by 16"

Take the square root of each part of the ratio of 1:16 and we get 1:4

So this is the scale factor. It tells us how the linear components of the circles relate to one another. If the circumference of the smaller circle is 1,then the larger circle has a circumference of 4.

Therefore, the circumference has been multiplied by 4

4 0

2 years ago

Define properties of angles on a straight line

Vikki [24]

The sum of all the angles on one side of a straight line is always 180 degrees. For example: The sum of ∠1, ∠2, and ∠3 is 180 degrees

4 0

2 years ago

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