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Lorico [155]
3 years ago
6

one hose can fill a goldfish pond in 14 minutes, and the two hoses can fill the same pond in 10 minutes, find how long it takes

the second hose to fill the pond alone
Mathematics
1 answer:
likoan [24]3 years ago
4 0

Answer:

35

Step-by-step explanation:

\frac{1}{14} +\frac{1}{t} =\frac{1}{10}

Solving this ^^ would equal t=35.

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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
*in the image above x=23 cm. find the surface area of the figure <br> (help pls)
svlad2 [7]

Answer:

3174cm^{2}

Step-by-step explanation:

Each square has an area of 529cm^{2}

So we multiply that by the number of squares which is 6.

8 0
2 years ago
What is 2.1 with 1repeating as a mixed number
swat32

Answer:

  1. 2 1/10. is the answer i think
4 0
3 years ago
Work out the percentage change to 2 decimal places when a price of £70 is increased to £99
MaRussiya [10]

Answer:

41.43%

Step-by-step explanation:

Change:

99 - 70 = 29

% change:

29/70 × 100

= 41.42857143%

8 0
3 years ago
May anyone help please
lapo4ka [179]

Depending on how flexibly you interpret "about 20 times larger" to mean, the answers are B and D.

Check the ratios of the larger number to the smaller number:

A: (2.01 x 10^7)/(4.25 x 10^6) = 2.01/4.25 x 10^1 = 20.1/4.25 = 4.729

B: (8.21 x 10^-3)/(4.13 x 10^-4) = 8.21/4.13 x 10^1 = 82.1/4.13 = 19.879

C: (4.91 x 10^6)/(5.09 x 10^3) = 4.91/5.09 x 10^3 = 4910/5.09 = 964.637

D: (5.97 x 10^4)/(3.12 x 10^3) = 5.97/3.12 x 10^1 = 59.7/3.12 = 19.135

4 0
3 years ago
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