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11111nata11111 [884]
3 years ago
14

You have just used the network planning model and found the critical path length is 30 days and the variance of the critical pat

h is 25 days. The probability that the project will be completed in 33 days or less is equal to:_______.
Mathematics
1 answer:
joja [24]3 years ago
8 0

Answer:

0.726 is the probability that the project will be completed in 33 days or less.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 30 days

Variance = 25 days

Standard Deviation,

\sigma = \sqrt{\text{Variance}} = \sqrt{25} = 5

We assume that the distribution of path length is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

P(completed in 33 days or less)

P( x \leq 33) = P( z \leq \displaystyle\frac{33 - 30}{5}) = P(z \leq 0.6)

Calculation the value from standard normal z table, we have,  

P(x \leq 33) = 0.726 = 72.6\%

0.726 is the probability that the project will be completed in 33 days or less.

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Equation Form: x=−2,y=−2

Step-by-step explanation:

Eliminate the equal sides of each equation and combine.

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for x. x=−2

Evaluate y when x=−2.

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The solution to the system is the complete set of ordered pairs that are valid solutions.

(−2,−2)

The result can be shown in multiple forms.

Point Form:

(−2,−2)

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x=−2,y=−2

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Step-by-step explanation:

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Step-by-step explanation:

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2 years ago
A rock was thrown from the top of a cliff such that its distance above sea level was given by s(t)= at² + bt + c, where t is the
frutty [35]

Answer:

<h2>a) a = -3, b = 18, c = 48; </h2><h2>s(t) = -3t²+18t+48</h2><h2>b) 48m</h2><h2>c) 8secs</h2>

Step-by-step explanation:

The question is incomplete. Here is the complete question.

'A rock was thrown from the top of a cliff such that its distance above sea level was given by s(t)=at²+bt+c, where t is the time in seconds after the rock was released. After 1 second the rock was 63 m above sea level, after 2 seconds 72 m, and after 7 seconds 27 m. a. Find a, b and c and hence an expression for s(t). b. Find the height of the cliff. c. Find the time taken for the rock to reach sea level.'

Given the equation of the distance modelled as s(t)=at²+bt+c

If after 1 second the rock was 63 m, then 63 = a+b+c

If after 2 seconds, the distance was 72 m then 72 = 4a+2b+c

Also if after 7 seconds, the distance is 27 m, then 27 = 49a+7b+c

i) Solving the 3 equations simultaneously to get a, b and c we have;

a+b+c = 63 ... 1

4a+2b+c = 72 ...2

49a+7b+c = 27 ...3

Subtracting 2 from 1 and 3 from 2 we will generate 2 new equations as shown;

eqn 2- eqn1: 3a + b = 9...4

eqn 3- eqn 2: 45a + 5b = -45

eqn 3- eqn 2: 9a+b = -9 ... 5

solving 4 and 5 simultaneously

3a + b = 9 ...4

9a+b = -9 ... 5  

Taking the difference of 4 and 5 we have

6a - -9-9

6a = -18

a = -3

substituting a = -3 into equation 4 to get b we have;

3(-3)+b = 9

-9 + b = 9

b = 9+9

b = 18

substituting a = -3 and b = 18 into equation 1 to get c we have;

-3+18+c = 63

15+c = 63

c = 48

a = -3, b= 18 and c = 48

The distance function will be s(t) = -3t²+18t+48

ii) If the height of the cliff is modelled by the equation  s(t)=at²+bt+c

The height of the cliff is at when t = 0

s(0) = -3(0)²+18(0)+48

s(0) = 48m

The height of the cliff is 48m

iii) At the sea level, the height of the rock will be 0m, substituting this into the modeled equation for the height to get the time we have;

s(t)=at²+bt+c

0 = -3t²+18t+48

3t²-18t-48 = 0

t² - 6t - 16 =0

t² - 8t+2t - 16 = 0

t(t-8)+2(t-8) = 0

(t+2)(t-8) = 0

t = -2 or 8

Taking the positive value of the time, t = 8secs

Time taken for the rock to reach sea level is 8secs

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3 years ago
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