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Tomtit [17]
3 years ago
13

Manufacture of a certain component requires three different machining operations. Machining time for each operation has a normal

distribution, and the three times are independent of one another. The mean values are , , and min, respectively, and the standard deviations are , , and min, respectively. What is the probability that it takes at most hour of machining time to produce a randomly selected component
Mathematics
1 answer:
Sunny_sXe [5.5K]3 years ago
5 0

Answer:

Z = (60 - x + y + z) / √a + b + c

Step-by-step explanation:

Since it is a normal distribution, we must calculate the mean and standard deviation, since we do not have data, what we will do is leave them based on these:

Thus Total Mean time = M1 + M2 + M3

given:

M1 = x

M2 = y

M3 = z

Total Mean Time M = x + y + z

Now to calculate the standard deviation we first calculate the variance.

The total Variance V = V1 + V2 + V3

Given:

V1 = a

V2 = b

V3 = c

V = a + b + c

Thus Standard deviation SD of the complete operation is

SD = √ V

SD = √a + b + c

we need to find the probability that the mean time is less than or equal to 60 minutes, the first thing is to find the value of Z.

Formula of Z is:

Z = (X - M) / SD

In this case X = 60.

On plugging the values we get

Z = (60 - x + y + z) / √a + b + c

refer to the Z table and find the Probability of Z ≤ (60 - x + y + z) / √a + b + c

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amid [387]

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3 years ago
Which number, when rounded to the nearest tenth is 43.6?
andreev551 [17]

Answer:

d

Step-by-step explanation:

43.55 rounds the tenth up because it has a hundredth of five

7 0
2 years ago
Question
Jobisdone [24]

Answer:

The light bulb will reach the ground 1.25 seconds after it is dropped.

Step-by-step explanation:

We know that for an object that is in the air, the only force acting on it will be the gravitational force (where we are ignoring the air resistance)

Then the acceleration of the object is the gravitational acceleration, 32.17 ft/s^2

Then the acceleration of the light bulb is:

A(t) = (-32.17 ft/s^2)

Where the negative sign is because the acceleration is downwards.

Now, to get the velocity equation, we need to integrate the acceleration over time, we will get:

V(t) = (-32.17 ft/s^2)*t + V0

Where V0 is the initial velocity of the light bulb. Because it is dropped, the initial velocity will be zero, then V0 = 0m/s, then the velocity equation is:

V(t) =  (-32.17 ft/s^2)*t

Finally, to get the position equation we need to integrate again, we will get:

P(t) = (1/2)*(-32.17 ft/s^2)*t^2 + P0

Where P0 is the initial height of the object, and in this case, we know that it is equal to 25 ft.

Then the position equation is:

P(t) = (1/2)*(-32.17 ft/s^2)*t^2 + 25ft

The object will hit the ground when P(t) = 0 ft, then we need to solve that equation for t:

P(t) =  (1/2)*(-32.17 ft/s^2)*t^2 + 25ft = 0 ft

          25 ft =  (1/2)*(32.17 ft/s^2)*t^2

         2*25ft = (32.17 ft/s^2)*t^2

           50ft =  (32.17 ft/s^2)*t^2

         √( 50ft/(32.17 ft/s^2)) = t = 1.25 s

The light bulb will reach the ground 1.25 seconds after it is dropped.

8 0
3 years ago
Find the distance between each set of points. Round to the nearest tenth, when necessary. (-3, 2) and (1, -6)
vovangra [49]

Answer:

<h2>The answer is 8.9 units</h2>

Step-by-step explanation:

The distance between two points can be found by using the formula

d =  \sqrt{ ({x1 - x2})^{2} +  ({y1 - y2})^{2}  } \\

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-3, 2) and (1, -6)

The distance between them is

d =   \sqrt{ ({ - 3 - 1})^{2}  +  ({2 + 6})^{2} }   \\  =  \sqrt{ ({ - 4})^{2} +  {8}^{2}  }  \\  =  \sqrt{16 + 64}  \\  =  \sqrt{80}  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  = 4 \sqrt{5}  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  = 8.9442719...

We have the final answer as

8.9 units to the nearest tenth

Hope this helps you

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Rashid [163]

Answer:

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Step-by-step explanation:

Given: -3x(4-6x)

Distributive property of multiplication under which a number is multiplied by the sum of two number, the first number can be distributed to both of those number.

∴  -3x(4-6x)

solving it by using distributive property

= (-3x\times 4)-(-3x\times 6x)

= -(12x) + 18x^{2}

Opening parenthesis

=  -12x+18x^{2}

Hence, -12x+18x^{2} is the result after using distributive property.

3 0
3 years ago
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