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3 years ago

In a shipment of 400 parts, 14 are found to be defective. How many defective parts should be expected in a shipment of 1200?

Mathematics

1 answer:

Kipish [7]3 years ago

5 0

1200 parts/ 400 parts = 3

12 parts x 3 = 36 parts

In 1200 parts, 36 would be bad.

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3 years ago

From a group of 3 men and 4 women, a delegation of 2 is selected. What is the expected number of men in the delegation?

Ostrovityanka [42]

Answer:

The expected number of men in the delegation is 0.86.

Step-by-step explanation:

Number of men = 3

Number of women = 4

A delegation of 2 is selected.

Let X be the number of men selected. So, the possible values of X are 0,1,2.

$P(X=0)=\dfrac{^3C_0\times ^4C_2}{^7C_2}=\dfrac{2}{7}$

$P(X=1)=\dfrac{^3C_1\times ^4C_1}{^7C_2}=\dfrac{4}{7}$

$P(X=2)=\dfrac{^3C_2\times ^4C_0}{^7C_2}=\dfrac{1}{7}$

The expected number of men in the delegation is

$E(x)=0\times P(X=0)+1\times P(X=1)+2\times P(X=2)$

$E(x)=0\times \dfrac{2}{7}+1\times \dfrac{4}{7}+2\times \dfrac{1}{7}$

$E(x)=\dfrac{6}{7}$

$E(x)\approx 0.86$

Therefore, the expected number of men in the delegation is 0.86.

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3 years ago

What is the equation of a line that is parallel to -x+3y=6 and passes through the point (3,5)?

Elena-2011 [213]

For this case we have that by definition, the equation of the line in the slope-intersection form is given by:

Where:

m: It's the slope

b: It is the cut-off point with the y axis

By definition, if two lines are parallel then their slopes are equal.

We have the following line:

$-x + 3y = 6\\3y = x + 6\\y = \frac {1} {3} x + \frac {6} {3}\\y = \frac {1} {3} x + 2$

Thus, the slope is: $m_ {1} = \frac {1} {3}$

Then $m_ {2} = \frac {1} {3}$

So, the line is of the form:

$y = \frac {1} {3} x + b$

We substitute the point $(x, y) :( 3,5)$ and find b:

$5 = \frac {1} {3} (3) + b\\5 = b$

Thus, the equation is:

$y = \frac {1} {3} x + 5$

Answer:

$y = \frac {1} {3} x + 5$

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