Computer keyboard failures can be attributed to electrical defects or mechanical defects. a repair facility currently has 25 failed keyboards, 7 of which have electrical defects and 18 of which have mechanical defects.(a) how many ways are there to randomly select 6 of these keyboards for a thorough inspection (without regard to ) in how many ways can a sample of 6 keyboards be selected so that exactly three have a mechanical defect? (c) if a sample of 6 keyboards is randomly selected, what is the probability that no more than 2 of these will have an electrical defect?

The number of ways to select 6 keyboards is 177100.

The number of ways so that exactly three have a mechanical defect is 28560.

The probability that no more than 2 electrical defect is 0.806.

Step-by-step explanation:

Consider the provided information.

A repair facility currently has 25 failed keyboards, 7 of which have electrical defects and 18 of which have mechanical defects.

Part(A)

It is given that we need to find How many ways are there to randomly select 6 of these keyboards for a thorough inspection.

We need to select 6 keyboards out of 25.

Thus, the number of ways are:

Hence, the number of ways to select 6 keyboards is 177100.

Part(B)

In how many ways can a sample of 6 keyboards be selected so that exactly three have a mechanical defect?

We need to select 6 keyboards if exactly three have a mechanical defect that means the remain 3 have a electrical defect.

3 keyboard with electrical defects:

3 keyboard with mechanical defects:

This can be written as:

Thus, the number of ways so that exactly three have a mechanical defect is 28560.

Part(C)

If a sample of 6 keyboards is randomly selected, what is the probability that no more than 2 of these will have an electrical defect?

No more than 2 of these will have an electrical defect that means the number of electrical defect keyboards can be 0, 1 or 2.

P(No more than 2 electrical defect)={P(0 electrical defect)+P(1 electrical defect)+P(2 electrical defect)}

This can be written as:

Hence, the probability that no more than 2 electrical defect is 0.806.

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .