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Mademuasel [1]
3 years ago
6

A batch of 40 semiconductor chips is inspected by choosing a sample of 5 chips. Assume 10 of the chips do not conform to custome

r requirements. Round your answers to the nearest integer. a. How many different samples are possible? b. How many samples of 5 contain exactly one nonconforming chip? c. How many samples of 5 contain at least one nonconforming chip?
Mathematics
1 answer:
butalik [34]3 years ago
6 0

Answer:

a) 658008 samples

b) 274050 samples

c) 515502 samples

Step-by-step explanation:

a) How many ways sample of 5 each can be selected from 40 is just a combination problem since the order of selection isn't important.

So, the number of samples = ⁴⁰C₅ = 658008 samples

b) How many samples of 5 contain exactly one nonconforming chip?

There are 10 nonconforming chips in the batch, and 1 nonconforming chip for the sample of 5 be picked from ten in the following number of ways

¹⁰C₁ = 10 ways

then the remaining 4 conforming chips in a sample of 5 can be picked from the remaining 30 total conforming chips in the following number of ways

³⁰C₄ = 27405 ways

So, total number of samples containing exactly 1 nonconforming chip in a sample of 5 = 10 × 27405 = 274050 samples

c) How many samples of 5 contain at least one nonconforming chip?

The number of samples of 5 that contain at least one nonconforming chip = (Total number of samples) - (Number of samples with no nonconforming chip in them)

Number of samples with no nonconforming chip in them = ³⁰C₅ = 142506 samples

Total number of samples = 658008

The number of samples of 5 that contain at least one nonconforming chip = 658008 - 142506 = 515502 samples

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3x + 3<br> X + 8<br> What is the perimeter of each polygon?
Ganezh [65]

Answer:

D. 60

Step-by-step explanation:

4(3x + 3) = 5(x + 8)       12(4) + 12         5(4) + 40

12x + 12 = 5x + 40        48 + 12               20 + 40

-5x          -5x                   60                        60

7x + 12 = 40

 -12        -12

7x = 28

x = 4

6 0
3 years ago
Two cylinders are similar. The surface area of one is 49 cm ^ 2 , and the surface area of the other is 121 cm ^ 2 . Find the sca
dalvyx [7]

Answer:

7 : 17.29

Step-by-step explanation:

==>Given:

Two similar cylinders:

Surface area of Cylinder A = 49cm²

Surface area of Cylinder B = 121cm²

==>Required:

Scale factor between both cylinders

==>Solution:

We can easily get the scale factor between both by taking the following steps:

=>Set up a ratio of their surface area:

Smaller cone surface area : larger cone surface area

49:121

= 49/121

=>Simplify the ratio gotten:

Dividing the denominator and the numerator by 7, would give us,

7/17.29

= 7:17.29

8 0
3 years ago
Read 2 more answers
Solve the equations for all values of x by completing the square x^2+62=-16x
lorasvet [3.4K]

Answer:

x =  \sqrt{2} - 8\\x =  -\sqrt{2} - 8

Step-by-step explanation:

To complete the square, we first have to get our equation into ax^2 + bx = c form.

First we add 16x to both sides:

x^2 + 16x + 62 = 0

And now we subtract 62 from both sides.

x^2 + 16x = -62

We now have to add (\frac{b}{2})^2 to both sides of the equation. b is 16, so this value becomes (16\div2)^2 = 8^2 = 64.

x^2 + 16x + 64 = -62+64

We can now write the left side of the equation as a perfect square. We know that x+8 will be the solution because 8\cdot8=64 and 8+8=16.

(x+8)^2 = -62 + 64

We can now take the square root of both sides.

x+8 = \sqrt{-62+64}\\\\ x+8 = \pm \sqrt{2}

We can now isolate x on one side by subtracting 8 from both sides.

x = \pm\sqrt{2} - 8

So our solutions are

x =  \sqrt{2} - 8\\x =  -\sqrt{2} - 8

Hope this helped!

4 0
3 years ago
AYOOO PLZ HELP ASAP!!!
tamaranim1 [39]

Answer:

B.

Step-by-step explanation:

Well we know that

224=2^{5} *7

so we can get the 2 outside of the radical

x^{11} =(x^{5} )^{2} *x

and we can get the x^2 outside too.

y^8=y^5*y^3

and we also can get y outside.

so we have:

2x^{2}y\sqrt[5]{7xy^3}

7 0
2 years ago
Patterns are made using straight lines and arcs.
KIM [24]
5 rows were added to pattern B

7 0
3 years ago
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