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k0ka [10]
3 years ago
8

Find the measure of the angle between two forces of 30 pounds and 35 pounds if the magnitude of their resultant is 42 pounds

Mathematics
2 answers:
Harman [31]3 years ago
5 0

Answer:

100 degrees

Step-by-step explanation:

30^2+35^2-2*30*35cos80

=42

180-80=100

yKpoI14uk [10]3 years ago
4 0

Answer:

80 degrees

Step-by-step explanation:

42^2=30^2+35^2-2(30)(35)cosx

1764=2125-(2100)(cosx)

-361= -2100cosx

-361/-2100=cosx

0.1719047619=cosx

cos^-1x=80.10141556

Round off to the nearest degree=80

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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
butalik [34]

Answer:

a) 658008 samples

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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

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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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