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Romashka [77]
3 years ago
7

The first side of a triangle is twice the length of the second side; the third side is 20 feet less than three times the second

side. The perimeter of the triangle is 106 feet. Find the three sides.
Mathematics
1 answer:
oee [108]3 years ago
4 0
Let the second side be x

then,
first side = twice the length of the second side
= 2x

third side = 20 feet less than three times the second side
3 (second side ) - 20
= 3 (2x) -20
= 6x - 20

perimete of a triangle = sum of all sides,

substitute the values we know,
and you'll be left with this equation

106 = x + 2x + 6x - 20
106+ 20 = 9x
126 = 9x
126/9 = x
14 = x

so,

measure of second side = x = 14 feet

measure of first side = 2x = 2 (14) = 28 feet

measure of thurd side = 6x - 20 = 6 (14)-20 = 84- 20 = 64 feet.
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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

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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