Answer: 2.73 cm
Step-by-step explanation:
Given that :
Side (a) of cube = 4.4cm
Volume of a cube (V) = a^3
V = 4.4^3
V = 85.184cm^3
Therefore, volume of the sphere made = 85.184cm^3
Volume of sphere = 4/3 πr^3
Where r = radius
85.184 = (4/3)*(22/7)*r^3
85.184 = (88/21)*r^3
85.184 = 4.1905 * r^3
r^3 = 85.184 / 4.1905
r^3 = 20.327884
Take the cube root of both sides
r = 2.73 cm
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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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