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
8.4 inches
Explanation : The big line in the middle of 8 and 9 is equal to 8.5, but since there is a small unit that is missing, the answer is 8.4.
Answer:
2n - 11
Step-by-step explanation:
Note there is a common difference d between consecutive terms of the sequence, that is
d = - 7 - (- 9) = - 5 - (- 7) = - 7 + 9 = - 5 + 7 = 2
This indicates the sequence is arithmetic with n th term
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 9 and d = 2, thus
= - 9 + 2(n - 1) = - 9 + 2n - 2 = 2n - 11
