Answer:
See below.
Step-by-step explanation:
We know that
tanA + tan B
tan (A + B) = ---------------------
1 - tanAtanB
Substituting for A + B
tan (A + B) = tan pi/4 = 1.
tanA + tan B
So ------------------ = 1
1 - tanAtanB
Therefore tanA + tan B = 1 - tanAtanB.
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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Answer:get what
Step-by-step explanation:
Answer:
5 students are left out in the arrangement.
Step-by-step explanation:
If the number of rows = the number of columns
Then there must be an equal arrangement
Since the total number of students in the school is 2121
Then, the students that are left out in this arrangement = 2121 - (√2121 X √2121
Note the result of the square root would only consider the whole number, the digits after the decimal point signifies the remaining number that can't fit into the arrangement
so, √2121 = 46.05 (so 46 would be used)
= 2121 - (46 X 46)
= 2121 - 2116 = 5
Therefore 5 students are left out in the arrangement.
