3x +15 = 2x + 10 + x + 5
2 answers:
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This question is incomplete, the complete question is;
If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple are written in increasing order but are not necessarily distinct.
In other words, how many 5-tuples of integers ( h, i , j , m ), are there with n ≥ h ≥ i ≥ j ≥ k ≥ m ≥ 1 ?
Answer:
the number of 5-tuples of integers from 1 through n that can be formed is [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120
Step-by-step explanation:
Given the data in the question;
Any quintuple ( h, i , j , m ), with n ≥ h ≥ i ≥ j ≥ k ≥ m ≥ 1
this can be represented as a string of ( n-1 ) vertical bars and 5 crosses.
So the positions of the crosses will indicate which 5 integers from 1 to n are indicated in the n-tuple'
Hence, the number of such quintuple is the same as the number of strings of ( n-1 ) vertical bars and 5 crosses such as;
= [( n + 4 )! ] / [ 5!( n + 4 - 5 )! ]
= [( n + 4 )!] / [ 5!( n-1 )! ]
= [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120
Therefore, the number of 5-tuples of integers from 1 through n that can be formed is [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120
Answer:
2) x times the seventh root of x cubed
Step-by-step explanation:
Answer:
There is a 44.12% probability that the defective product came from C.
Step-by-step explanation:
This can be formulated as the following problem:
What is the probability of B happening, knowing that A has happened.
It can be calculated by the following formula
Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.
-In your problem, we have:
P(A) is the probability of the customer receiving a defective product. For this probability, we have:
In which is the probability that the defective product was chosen from plant A(we have to consider the probability of plant A being chosen). So:
is the probability that the defective product was chosen from plant B(we have to consider the probability of plant B being chosen). So:
is the probability that the defective product was chosen from plant B(we have to consider the probability of plant B being chosen). So:
So
P(B) is the probability the product chosen being C, that is 50% = 0.5.
P(A/B) is the probability of the product being defective, knowing that the plant chosen was C. So P(A/B) = 0.15.
So, the probability that the defective piece came from C is:
There is a 44.12% probability that the defective product came from C.