The 6 in the hundreds place tells you the quotient is at least 100. The non-zero digits in the 1s and 10s places tell you the quotient is more than 100.
Answer:
Probability Mass Function:
x: 0 1 2 3
P(x): 0.000064 0.004608 0.115902 0.884736
Step-by-step explanation:
We are given the following information:
We treat correct classification as a success.
P(correct classification) = 0.96
Then the number of classification follows a binomial distribution, where
where n is the total number of observations, x is the number of success, p is the probability of success.
Now, we are given n = 3 and x = 0, 1, 2, 3
We have to evaluate:
PMF:
x: 0 1 2 3
P(x): 0.000064 0.004608 0.115902 0.884736
Answer:
No, mn is not even if m and n are odd.
If m and n are odd, then mn is odd as well.
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Proof:
If m is odd, then it is in the form m = 2p+1, where p is some integer.
So if p = 0, then m = 1. If p = 1, then m = 3, and so on.
Similarly, if n is odd then n = 2q+1 for some integer q.
Multiply out m and n using the distribution rule
m*n = (2p+1)*(2q+1)
m*n = 2p(2q+1) + 1(2q+1)
m*n = 4pq+2p+2q+1
m*n = 2( 2pq+p+q) + 1
m*n = 2r + 1
note how I replaced the "2pq+p+q" portion with r. So I let r = 2pq+p+q, which is an integer.
The result 2r+1 is some other odd number as it fits the form 2*(integer)+1
Therefore, multiplying any two odd numbers will result in some other odd number.
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Examples:
- 3*5 = 15
- 7*9 = 63
- 11*15 = 165
- 9*3 = 27
So there is no way to have m*n be even if both m and n are odd.
The general rules are as follows
- odd * odd = odd
- even * odd = even
- even * even = even
The proof of the other two cases would follow a similar line of reasoning as shown above.
