You just simplify the fraction (so, 8/6 which is 4/3)
So your comes 4(square root of 35)/ 3 (square root of 15)
The mean of the data set is 26 because the sum of all the data points divided by the number of data points is 26.4 repeating which rounds to 26.
Answer:
11.55
Step-by-step explanation:
SOH CAH TOA reminds you ...
Tan = Opposite/Adjacent
The angle at lower left is the complement of 60°, so is 30°. Then the side x satisfies the equation ...
tan(30°) = x/20
Multiplying by 20 gives ...
20·tan(30°) = x ≈ 11.55
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.
