Prove that if m + n and n + p are even integers, where m, n, and p are integers, then m + p is even.
m=2k-n, p=2l-n
Let m+n and n+p be even integers, thus m+n=2k and n+p=2l by definition of even
m+p= 2k-n + 2l-n substitution
= 2k+2l-2n
=2 (k+l-n)
=2x, where x=k+l-n ∈Z (integers)
Hence, m+p is even by direct proof.
Answer:
70%
Step-by-step explanation:
Since it can't go over 100%, and our numbers are 7 and 3, they are 70% and 30%, which add up to 100%.
Answer:
12
Step-by-step explanation:
You need the greatest common factor of 168 and 60.
168 = 2^3 * 3 * 7
60 = 2^2 * 3 * 5
For the GCF, you need common factors with the lower exponent.
Between 2^3 and 2^2, choose 2^2.
Then you have 3 as a common factor.
5 and seven are not common.
GCF = 2^2 * 3 = 12
Answer: 12
Answer: 601
Step-by-step explanation:
The formula to find the minimum sample size(n) , if the prior population proportion is unknown:
, where E = margin of error , 
= critical z-value for confidence level c.
Given : E = 0.04
Z-value for 95% confidence = 1.96
So, the minimum sample size required = 
Hence, the minimum sample size required = 601
Answer:
5500 pounds
Step-by-step explanation:
if you mean 2¾
in 2 tons there's 4000 pounds
in ¾ of a ton there is 1500 pounds
4000 + 1500 = 5500 pounds
