Answer with explanation:
We have to prove that, For any integer m, 2 m×(3 m + 2) is divisible by 4.
We will prove this result with the help of Mathematical Induction.
⇒For Positive Integers
For, m=1
L HS=2×1×(3×1+2)
=2×(5)
=10
It is not divisible by 4.
⇒For Negative Integers
For, m= -1
L HS=2×(-1)×[3×(-1)+2]
=-2×(-3+2)
= (-2)× (-1)
=2
It is not divisible by 4.
False Statement.
The probability of getting a 5 from the first rolling is 1/6. The probability of getting an even number is 1/2 (= 1/6 (for a 2) + 1/6 (for a 4) + 1/6 (for a 6)). As the two rollings are independent, you can just multiply two probability values to come up with a final answer. That is, (1/6)·(1/2) = 1/12.
Note that I did not write this. This answer comes from Wyzant. I am only linking this to you so that you'll get the answer quickly.
The number of data values between the lower quartile and the median is less than the number of data values between the upper quartile and the median.
Hope this helps!
