Answer:
The correct option is D.
Step-by-step explanation:
We have to find the expresses this statement: A quantity x is equal to the sum of the squares of a and b.
The square of a can be written as a² and the square of b can be written as b².
The sum of squares of a and b can be written as

Since the quantity x is equal to the sum of the squares of a and b, therefore

Therefore option D is correct.
Answer:
Standard deviation of given data = 3.16227
Step-by-step explanation:
<u><em>Step(i)</em></u>:-
Given sample size 'n' = 5
Given data 4, 6,8,10,12

Mean of the sample x⁻ = 8
Standard deviation of the sample

<u><em>Step(ii)</em></u>:-
Given data
x : 4 6 8 10 12
x-x⁻ : 4 - 8 6-8 8-8 10-8 12-8
(x-x⁻) : -4 -2 0 2 4
(x-x⁻)² : 16 4 0 4 16

S.D = √10 = 3.16227
<u><em> Final answer</em></u>:-
The standard deviation = 3.16227
1) The outcomes for rolling two dice, the sample space, is as follows:
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
There are 36 outcomes in the sample space.
2) The ways to roll an odd sum when rolling two dice are:
(1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (3, 6), (4, 1), (4, 3), (4, 5), (5, 2), (5, 4), (5, 6), (6, 1), (6, 3), (6, 5). There are 18 outcomes in this event.
3) The probability of rolling an odd sum is 18/36 = 1/2 = 0.5