You roll a six-sided number cube. which events are mutually exclusive? a) rolling a multiple of 2 and a multiple of 4 b) rolling a multiple of 3 and a multiple of 6 c) rolling an even number and an odd number d) rolling a prime number and an even number

C) Rolling an even number and an odd number.

Step-by-step explanation:

We are asked to choose the correct option that represents two mutually exclusive events.

Since we know that mutually exclusive events are those events, who can not happen at the same time. As we cannot have both heads and tails in one toss, either we will get heads or we will get tails.

Let us check our given choices one by one.

A) Rolling a multiple of 2 and a multiple of 4.

Multiples of 2: 2, 4, 6,..

Since 4 is a multiple of 2, so both events are not mutually exclusive and option A is not a correct choice.

B) Rolling a multiple of 3 and a multiple of 6.

Multiples of 3: 3, 6, 9,...

Since 6 is a multiple of 3, so both events are not mutually exclusive and option B is not a correct choice.

C) Rolling an even number and an odd number.

Odd numbers on a cube: 1, 3, 5.

Even numbers on a cube: 2, 4, 6.

Since on one roll of dice we can either have an odd or an even number, both events are not possible with a single roll, therefore, option C is the correct choice.

D) Rolling a prime number and an even number.

Prime number on a cube: 2, 3, 5.

Even numbers on a cube: 2, 4, 6.

We can clearly see that 2 is a prime number and it is even as well, therefore, option D is not a correct choice.

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?

cluster sampling.

step-by-step explanation: