Astandard deck of cards has 52 cards. the cards have one of two colors: 26 cards in the deck are red and 26 are black. the cards have one of four denominations: 13 cards are hearts (red), 13 cards are diamonds (red), 13 cards are clubs (black), and 13 cards are spades (black). two cards are selected at random. event c is defined as the event that the first card is clubs, event r as the event that the first card is red, and event b as the event that the second card is black. which events are disjoint?

S={(heart), (diamond), (club), (spade)}

Step-by-step explanation:

In probability, a set is a well-defined collection of objects, product of an independent successful operation.

A sample space is the combination of all possible outcomes in an operation, so in this case, when we select one card and record the denomination, then we need to check what characteristic from the card are we looking for, from the problem we can see that is the denomination by itself, not the color, the number of the card, or anything else, and we only have 4 options of denomination so the sample space would be:

S={(heart), (diamond), (club), (spade)}

Credit to this answer goes to @ibranoguera

Hope this helps :))

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

(3x-8) or (3x+8)

step-by-step explanation: