PLZ
You are going to pull two cards from a standard deck of 52 cards (without replacement) and record whether you got a face card (jack, queen, king, or ace) or a number card (2-10). Which list of events correctly makes up the sample space?
A) two number cards, two face cards, one number card and one face card, one face card and one number card
B) two number cards, two face cards, one number card and one face card
C) two number cards, two face cards
D) number card, face card

A) two number cards, two face cards, one number and one face card, one face and one number card

Step-by-step explanation:

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3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

tangent

step-by-step explanation: