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D. (the last one)

Step-by-step explanation:

The horizontal row lists the 3 outcomes of the spinner.

The vertial column lists the 2 outcomes of the card selection.

In the resulting sample space of 2x3=6, each table cell should contain the combination of the row value and the column value.

So in the "Orange" column, all cells below it should start with Orange. Same for the other columns.

In the Purple row, each cell should end with Purple.

Only that way, each table cell represents a possible outcome.

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this