You pick a card from a shuffled pack and draw a king. You put it back in the pack, shuffle, and then pick another card. This time you draw a queen. How are the two events of picking a king and picking a queen related?

The events are independent. They are not related at all. This is because you put the card back in, keeping the total number of cards the same. If you did not put the card back, then the second draw (selecting the queen) would be dependent on the first event (selecting the king)

The probability of picking a king is 4/52 = 1/13

If you do not put the card back, then there are 52-1 = 51 cards left and 4 queens, so 4/51 is the probability of getting a queen. Again, this is assuming you do not put the first card back. Putting that first card back would make the queen's probability 4/52 = 1/13, which is the same as selecting that king.

(a) the volume of the cone is 20/3 in3

hence, option a is correct.

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet