Two cards are drawn from a deck of 52 cards. What is the probability that the first card drawn is a king and the second card drawn is a heart, given that the first card is
replaced? (Hint: A deck has 4 kings and 13 hearts)

1) P(First card was a king) =  1/13 2.) 1/4

Step-by-step explanation:

1) P(First card was a king) = n(King)/n(Total) = 4/52 = 1/13

2. P(Heart)13/52 = 1/4

1/52

Step by step explanation:

First, find the probability that the first card will be a King. Since there are 4 possible kings, and 52 cards, the probability is 4/52.

Then, find the probability that the second card will be a heart. "given that the first card is replaced" means that there are 13 possible hearts regardless of the suit of the first card. So 13/52 is the probability.

To find the probability of both occurrences, multiply them.

4/52 * 13/52 = 52/2704

52/2704 can be simplified to 1/52. So that is the probability that the first card will be a king and the second card will be a heart.

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

< coa = 150 ( given)

as ba and bc are tangents

so oc and oa is perpendicular to cb and ab respectively because in circle normal passes through centre

so in quadrilateral oabc

< coa + < oab + < ocb + < abc = 360

150 +90+90 + < abc = 360

330 + < abc = 360

< abc = 360 -330 = 30

so < abc = 30

⭐dhruv⭐