Cards from an ordinary deck of 52 playing cards are turned face up one at a time. If the 1st card is an ace, or the 2nd a two, or the 3rd a three, or . . . , or the 13th a king, or the 14th an ace, or the 15th a two, and so on, we say that a match occurs. Compute the expected number of matches that occur.

Expected number of matches that occur = 4 matches

Step-by-step explanation:

First of all, let X_i be the event that when we turn over card i if it matches the required cards face.

Thus, for example X_1 is the event that turning over one card results in an ace while X_2 is the event that turning over second card reveals a deuce.

The number of matched cards "N" is given by the sum of this indicator random variable as shown in the attached file;

50-60=10

step-by-step explanation:

80° is the measure of gh

step-by-step explanation:

circle f is congruent to circle j

we have two circle with center f and j.

both circles are congruent. the radius of the circle would be equal.

see the attachment for the circle.

we are given ∠efd ≅ ∠gjh

therefore, arc (ed) = arc (gh)     (∴ circle f is congruent to circle j)

but ∠dfe=80°=arc (ed)

therefore, arc (gh) = 80°

thus, 80° is the measure of gh