Astandard deck of cards is dealt to four players, each receiving thirteen cards. if the first player gets exactly five hearts, what is the chance the second player gets exactly four hearts?

0.000024

Step-by-step explanation:

If the first player gets exactly five hearts, there are 39 cards left, 8 of which are hearts.

So, the probability of getting one heart is 8/39, for the second heart the probability is 7/38 and 6/37 and 5/36 for the 3rd and 4th hearts.

There are still 4 hearts in the deck, and the probability of getting a non heart is (35-4)/35=31/35, (34-4)/34=30/34,..., (27-4)/27=23/27 for the next 9 cards.

As the event of taking a card is independent of the previous result, the probability the second player gets exactly 4 hearts is

(8/39)*(7/38)*(6/37)*(5/36)*(31/35)*(30/34)***(23/27)

= 0.000024

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq