In American roulette, the wheel has the 38 numbers00, 0, 1, 2, ..., 34, 35, and 36 marked on equally spaced slots. If a player bets $1.00 on a number and wins, then the player keeps the dollar and receives an additional $35.00. Otherwise, the dollar is lost. Find the expected net gain to the player for one play of

The expected net gain to the player for one play is -$0.0526.

Step-by-step explanation:

To find the expected net gain, we multiply each outcome by its probability:

Player wins:

Earns $35.

1 out of 38 numbers, so probability 1/38.

Player loses:

Loses $1.

37 out of 38 numbers, so probability 37/38.

Expected value:

The expected net gain to the player for one play is -$0.0526.

6 hours 48 min

step-by-step explanation:

68÷5=13.6

13.6×30=408min=6 hours 48 min.

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step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl