Suppose you pay $3.00 to roll a fair die with the understanding that you will get back $9.00 for rolling a 1 or a 6, nothing otherwise. what is your expected value?

Expected winnings are earnings minus cost

Earnings:

9* 1/6 + 0 * 1/6 + 0*1/6 + 0*1/6 + 0 * 1/6 + 9 * 1/6

9/6+9/6 = 18/6 = 3

Winnings:

earnings - cost =3-3 = 0

80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

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find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: