Seventy hundredth is the same as 0.07
2 answers:
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Answer:
The value of E [Z] is 0.50.
Step-by-step explanation:
The expected value is computed using the formula:
Denote the three dices as follows:
X₁ = a four-sided die
X₂ = a six-sided die
X₃ = a 12-sided die
Define the indicator variables as follows:
The probability of rolling a 4 in the three dices are as follows:
Compute the value of E [Z] as follows:
Thus, the value of E [Z] is 0.50.
Ok, here we go. Pay attention. The formula for the arc length is 
. That means that to use that formula we have to find the derivative of the function and square it. Our function is y = 4x-5, so y'=4. Our formula now, filled in accordingly, is 
(that 1 is supposed to be negative; not sure if it is til I post the final answer). After the simplification we have the integral from -1 to 2 of 
. Integrating that we have 
from -1 to 2. 
gives us 
. Now we need to do the distance formula with this. But we need 2 coordinates for that. Our bounds are x=-1 and x=2. We will fill those x values in to the function and solve for y. When x = -1, y=4(-1)-5 and y = -9. So the point is (-1, -9). Doing the same with x = 2, y=4(2)-5 and y = 3. So the point is (2, 3). Use those in the distance formula accordingly: 
which simplifies to 
. The square root of 153 can be simplified into the square root of 9*17. Pulling out the perfect square of 9 as a 3 leaves us with . And there you go!