Answer:
a) ![\mathrm{E}[\mathrm{T}]=\sum_{\mathrm{H}}^{5} \frac{200}{101-i}](https://tex.z-dn.net/?f=%5Cmathrm%7BE%7D%5B%5Cmathrm%7BT%7D%5D%3D%5Csum_%7B%5Cmathrm%7BH%7D%7D%5E%7B5%7D%20%5Cfrac%7B200%7D%7B101-i%7D)
b) ![\mathrm{Var}[\mathrm{T}]=\sum_{k=1}^{5} \frac{(200)^{2}}{(101-i)^{2}}](https://tex.z-dn.net/?f=%5Cmathrm%7BVar%7D%5B%5Cmathrm%7BT%7D%5D%3D%5Csum_%7Bk%3D1%7D%5E%7B5%7D%20%5Cfrac%7B%28200%29%5E%7B2%7D%7D%7B%28101-i%29%5E%7B2%7D%7D)
Step-by-step explanation:
Given:
The lifetimes of the individual items are independent exponential random variables.
Mean = 200 hours.
Assume, Ti be the time between ( 
)st and the 
failures. Then, the 
are independent with 
being exponential with rate 
Therefore,
a) ![E[T]=\sum_{i=1}^{5} E\left[\tau_{i}\right]](https://tex.z-dn.net/?f=E%5BT%5D%3D%5Csum_%7Bi%3D1%7D%5E%7B5%7D%20E%5Cleft%5B%5Ctau_%7Bi%7D%5Cright%5D)
![\therefore \mathrm{E}[\mathrm{T}]=\sum_{\mathrm{H}}^{5} \frac{200}{101-i}](https://tex.z-dn.net/?f=%5Ctherefore%20%5Cmathrm%7BE%7D%5B%5Cmathrm%7BT%7D%5D%3D%5Csum_%7B%5Cmathrm%7BH%7D%7D%5E%7B5%7D%20%5Cfrac%7B200%7D%7B101-i%7D)
The variance is given by, ![\mathrm{Var}[\mathrm{T}]=\sum_{i=1}^{5} \mathrm{Var}[T]](https://tex.z-dn.net/?f=%5Cmathrm%7BVar%7D%5B%5Cmathrm%7BT%7D%5D%3D%5Csum_%7Bi%3D1%7D%5E%7B5%7D%20%5Cmathrm%7BVar%7D%5BT%5D)
![\therefore \mathrm{Var}[\mathrm{T}]=\sum_{k=1}^{5} \frac{(200)^{2}}{(101-i)^{2}}](https://tex.z-dn.net/?f=%5Ctherefore%20%5Cmathrm%7BVar%7D%5B%5Cmathrm%7BT%7D%5D%3D%5Csum_%7Bk%3D1%7D%5E%7B5%7D%20%5Cfrac%7B%28200%29%5E%7B2%7D%7D%7B%28101-i%29%5E%7B2%7D%7D)
Note that the formula for the circumference of a circle is πd, while the formula for the area of a circle is πr².
π≈3.14
A. C=πd
Simply plug in the numbers into the formula.
Diameter=Radius*2
17*2=34
C=34(π)
B. (π)(5²)
Plug in the numbers into the formula. Remember that half of the diameter is the radius.
C. (π)(4.5)
There are two possible formulas that could be used to calculate the circumference of a circle: πd and 2πr.
The expression above is simply multiplying the circle's radius times pi. Therefore, it is not a method that could be used to find the circumference of a circle.
D. (π)(6.5²)
Remember that the formula for calculating the area of a circle is πr².
Half of the diameter is 6.5 (13.5/2=6.5). 6.5 cm. is the radius. Now just plug the numbers into the formula.
(π)(6.5²)
Therefore, the last answer choice is the correct answer.
Answer:
65 feet below sea level.
Step-by-step explanation:
With the information provided, we can create the following equation for the position of the sea lion (p)
p = 3x - 10
In this equation, x would be the final position of the seal when it caught the fish. Since we are told that the seal's position is 25 feet below sea level then we can plug in this value as x and solve for p...
p = (3 * 25) - 10
p = 75 - 10
p = 65
Finally, we can see that the sea lion's position is 65 feet below sea level.
Well let's see what floor each one lands on and figure out which one is higher.
Something to note:
down = subtracting
up = adding
if something says it's doing something more than once, add it the number of times it's doing that thing. (You can also multiply it by that number but the adding way is a bit easier to understand and explain)
<u>Elevator 1:</u>
6 + 7 + 7 - 10 = 10
<u>Elevator 2:</u>
20 - 5 - 5 - 5 + 12 = 17
Elevator 2 ends on a higher floor (reasoning above)
Solution: The number of ways we can arrange 3 blue marbles if a set of 5 marbles is selected is:
Therefore, there are 10 ways we could arrange 3 blue marbles.
