Rate = cm/hour = 40/20 = <u>2 cm/hr</u>
Answer:
Step-by-step explanation:
Given that,
f(x, y) = xe^−x(1 + y) x ≥ 0 and y ≥ 0
It is f(x, y)= 0 otherwise
To find probability of life time, we will take the double integral of the function with respect to X and Y
Y ranges from 0 to ∞
X exceed 5, so it ranges from 5 to ∞
∫ ∫ f(x, y) dxdy
∫ ∫ xe^−x(1 + y) dxdy
∫ ∫ x•e^(−x -xy) dxdy
Separating the exponential
∫ ∫ x•e^(−x) • e^(-xy) dxdy
Integrating with respect to y and keeping x as a constant.
∫ x•e^(−x) • e^(-xy) / -x dx
∫ - e^(−x) • e^(-xy) dx y = 0 to y=∞
∫ - e^(−x) • [e^(-∞) - e^(0) ]dx
∫ - e^(−x) • [ 0 - 1] dx
∫ - e^(−x) • -1 dx
∫ e^(−x) dx
Now integrating this
e^(-x) /-1 from x=5 to x=∞
-e^(-x) from x=5 to x=∞
- [ e^(-∞) - e^(-5)]
- (0-e^(-5))
- - e^(-5)
e^(-5) = 0.006738
To 3d.p =0.007
Then probability that the life time X exceed 5 is 0.007
There are 120 different ways the people can line up
<h3>How to determine the number of ways?</h3>
The number of people that arrived is:
n = 5
Take the factorial to calculate the number of ways they can line up
n! = 5!
Expand
n! = 5* 4 * 3 * 2 * 1
Evaluate
n! = 120
Hence, there are 120 different ways the people can line up
Read more about permutation at:
brainly.com/question/11732255
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Answer:
z = 35
Step-by-step explanation:
-9 + z = 26
Add 9 on both sides to leave the z alone
z = 35
You can verify this by adding 35 into -9 which leads you to the answer: 26