Answer:
There is an 85% probability that the sprinkler head will be activated.
Step-by-step explanation:
We have these following probabilities:
50% of the first sprinkler being triggered
90% of the first sprinkler being reliable
50% of the second sprinkler being triggered
80% of the second sprinkler being reliable.
What is the probability that the sprinkler head will be activated?
![P = P_{1} + P_{2}](https://tex.z-dn.net/?f=P%20%3D%20P_%7B1%7D%20%2B%20P_%7B2%7D)
is the probability of the first sprinkler being triggered and activated. So:
![P_{1} = 0.5*0.9 = 0.45](https://tex.z-dn.net/?f=P_%7B1%7D%20%3D%200.5%2A0.9%20%3D%200.45)
is the probability of the second sprinkler being triggered and activated. So:
![P_{2} = 0.5*0.8 = 0.40](https://tex.z-dn.net/?f=P_%7B2%7D%20%3D%200.5%2A0.8%20%3D%200.40)
![P = P_{1} + P_{2} = 0.40 + 0.45 = 0.85](https://tex.z-dn.net/?f=P%20%3D%20P_%7B1%7D%20%2B%20P_%7B2%7D%20%3D%200.40%20%2B%200.45%20%3D%200.85)
There is an 85% probability that the sprinkler head will be activated.
Answer:
![\sqrt{418}](https://tex.z-dn.net/?f=%5Csqrt%7B418%7D)
Step-by-step explanation:
The length of a diagonal of a square is
, where a is the length of one side.
If the area of a square garden is 209m, we know that the side length must be
m, since the area of a square is it’s side length squared.
Now we can substitute inside the formula.
![\sqrt{2}\cdot\sqrt{209}](https://tex.z-dn.net/?f=%5Csqrt%7B2%7D%5Ccdot%5Csqrt%7B209%7D)
When multiplying roots, the multiplication problem can simplify down to whatever is in the roots multilpied by each other.
So, ![209\cdot 2 = 418](https://tex.z-dn.net/?f=209%5Ccdot%202%20%3D%20418)
So the length of the diagonal is
m.
Hope this helped!
Answer:
( About ) 1,099 pounds
Step-by-step explanation:
The force required to keep this truck from rolling down the hill is opposed by the force of friction, comparative to the 2600 pounds of force against this friction. It should be that this opposing force is at work more towards the bottom of this hill, and thus the question asks the magnitude of latter force to keep this truck idle -
|| F || = sin( 25 ) * ( Fg ) = sin( 25 ) * ( 2600 lb ) = ( About ) 1098.80748 pounds
<u><em>This can be rounded to a solution of 1099 pounds</em></u>
Answer:
32672.64 pounds
Step-by-step explanation:
Diameter = 10ft
Radius = d / 2 = 10 / 2 = 5ft
Density (p) = 62.4 pounds/ft³
Volume of a hemisphere = 4/3Πr³
V = 4/3 * π * 5³
V = 4/3 * 392.7
v = 523.6ft³
but density ρ = mass / volume
mass = density * volume
Mass = 62.4 * 532.6
Mass = 32672.64pounds
The weight of the water in full tank is 32672.64 pounds
Answer:
11 : 38
Step-by-step explanation: