Answer:
0.0137
Step-by-step explanation:
Let X be the random variable that measures the number of incoming calls every ten minutes.
If the incoming calls to the system are Poisson distributed with a mean equal to 5 every 10 minutes, then the probability that there are k incoming calls in 10 minutes is
If the phone-answering system is capable of handling ten calls every 10 minutes, we want to find
P(X>10), or the equivalent 1 - P(X≤ 10).
But
1 - P(X≤ 10)= 1 -(P(X=0)+P(X=1)+...+P(X=10)) =
So, the probability that in a 10-minute period more calls will arrive than the system can handle is 0.0137
The two angles are adjacent on a straight line so they are supplementary. Thus 8x+5+13x-14=180
21x-9=180
21x=189
x=9
Answer:
Step-by-step explanation:
Given that
To find tangent, normal and binormal vectors at (0,0,1)
i) Tangent vector
At the particular point, r'(t) = (1,1,e)
Tangent vector = 
ii) Normal vector
T'(t) = 
At that point T'(t) = (0,0,e)/e = (0,0,1)
iii) Binormal
B(t) = TX N
= ![\left[\begin{array}{ccc}i&j&k\\1&1&e^t\\0&0&e^t\end{array}\right] \\= e^t(i-j)](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Di%26j%26k%5C%5C1%261%26e%5Et%5C%5C0%260%26e%5Et%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%3D%20e%5Et%28i-j%29)
How fast the volume of the sphere is changing when the surface area is 10 square centimeters is it is increasing at a rate of 30 cm³/s.
To solve the question, we need to know the volume of a sphere
<h3>
Volume of a sphere</h3>
The volume of a sphere V = 4πr³/3 where r = radius of sphere.
<h3>How fast the volume of the sphere is changing</h3>
To find the how fast the volume of the sphere is changing, we find rate of change of volume of the sphere. Thus, we differentiate its volume with respect to time.
So, dV/dt = d(4πr³/3)/dt
= d(4πr³/3)/dr × dr/dt
= 4πr²dr/dt where
- dr/dt = rate of change of radius of sphere and
- 4πr² = surface area of sphere
Given that
- dr/dt = + 3 cm/s (positive since it is increasing) and
- 4πr² = surface area of sphere = 10 cm²,
Substituting the values of the variables into the equation, we have
dV/dt = 4πr²dr/dt
dV/dt = 10 cm² × 3 cm/s
dV/dt = 30 cm³/s
So, how fast the volume of the sphere is changing when the surface area is 10 square centimeters is it is increasing at a rate of 30 cm³/s.
Learn more about how fast volume of sphere is changing here:
brainly.com/question/25814490
Answer:
you didn't put the different statements to choose from
