The question is incomplete. Here is the complete question.
Nite Time Inn has a toll-free telephone number so that customers can call at any time to make a reservation. A typical call takes about 4 minutes to complete, and the time required follows an exponential distribution. find the probability that a call takes
a) 3 minutes or less
b) 4 minutes of less
c) 5 minutes of less
d) Longer than 5 minutes
e) Longer than 7 minutes
Answer: a) P(X<3) = 0.882
b) P(X<4) = 0.908
c) P(X<5) = 0.928
d) P(X>5) = 0.286
e) P(X>7) = 0.174
Step-by-step explanation: <u>Exponential</u> <u>distribution</u> is related with teh amount of time until some specific event happens.
If X is a continuous random variable, probability is calculated as:
![P(X](https://tex.z-dn.net/?f=P%28X%3Cx%29%20%3D%201-me%5E%7B-mx%7D)
in which:
m is decay parameter, given by: ![m=\frac{1}{mean}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%7D%7Bmean%7D)
For the Nite Time Inn calls:
![m=\frac{1}{4}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%7D%7B4%7D)
m = 0.25
(a) P(X<3)
![P(X](https://tex.z-dn.net/?f=P%28X%3C3%29%20%3D%201-0.25e%5E%7B-0.25.3%7D)
![P(X](https://tex.z-dn.net/?f=P%28X%3C3%29%20%3D%201-0.25e%5E%7B-0.75%7D)
![P(X](https://tex.z-dn.net/?f=P%28X%3C3%29%20%3D%201-0.25%2A0.472)
P(X < 3) = 0.882
<u>The probability the call takes less than 3 minutes is 0.882.</u>
(b) P(X<4)
![P(X](https://tex.z-dn.net/?f=P%28X%3C4%29%20%3D%201-0.25e%5E%7B-0.25.4%7D)
![P(X](https://tex.z-dn.net/?f=P%28X%3C4%29%20%3D%201-0.25e%5E%7B-1%7D)
P(X < 4) = 0.908
<u>The probability the call takes less tahn 4 minutes is 0.908.</u>
(c) P(X<5)
![P(X](https://tex.z-dn.net/?f=P%28X%3C5%29%20%3D%201-0.25e%5E%7B-0.25.5%7D)
![P(X](https://tex.z-dn.net/?f=P%28X%3C5%29%20%3D%201-0.25e%5E%7B-1.25%7D)
P(X < 5) = 0.928
<u>The probability of calls taking less than 5 minutes is 0.928.</u>
(d) P(X>5)
Knowing that the sum of probabilities of less than and more than has to equal 1:
P(X<x) + P(X>x) = 1
P(X>x) = 1 - P(PX<x)
![P(X>x) = 1-(1-me^{-m*x})](https://tex.z-dn.net/?f=P%28X%3Ex%29%20%3D%201-%281-me%5E%7B-m%2Ax%7D%29)
![P(X>x)=me^{-mx}](https://tex.z-dn.net/?f=P%28X%3Ex%29%3Dme%5E%7B-mx%7D)
For P(X>5):
![P(X>5) = 0.25e^{-1.25}](https://tex.z-dn.net/?f=P%28X%3E5%29%20%3D%200.25e%5E%7B-1.25%7D)
P(X > 5) = 0.286
<u>The probability of calls taking more than 5 minutes is 0.286.</u>
(e) P(X>7)
![P(X>7)=0.25e^{-0.25.7}](https://tex.z-dn.net/?f=P%28X%3E7%29%3D0.25e%5E%7B-0.25.7%7D)
![P(X>7)=0.25e^{-1.75}](https://tex.z-dn.net/?f=P%28X%3E7%29%3D0.25e%5E%7B-1.75%7D)
P(X > 7) = 0.174
<u>The probability of calls taking more than 7 minutes is 0.174.</u>
Answer:
-22
Step-by-step explanation:
-14+(-12)+4
=-14-12+4
=-26+4
=-22
Answer:
im pretty sure that the answer is D i know for a fact that it is D
<h3>
Answer: Choice A. P = 1000M</h3>
===========================================================
Explanation:
Use the log rule
log(A/B) = log(A) - log(B)
this works for any valid log base
So we can say
- log(P/N) = log(P) - log(N)
- log(M/N) = log(M) - log(N)
meaning that
- log(P/N) = 8 turns into log(P) - log(N) = 8
- log(M/N) = 5 turns into log(M) - log(N) = 5
We have this system of equations
![\begin{cases}\log(P)-\log(N) = 8\\ \log(M)-\log(N) = 5\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D%5Clog%28P%29-%5Clog%28N%29%20%3D%208%5C%5C%20%5Clog%28M%29-%5Clog%28N%29%20%3D%205%5Cend%7Bcases%7D)
Subtract the equations straight down. You'll find the log(N) terms cancel out and we have the new equation log(P) - log(M) = 3 which transforms into log(P/M) = 3
Lastly, convert the log equation into its exponential equivalent form using the idea that log(b,x) = y turns into y = b^x, where b is the base
Throughout this problem, the base wasn't given. Instead its implied we're talking about base 10.
So,
log(P/M) = 3
P/M = 10^3
P/M = 1000
P = 1000M
-------------------------------------
Alternatively,
log(P/N) = 8 turns into P/N = 10^8
log(M/N) = 5 turns into M/N = 10^5
meaning that we can divide the two equations to get P/M = (10^8)/(10^5). That simplifies to P/M = 1000 and rearranges to P = 1000M
Answer:
1 inch = 2.54cm
You are given 10cm wide and 60 inches wide, so you have to convert either the 60 inches or the 10cm to a similar unit to figure out the scale factor. I will convert the 60 inches.
60 x 2.54 = 152.4cm
152.4/ 10 = 15.24 -> Scale Factor
I don't know what you were supposed to work out, but here's some stuff I've worked out for you.