1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
allsm [11]
3 years ago
9

A bus travels on an east-west highway connecting two cities A and B that are 100 miles apart. There are 2 services stations alon

g the route. The first service station is located 20 miles from city A, and the second service station is located 30 miles from city B. If the bus breaks down at a random point along the route, find the expected value of the distance of the bus from the nearest service station.
Mathematics
1 answer:
melamori03 [73]3 years ago
3 0

Answer:

51/4

Step-by-step explanation:

To begin with you have to understand what is the distribution of the random variable. If X represents the point where the bus breaks down. That is correct.  

X~ Uniform(0,100)

Then the probability mass function is given as follows.

f(x) = P(X=x) = 1/100  \,\,\,\, \text{if} \,\,\,\, 0 \leq x \leq 100\\f(x) = P(X=x) = 0  \,\,\,\, \text{otherwise}

Now, imagine that the D represents the distance from the break down point to the nearest station. Think about this, the first service station is 20 meters away from city A, and the second station is located  70 meters away from city A then the mid point between 20 and 70  is (70+20)/2 = 45 then we can represent D as follows

D(x) =\left\{ \begin{array}{ll}  x  & \mbox{if } 0\leq x \leq 20 \\  x-20 & \mbox{if } 20\leq x < 45\\                70-x & \mbox{if } 45 \leq x \leq 70\\                x-70 & \mbox{if } 70 \leq x \leq 100\\ \end{array}\right.

Now, as we said before X represents the random variable where the bus breaks down, then we form a new random variable Y = D(X), Y is a random variable as well, remember that there is a theorem that says that

E[Y] = E[D(X)] = \int\limits_{-\infty}^{\infty} D(x) f(x) \,\, dx

Where f(x) is the probability mass function of X. Using the information of our problem

E[Y] = \int\limits_{-\infty}^{\infty}  D(x)f(x) dx \\= \frac{1}{100} \bigg[ \int\limits_{0}^{20} x dx +\int\limits_{20}^{45} (x-20) dx +\int\limits_{45}^{70} (70-x) dx +\int\limits_{70}^{100} (x-70) dx  \bigg]\\= \frac{51}{4} = 12.75

You might be interested in
HELP! ASAP! Am I correct!?!?
LenKa [72]
It isn't because, it isn't consistent, and it doesn't follow any of the other answer choices. :)

3 0
3 years ago
Joe borrowed 12 books from the library four books were for himself the rest were for his little brother how can the number of bo
AlexFokin [52]

Answer:

subtract 4 from 12

Step-by-step explanation:

3 0
3 years ago
Which of the following graphs shows a parabola with a vertex of (1,-9) and solutions of (-2,0) and (4,0)?
Mariulka [41]

Answer:

Hello,

Step-by-step explanation:

Roots are -2 and 4

y=k*(x+2)(x-4)

Vertex = (1,-9) is a point of the parabola

-9=k*(1+2)(1-4) ==> k=1

Equation of the parabola is y=(x+2)(x-4)

But you don' t have given the graphs !!!!

3 0
2 years ago
A sandbox has a volume of 648 cubic feet. what is the volume, in cubic yards, of the sandbox?
Eduardwww [97]
We know that

1 cubic yards equals to--------------> 27 <span>cubic feet
then
</span><span>I apply a rule of three
if  </span>1 cubic yards ------------------- 27 ft³
  X----------------------------------> 648 ft³
X=648/27=24 cubic yards

the answer is 24 cubic yards
6 0
3 years ago
A local fun park charges an admission fee plus a fee for each Go-Kart ride. Admission plus five
tino4ka555 [31]

The admission price is $6 and the rides are $2 each.

8 0
2 years ago
Other questions:
  • A ride at an amusement park moves the riders in a circle at a rate of 6.0 m/s. The radius of the ride is 9.0 meters. Which of th
    7·1 answer
  • Calcium is essential to tree growth because it promotes the formation of wood and maintains cell walls. In 2010, the concentrati
    13·1 answer
  • Ill give brainliest! Sorry its sideways.​
    8·2 answers
  • Pyramid A is a square pyramid with a base side length of 14 inches and a height of 6 inches. Pyramid B has a volume of 3,136 cub
    5·2 answers
  • Factorise<br>21x squared - 14x​
    11·1 answer
  • When the input is -5 the output is ___?
    5·1 answer
  • Isabella invested $1300 in an account that pays 4.5% compounded annually. Assuming no deposits or withdrawals are made , find ho
    6·1 answer
  • Which quotient matches the description of solving with partial quotients for 240÷15
    7·1 answer
  • 1. A bag contains four green gumballs, three blue gumballs, and two red gumballs, all the same size and shape.
    10·1 answer
  • Enter the median of the following dataset 7,15,12,13,8,11
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!