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QveST [7]
3 years ago
10

The manager of a gas station has observed that the times required by drivers to fill their car's tank and pay are quite variable

. In fact, the times are exponentially distributed with a mean of 7.5 minutes. What is the probability that a car can complete the transaction in less than 5 minutes?
Mathematics
1 answer:
maw [93]3 years ago
7 0

Answer: 0.49

Step-by-step explanation:

The mean= E[x]=1/l= 7.5 min

l=1/7.5 =10/75=2/15

The exponential distribution's  probability density function is looking like that:

F(x)= l*e^(-l*x) = 2/15*e^(-2*x/15)

P(0<x<5)= e^(-0*2/15)- e^(-5*2/15)=1- e^(-2/3)= approx 0.49

You might be interested in
Solve the system of linear equations.
icang [17]

Answer: The set does not have a solution

Step-by-step explanation:

Adding Equations 1 & 3 we get 5x = 7. This gives x = 7/5

Putting this value of x in eq. 2 we get

-2y + 2z = -1-(7/5) or

2y - 2z = 12/5  or  5y - 5z = 6

Multiplying eq. 1 by 2  we get  

4x + 2y - 2z = 6

adding this with eq. 2 we get 5x = 5 or x = 1

As the common solution for x from equations 1&3 does not satisfy eq. 1&2 it comes out that the three equations do not have a common solution.

Same can be verified by using different sets of two equations also.

7 0
3 years ago
Need help can someone help me
Hunter-Best [27]

The absolute value of B is 1 3/5 because although B is in the negatives, absolute value makes it positive.

7 0
3 years ago
Read 2 more answers
(1 point)
alina1380 [7]
ANSWER—C.................................
3 0
3 years ago
How to multiply a whole number by a fraction like 4/6 x 4 etc .​
jeka57 [31]

Answer:

See below, please!

Step-by-step explanation:

To multiply a whole number by a fraction, set up both numbers so that they have a numerator and denominator, multiply the corresponding parts, and simplify.

Ex: \frac{4}{6}*\frac{4}{1}. Both of them are in fraction form, right? Now multiply the numerator and denominator together. Doing this, you get 16/6. Now simplify. Look for a common factor between both the numerator and denominator. We can see that one common factor is 2. So, our simplified fraction is 8/3.

Hope this helped!  

6 0
3 years ago
Help me please !!!!!!!!!!!!!!
tensa zangetsu [6.8K]

Answer:

\large\boxed{V=\dfrac{49\pi}{3}\ in^3}\approx51.29\ in^3}

Step-by-step explanation:

The formula of a volume of a cone:

V=\dfrac{1}{3}\pi r^2H

r - radius

H - height

We have

r = (7 : 2) in = 3.5 in

H = 4 in

Substitute:

V=\dfrac{1}{3}\pi(3.5)^2(4)=\dfrac{1}{3}\pi(12.25)(4)=\dfrac{49\pi}{3}\ in^3

\pi\approx3.14\\\\V\approx\dfrac{(49)(3.14)}{3}\approx51.29\ in^3

5 0
3 years ago
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