Answer: The probability that a randomly selected tire will have a tread-life of less than 65,000 miles is 0.7872 .
Step-by-step explanation:
The cumulative distribution function for exponential distribution is :-
, where
is the mean of the distribution.
As per given , we have
Average tread-life of a certain brand of tire : ![\lambda=\text{42,000 miles }](https://tex.z-dn.net/?f=%5Clambda%3D%5Ctext%7B42%2C000%20miles%20%7D)
Now , the probability that a randomly selected tire will have a tread-life of less than 65,000 miles will be :
![P(X\leq 65000)=1-e^{\frac{-65000}{42000}}\\\\=1-e^{-1.54761}\\\\=1-0.212755853158\\\\=0.787244146842\approx0.7872](https://tex.z-dn.net/?f=P%28X%5Cleq%2065000%29%3D1-e%5E%7B%5Cfrac%7B-65000%7D%7B42000%7D%7D%5C%5C%5C%5C%3D1-e%5E%7B-1.54761%7D%5C%5C%5C%5C%3D1-0.212755853158%5C%5C%5C%5C%3D0.787244146842%5Capprox0.7872)
Hence , the probability that a randomly selected tire will have a tread-life of less than 65,000 miles is 0.7872 .
Answer: More Info
Step-by-step explanation:
The height of flagpole is 12.5 feet.
Step-by-step explanation:
Given,
Height of woman = 5 foot
Shadow of woman = 6 feet
Ratio of height to shadow = 5:6
Shadow of flagpole = 15 foot
Height of flagpole = x
Ratio of height to shadow = x:15
Using proportion;
Ratio of height to shadow :: Ratio of height to shadow
![5:6::x:15\\](https://tex.z-dn.net/?f=5%3A6%3A%3Ax%3A15%5C%5C)
Product of mean = Product of extreme
![6*x=15*5\\6x=75](https://tex.z-dn.net/?f=6%2Ax%3D15%2A5%5C%5C6x%3D75)
Dividing both sides by 6
![\frac{6x}{6}=\frac{75}{6}\\x=12.5](https://tex.z-dn.net/?f=%5Cfrac%7B6x%7D%7B6%7D%3D%5Cfrac%7B75%7D%7B6%7D%5C%5Cx%3D12.5)
The height of flagpole is 12.5 feet.
Keywords: ratio, proportion
Learn more about proportion at:
#LearnwithBrainly
$412 i am pretty sure that is right if not i'm sorry but good luck :)
System of equations:
We'll need one equation for the amount of pizzas, and another for the total cost of the pizzas. In this case, x will represent small pizzas, and y will represent large pizzas.
3x + 4y = 100
x + y = 30
Solving the system of equations:
First, we need to solve for one variable in one equation.
x + y = 30
x = 30 - y
Then, we'll take our equation that is solved for x and plug it into the other equation from above.
3(30 - y) + 4y = 100
Next, we solve for y.
90 - 3y + 4y = 100
90 + y = 100
y = 10
Finally, we take our value for y and plug it back in to the very first equation and solve for x.
x = 30 - 10
x = 20
Answer:
The student has sold 10 large pizzas and 20 small pizzas.
Hope this helps!! :)