Answer:
And we can find this probability with the complement rule:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the disagreements of a population, and for this case we know the distribution for X is given by:
Where 
and 
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability with the complement rule:
So we know the tank already has 5 gallons and we need 9. This means we need 4 more gallons in order to fill up the tank.
If 1/4 gallon is being filled per minute we need to find out how many 1/4 gallons makes up 4 gallons in total.
4 of the 1/4 gallons makes up 1 whole gallon. So since we need 4 whole gallons we would need 16 of the 1/4 gallons.
This means that it will take 16 minutes for the tank to hold 9 gallons of water.
Answer:
t = 2.52 seconds
Step-by-step explanation:
h=139-15t-16t^2
We want to know when the ball hits the ground
That would be when h=0
0 = 139-15t-16t^2
We can use the quadratic formula to find t
t = -b ± sqrt(b^2-4ac)
----------------------
2a
where a = -16 b = -15 and c = 139
t = -(-15) ± sqrt((-15)^2-4(-16)139)
----------------------
2(-16)
t = (15) ± sqrt(225+8896)
----------------------
-32
t = (15) ± sqrt(9121)
----------------------
-32
t = 15+ sqrt(9121) t = 15- sqrt(9121)
-------------------- or -------------------
-32 -32
-3.453247707 or 2.515747707
Since time cannot be negative
2.515747707
Round to the nearest hundredth
t = 2.52 seconds
C=11.27π feet
Diameter=11.27 feet. Hope it help!
