Answer: 0.5
Step-by-step explanation:
Given : Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa.
i.e. Flight time = 2(60) +5= 125 minutes [∵ 1 hour = 60 minutes]
Actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes.
i.e. In minutes the flight times are between 120 minutes and 140 minutes.
Let x be a uniformly distributed variable in [120 minutes, 140 minutes] that represents the flight time.
Since the probability density function for x uniformly distributed in [a,b] is 
⇒ Probability density function for flight time : 
5 minutes late than usual time = Flight time+ 5 = 125+5 = 130 minutes
Now , the probability that the flight will be no more than 5 minutes late will be :-
![\int^{130}_{120} \dfrac{1}{20}\ dx\\\\=\dfrac{1}{20}[x]^{130}_{120}\\\\= \dfrac{130-120}{20}\\\\=\dfrac{1}{2}=0.5](https://tex.z-dn.net/?f=%5Cint%5E%7B130%7D_%7B120%7D%20%5Cdfrac%7B1%7D%7B20%7D%5C%20dx%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D%7B20%7D%5Bx%5D%5E%7B130%7D_%7B120%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7B130-120%7D%7B20%7D%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D%7B2%7D%3D0.5)
Hence, the probability that the flight will be no more than 5 minutes late is 0.5.
Any tangent line to the curve has a slope given by 
.
Since 
, the denominator ranges from 3 to 5, so the range of slopes is 
.
There is 3 feet in a yard.
8 yards x 3 = 24 feet.
That means 8 yards is greater than 20 feet since 24 feet is > 20 feet.
Answer:
Electric force = 8.20x10⁻⁸ N
Gravitational force = 3.61x10⁻⁴⁷ N
Step-by-step explanation:
1. The electric force can be found using the following equation:
Where:
K: is the Coulomb's constant = 9x10⁹ N.m²/C²
: is the charge of the proton = 1.6x10⁻¹⁹ C
: is the charge of the electron = -1.6x10⁻¹⁹ C
d: is the distance = 5.3x10⁻¹¹ m
Hence, the magnitude of the electric force is:
2. The gravitational force can be calculated as follows:
Where:
: is the electron's mass = 9.1x10⁻³¹ kg
: is the proton's mass = 1.67x10⁻²⁷ kg
G: is the gravitational constant = 6.67x10⁻¹¹ N.m²/kg²
Therefore, the gravitational force is:
As we can see, the gravitational force is much less than the electric force.
I hope it helps you!
