Answer:
The rate at which the distance between them is changing at 2:00 p.m. is approximately 1.92 km/h
Step-by-step explanation:
At noon the location of Lan = 300 km north of Makenna
Lan's direction = South
Lan's speed = 60 km/h
Makenna's direction and speed = West at 75 km/h
The distance Lan has traveled at 2:00 PM = 2 h × 60 km/h = 120 km
The distance north between Lan and Makenna at 2:00 p.m = 300 km - 120 km = 180 km
The distance West Makenna has traveled at 2:00 p.m. = 2 h × 75 km/h = 150 km
Let 's' represent the distance between them, let 'y' represent the Lan's position north of Makenna at 2:00 p.m., and let 'x' represent Makenna's position west from Lan at 2:00 p.m.
By Pythagoras' theorem, we have;
s² = x² + y²
The distance between them at 2:00 p.m. s = √(180² + 150²) = 30·√61
ds²/dt = dx²/dt + dy²/dt
2·s·ds/dt = 2·x·dx/dt + 2·y·dy/dt
2×30·√61 × ds/dt = 2×150×75 + 2×180×(-60) = 900
ds/dt = 900/(2×30·√61) ≈ 1.92
The rate at which the distance between them is changing at 2:00 p.m. ds/dt ≈ 1.92 km/h
Answer:
a. Discrete probability distribution, frequent rider club, 0.65 of 20
b. 13
c. $60
d. $57.50
Step-by-step explanation:
a. X follows a discrete probability distribution because it involves discrete random variables which have probability mass function and frequency.
f(x) =0.65 of 20 passengers
b. if 0.65 0f 20 passengers are frequent riders,
then, the frequent riders will be 13 passengers
c. expected revenue will be $3 *20 passengers which will be $60.
the total number of passengers given tickets is 20 and the price for each is $3. thus, making the parameters to be price and number of passengers.
d. if the frequent riders are charged $2, then the amount paid by this group will be $2*13 which is $26
and if $4.50 is paid by the regular passengers it will be $4.50*(20-13) which is $31.50.
therefore, expected revenue will be $26+$31.50 equals $57.50
A. (140x110)+[(50x70)/2] = 15,400+1750= 17,150cm^2
b. (4x6)/2= 12cm^2
