Complete question :
Between 12:00 PM and 1:00 PM, cars arrive at Citibank’s drive-thru at the rate of 6 cars per hour (0.1 car per minute). The following formula from statistics can be used to determine the probability that a car will arrive within t minutes of 12:00 PM. F(t)=1−e^−0.1t
Determine how many minutes are needed for the probability to reach 80%.
Answer:
16.09 minutes
Step-by-step explanation:
Given the function :
F(t)=1−e^−0.1t
To attain 80% probability ; 80% = 0.8
0.8 = 1 - e^-0.1t
0.8 - 1 = - e^-0.1t
-0.2 = - e^-0.1t
Take the In of both sides
In(0.2) = In( e^-0.1t)
−1.609437 = - 0.1t
Divide both sides by - 0.1
−1.609437 / -0.1 = - 0.1t / 0.1
16.09 = t
Hence, the time it'll take will be 16.09 minutes
Answer:
x⁴ - y⁴= (x²)²- (y²)² = (x² + y²)(x²- y²) = (x²+y²)(x)²-(y)²=(x²+y²)(x+y)(x-y)
49x²-16/25= (7x)²- (4/5)²=(7x+4/5)(7x-4/5)
Y = x² + 4x + 4.. Since the coefficient of x² =1, is positive, then this parabola opens upward & has a minimum.
Its axis of symmetry is = -b/a = -4/1 = 4 (so x=4)
1) When x=4, y= 4²+4(4)+4 => y=36 so the VERTEX has a minimum is at (4,36)
2)FOCUS.: To be able to calculate the focus, rewrite the equation in a standard form: y-k =a(x-h)² & y = x² + 4x + 4 could be written y=(x+2)², this means that k=0 & h=-2.
Now p being the distance between the VERTEX & the FOCUS, we apply the formula (x-2)² = 4P (y-k) , but k=0 & h=2 then (x-2)² = 4P(y-0) then P =1/4
3) DRECTRICE : y=k-P = 0-1/4 ==> y=-1/4 is the directrix
875 x 12 = 10500ft squared
950 x 6 = 5700ft squared
10500 + 5700 = 16200
the total floor area is 16200 squared feet
Obtuse because it only takes one obtuse angle to make an obtuse triangle
