We know that
the equation of the parabola is of the form
y=ax²+bx+c
in this problem
y=1/4x²−x+3
where
a=1/4
b=-1
c=3
the coordinates of the focus are
(-b/2a,(1-D)/4a)
where D is the discriminant b²-4ac
D=(-1)²-4*(1/4)*3-----> D=1-3---> D=-2
therefore
x coordinate of the focus
-b/2a----> 1/[2*(-1/4)]----> 2
y coordinate of the focus
(1-D)/4a------> (1+2)/(4/4)---> 3
the coordinates of the focus are (2,3)
Answer:
y = 56/3
Step-by-step explanation:
We need to write equations to solve
Let the two numbers be x and y
The sum is 56
x+y = 56
The first number is 2 times greater than the second number.
x = 2*y
Substitute this into the first equation
x+y = 56
2y+y=56
3y = 56
y = 56/3
The base charge is 35 dollars per day. He rented the car for 3 days, so before you add in the mileage you have to multiply 35 x 3 days for 105 dollars. Then you have to take the remaining charge and divide it by the charge per mile to get the number of miles driven. Lets set up the equation.
d= number of days rented
m= number of miles driven
35(d) + .15(m) = 117.25
35(3) + .15m = 117.25
105 + .15m = 117.25
.15m = 117.25 - 105
.15m = 12.25
m = 12.25/.15
m = 81.67
So he drove 81.67 miles
Answer:
a.0.12
b. Dependent
Step-by-step explanation:
a. The two events mentioned here are " print book is purchases" and "customer using gift card". P(P)=0.6 and P(C)=0.2. we have to calculate the probability of print book selection for purchase and payment is made through gift card i.e. P(P∩C). P(P∩C)=P(P)*P(C)=0.6*0.2=0.12.
b. If P(A∩B)=P(A)*P(B), then the two events are independent. Here in the given situation two independent variables are "purchase of e-book" and "payment made using gift card"
P(E)=0.4
P(G)=0.2
P(E and G)=P(E∩G)=0.1
P(E)*P(G)=0.4*0.2=0.08 that is not equal to 0.1. So, the two events "e-book is purchased" and "Payment made by customer using gift card" are not independent.
