In order to construct this equation, we will use the variables:
V to represent mixture volume (40 ml)
C to represent mixture concentration (0.32)
v₁ to represent volume of first solution (40 / 4 = 10 ml)
c₁ to represent concentration of first solution (0.2)
v₂ to represent the volume of the second solution (40 * 3/4 = 30 ml)
c₂ to represent the concentration of the second solution
We know that the total amount of substance, product of the volume and concentration, in the final solution is equal to the individual amounts in the two given solutions. Thus:
VC = v₁c₁ + v₂c₂
40(0.32) = 10(0.2) + 30c
S = d/t
st = d
t = d/s
The time going is t1.
The time returning is t2.
The total time is 4 hours, so we have t1 + t2 = 4
The speed of the current is c.
The speed going is 9 + c.
The speed returning is 9 - c.
t1 = 16/(9 + c)
t2 = 16/(9 - c)
t1 + t2 = 16/(9 + c) + 16/(9 - c)
4 = 16/(9 - c) + 16/(9 + c)
1 = 4/(9 - c) + 4/(9 + c)
(9 + c)(9 - c) = 4(9 - c) + 4(9 + c)
81 - c^2 = 36 - 4c + 36 + 4c
81 - c^2 = 72
c^2 = 9
c^2 - 9 = 0
(c + 3)(c - 3) = 0
c + 3 = 0 or c - 3 = 0
c = -3 or c = 3
We discard the negative answer, and we get c = 3.
The speed of the current is 3 mph.
Answer:
A = 250(1 + 0.016)^0.75.
Step-by-step explanation:
9 months = 0.75 years
So A = 250(1 + 0.016)^0.75.
Answer:
a) f(-1/2) = -2 is NOT TRUE.
b) f(0) =3/2 is TRUE.
c) f(1) = -1 is NOT TRUE.
d) f(2) = 1 is NOT TRUE.
e) f(4) = 7/2 is TRUE.
Step-by-step explanation:
Here, the given function is 
Now, checking for each values for the given function:
a) Putting x = (-1/2):

and (5/4) ≠ -2
Hence, f(-1/2) = -2 is NOT TRUE.
b)Putting x = 0 :

Hence, f(0) =3/2 is TRUE.
c) Putting x = 1:

Hence, f(1) = -1 is NOT TRUE.
d)Putting x = 2:

and (5/2) ≠ 1
Hence, f(2) = 1 is NOT TRUE.
e)Putting x = 4:

Hence, f(4) = 7/2 is TRUE.
Answer:
C
Step-by-step explanation:
AP Classroom says so