1/(3b)=4/5 multiply both sides by 5
5/(3b)=4 multiply both sides by 3b
5=12b divide both sides by 12
b=5/12 (not sure why you don't have that as an option in your answers, perhaps I misunderstood your description of the original equation...)
Answer:
![\[\frac{1}{24}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B1%7D%7B24%7D%5C%5D)
Step-by-step explanation:
Let the total number of batteries produced daily be represented by x.
7/8 of the batteries are packaged immediately.
So the total number of packaged batteries = ![\[\frac{7x}{8}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B7x%7D%7B8%7D%5C%5D)
Remaining batteries = ![\[x-\frac{7x}{8}\]](https://tex.z-dn.net/?f=%5C%5Bx-%5Cfrac%7B7x%7D%7B8%7D%5C%5D)
= ![\[\frac{x}{8}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7Bx%7D%7B8%7D%5C%5D)
Two third of the remaining batteries are sent to charity.
So the total number of batteries sent to charity= ![\[\frac{2}{3} * \frac{x}{8}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B2%7D%7B3%7D%20%2A%20%5Cfrac%7Bx%7D%7B8%7D%5C%5D)
= ![\[\frac{x}{12}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7Bx%7D%7B12%7D%5C%5D)
Remaining batteries are faulty.
So the total number of faulty batteries = ![\[\frac{x}{8} - \frac{x}{12}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7Bx%7D%7B8%7D%20-%20%5Cfrac%7Bx%7D%7B12%7D%5C%5D)
= ![\[\frac{3x - 2x}{24}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B3x%20-%202x%7D%7B24%7D%5C%5D)
= ![\[\frac{x}{24}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7Bx%7D%7B24%7D%5C%5D)
So the faction of batteries which are faulty =
= ![\[\frac{x}{24} \div x\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7Bx%7D%7B24%7D%20%5Cdiv%20x%5C%5D)
= ![\[\frac{1}{24}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B1%7D%7B24%7D%5C%5D)
Answer:
(B)
Step-by-step explanation:
Volume of fluid in the tank =1000 gallons
Initial Amount of Salt in the tank, A(0)= 30 pounds
Incoming brine solution of concentration 2 pounds of salt per gallon is pumped in at a rate of 4 gallons per minute.
Rate In=(concentration of salt in inflow)(input rate of brine)

The resulting mixture is pumped out at the same rate, therefore:
Rate Out =(concentration of salt in outflow)(output rate of brine)

Therefore:
The rate of change of amount of salt in the tank,

(0,5)(4,0)
slope = (0 - 5) / (4 - 0) = -5/4
y = mx + b
slope(m) = -5/4
use either of ur sets of points....(0,5)...x = 0 and y = 5
now we sub and find b, the y int
5 = -5/4(0) + b
5 = b
so ur equation is : y = -5/4x + 5...but we need it in standard form...
y = -5/4x + 5
5/4x + y = 5....multiply everything by common denominator of 4
5x + 4y = 20 <== standard form of Ax + By = C