Answer:
Step-by-step explanation:
Given that water leaks from a vertical cylindrical tank through a small hole in its base at a rate proportional to the square root of the volume of the water remaining. The tank intitially contains 300 liters and 23 liters leak out during the first day
Let V represent the volume at time t.
Rate of change of V is 
where k represents the constant of proportionality
We separate the variables and integrate
Use the fact when t =0, V =300
Now use the fact when t =1 V= 300-23 = 277
k is negative because there is leak
So equation is
Using this
A) when half empty V = 150
t = 
so it takes 3.75 days
B) When t =3
V = 233.7515
Profit is the difference between a companies revenue and its expenses.
Ax + 3y = 48....subtract 3y from both sides
Ax = 48 - 3y...divide both sides by x
A = (48 - 3y) / x <==
Answer:
1
Step-by-step explanation:
it's really hard to understand the options that are given but 7/8 is only 1/8 away from 1. So I would choose 1. 0 is wrong. 1/2 is wrong. I dont know what the options 7 and 8 are doing there but I would go with 1
Answer: 0.205
Step-by-step explanation:
The probability in one flip is equal to 0.5.
Now, if we do 10 flips, we want 4 times that the coin ends in heads and the other 6 times it must end in tails, so the probability is:
0.5^4*0.5^6 = 0.5^10
Now, this is the case where in the first 4 flips we get heads and in the other 6 we get tails, but we have other ways to get only 4 heads (for example in the last 4 flips, 2 at the beginning and 2 at the end, etc)
So we also need to calculate all the possible permutations of 4 heads in 10 flips. this is:
C = 10!/(10 - 4)!*4! = (10*9*8*7)/(4*3*2*1) = 210
So the probability that we are looking for is:
P = (0.5^10)*210 = 0.205
