This is a system of equations. The first equation represents the tank being emptied and the second equation represents the tank being filled:
k = -10t + 528
k = 14t
To solve this system of equations, we will use substitution. The second equation says that k is equal to 14t, so we can substitute 14t for k in the first equation.
14t = -10t + 528
24t = 528
t = 22
Now that we have t, we can use it to find k by plugging it in to the second equation:
k = 14(22)
k = 308
So, it will take 22 minutes for both tanks to hold equal amounts of water. They will each hold 308 kiloliters.
Answer:
There are a total of 2011 integer divisors.
Step-by-step explanation:
The only primes p such that 1/p has finite spaces after the coma are 2 and 5. If we divide a number with last digit odd we will obtain 1 extra digit after the decimal point and if we divide a number by 5 we will obtain 1 more digit if that number has a last digit in the decimal which is not a multiple of 5.
If we take powers of those primes we will obtian one more digit each time. In order to obtain more digits it is convinient to divide by a power of 2 instead of a power of 5, because the resulting number will be smaller.
If we want 2010 digits after the decimal point, we need to divide 1 by 2 a total of 2010 times, hence f(2010) = 2²⁰¹⁰, which has as positive integer divisors every power of 2 between 0 and 2010, hence there are a total of 2011 integer divisors of f(2010).
Answer:
Step-by-step explanation:
Given : In a state where license plates contain six digits.
Probability of that a number is 9 = 
[Since total digits = 10]
We assume that each digit of the license number is randomly selected .
Since each digit in the license plate is independent from the other and there is only two possible outcomes for given case (either 9 or not), so we can use Binomial.
Binomial probability formula: 
, where n= total trials , p = probability for each success.
Let x be the number of 9s in the license plate number.
Then, the probability that the license number of a randomly selected car has exactly two 9's will be :
Hence, the required probability = 0.098415
