216/10 = 21.6 = 22
22 x 3.99 = 87.78
22 x 4.99 = 109.78
216 x 1.00 = $216
87.78+109.78 = 197.56
216 - 197.56 = 18.43
Your profit will be $18.43
Rewrite as:
4y=x^2-12x+68
divide by four:
y= x^2/4-3x+17
your answer would be
(6,8)
Answer:
257 is prime.
Step-by-step explanation:
To evaluate if a number is prime, we just need to evaluate it for the prime numbers that are equal or lesser than the said number's square root.
In this case, √257 = 16.03 so we just need to see if 257 is divisible by <u>2, 3, 5, 7, 11 and 13</u> (the prime numbers that come before 16)
- 257 is odd, so it is not divisible by 2.
- The sum of its digits is 14, therefore, it is not divisible by 3.
- 257 ends in 7, therefore it's not divisible by 5.
- 257/ 7 = 36.71 so it's not divisible by 7.
- 257/ 11 = 23.36 so it's not divisible by 11
- Finally 257 / 13= 19.76 so it's not divisible by 13.
Therefore, 257 is prime.
Answer: *1*.0325
Step-by-step explanation: When you round it to the nearest tenths place the 3 behind the 0 is less than 4 therefore everything behind the 0 gets taken away. The 0 has no value so you could take it away too along with the decimal point and it will turn into just 1.
Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.
Step-by-step explanation:
Salt in the tank is modelled by the Principle of Mass Conservation, which states:
(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)
Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:

By expanding the previous equation:

The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:

Since there is no accumulation within the tank, expression is simplified to this:

By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:
, where
.

The solution of this equation is:

The salt concentration after 8 minutes is:

The instantaneous amount of salt in the tank is: