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:
0.41567 is:
... rational because it can be expressed as a fraction (e.g., 41567/100000)
... not irrational for the same reason
... not whole (obviously)
... not integer (obviously)
Yes correct x is 48.02 here is why.
simplify 45.6/109.2 to 0.417582
multiply both sides by 115
simplify 0.417582 x 115 to 48.021978
switch sides
Answer: x = 48.021978
Answer:
Since the equation is undefined for -2
Therefore, NO SOLUTION for the given equation.
Step-by-step explanation:
Considering the expression
as
so equation becomes
So the following points are undefined
Since the equation is undefined for -2
Therefore, NO SOLUTION for the given equation.
Answer:
a.) .95
b.) The expected number of baskets is 10.50.
c.) 1.7748
Step-by-step explanation:
a.) This is a binomial distribution as there are two possibilities: makes a free throw or doesn't. This means that you can use the binomial function on a calculator to figure out the answer. Use the binomial CDF function on a calculator and the number of trials=15, probability of success=.7, lower bound=0, upper bound=7. Once you have evaluated the answer, .0500, it will need to be subtracted from1, as you want everything not included in this section. The answer to part a is thus 1-.0500=.95.
b.) The expected value is calculated by taking the total number of shots and multiplying it by the probability of making the shot: 15×.7=10.5 shots.
c.) The standard deviation of a binomial distribution can be calculated by the formula 
. Plugging in the numbers you get 
=1.7748.
