Answer:
Therefore
Step-by-step explanation:
Given that, a large tank contains 700 gallons of pure water.
At a time t , A(t)is the amount of salt in the tank .
The differential equation of rate of change of salt is
First we find and
=(concentration of salt ).(input rate of brine)
=(3 lb/gal).(7 gal/ min )
=21 lb/min
Since the rate of solution which is pumped out is same rate of pumped in..
= (the concentration of salt in the tank).(output rate)
lb/min
lb/min
Therefore,
....(1)
Here and Q = 21
The integrating factor of the differential equation is
=
Multiply the integrating factor the both sides of ODE of (1)
Integrating bot sides
[c is an arbitrary constant]
At the initial time, the tank contains 700 gallons of pure water.
It means A(0)=0
Putting A=0 ,t=0
Therefore
1/4 = 0.25
0.25+ 5 + 5.25
120 /5.25
= 22.9 pieces
Binomial
Binomial distribution can be used because the situation satisfies all the following conditions:1. Number of trials is known and remains constant (n=10)2. Each trial is Bernoulli (i.e. exactly two possible outcomes) (defective/normal)3. Probability is known and remains constant throughout the trials (p=5%)4. All trials are random and independent of the others (assumed from context)The number of successes, x, is then given by
where
Substituting values, p=0.05, n=10, X=exactly 1
for X=1 (defective out of n)
P(X=1)=C(10,1)0.05^1*(1-0.05)^(10-1)
=10!/(1!9!)*0.05*0.95^9
=10*0.05*0.0630249
=0.315125 (to 6 places of decimal)
Answer:
The last one
Step-by-step explanation:
"Range of the function"
Domain of the function: All real numbers
Range of the function:
To find the domain and range of the inverse of the function, just swap the domain and range from the original function, so
Range of the inverse: All real numbers
Domain of the inverse function:
Given:
First term of an arithmetic sequence = 5
Second term = 3
To find:
The explicit formula for the given arithmetic sequence.
Solution:
We have,
First term:
Second term:
Common difference is
Now, the explicit formula for an arithmetic sequence is
where, a is first term and d is common difference.
Putting a=5 and d=-2, we get
It can also be written as
Here, n is an integer greater than or equal to 1.
Domain is the set of input values.
Therefore, the explicit equation is or and domain is all interest greater than or equal to 1.