Answer:
games
Step-by-step explanation:
Employees: 8
Sales last month: g
Average:
To find out how many games Chris sold, we have to take the average and subtract 17.
Since there are no more values we can use, this is as simple as we can get it. If we knew how many games they sold last month, we could get an exact answer for Chris using this expression.
Answer:
-50 ml of 3% alcohol solution and 150 ml of 8% alcohol solution
Step-by-step explanation:
For us to solve this type of mixture problem, we must represent the problem in equations. This will be possible by interpreting the question.
Let the original volume of the first alcohol solution be represented with x.
The quantity of the first alcohol solution needed for the mixture is 3% of x
⇒
= 0.03x
Let the original volume of the second alcohol solution be represented with y.
The quantity of the second alcohol solution needed for the mixture is 5% of y
⇒
= 0.05y
The final mixture of alcohol solution is 6% of 100 ml
⇒
= 6 ml
Sum of values of two alcohol solutions = Value of the final mixture
0.03x + 0.05y = 6 ml ..........(1)
Sum of original quantity of each alcohol solution = Original volume of the of mixture
x + y = 100 ml ..........(2)
For easy interpretation, I will be setting up a table to capture all information given in the question.
Component Unit Value Quantity(ml) Value
3% of Alcohol solution 0.03 x 0.03x
8% of Alcohol solution 0.08 y 0.08y
Mixture of 100ml of 6% 0.06 100 6
x + y = 100 0.03x + 0.08y =6
Looking at the equations we derived, we have two unknowns in two equations which is a simultaneous equation.
0.03x + 0.05y = 6 ml ..........(1)
x + y = 100 ml ..........(2)
Using substitution method to solve the simultaneous equation.
Making x the subject of formula from equation (2), we have,
x = 100 - y ..........(3)
Substituting x = 100 - y from equation (3) into equation (1)
0.03(100 - y) + 0.05y = 6
3 - 0.03y + 0.05y = 6
Rearranging the equation,
0.05y - 0.03y = 6 - 3
0.02y = 3
y = 150 ml
Substituting y = 150 ml into equation (3) to get x
x = 100 - 150 ml
x = - 50 ml
The quantity of the first alcohol solution needed for the mixture for 3% is - 50 ml
The quantity of the second alcohol solution needed for the mixture for 5% is 150 ml
This solution means 50 ml of the first alcohol solution must be removed from the mixture with 150 ml of the second alcohol solution to get a final mixture of 100 ml of 6% alcohol solution.
Answer:
The solution
Step-by-step explanation:
<u><em>Explanation</em></u>:-
Consider the initial value problem y′+3 y=9 t,y(0)=7
<em>Step(i)</em>:-
Given differential problem
y′+3 y=9 t
<em>Take the Laplace transform of both sides of the differential equation</em>
L( y′+3 y) = L(9 t)
<em>Using Formula Transform of derivatives</em>
<em> L(y¹(t)) = s y⁻(s)-y(0)</em>
<em> By using Laplace transform formula</em>
<em> </em><em> </em>
<em>Step(ii):-</em>
Given
L( y′(t)) + 3 L (y(t)) = 9 L( t)
Taking common y⁻(s) and simplification, we get
<em>Step(iii</em>):-
<em>By using partial fractions , we get</em>
On simplification we get
9 = A s(s+3) +B(s+3) +C(s²) ...(i)
Put s =0 in equation(i)
9 = B(0+3)
<em> B = 9/3 = 3</em>
Put s = -3 in equation(i)
9 = C(-3)²
<em>C = 1</em>
Given Equation 9 = A s(s+3) +B(s+3) +C(s²) ...(i)
Comparing 'S²' coefficient on both sides, we get
9 = A s²+3 A s +B(s)+3 B +C(s²)
<em> 0 = A + C</em>
<em>put C=1 , becomes A = -1</em>
<u><em>Step(iv):-</em></u>
Applying inverse Laplace transform on both sides
<em>By using inverse Laplace transform</em>
<em></em><em></em>
<u><em>Final answer</em></u>:-
<em>Now the solution , we get</em>