Solution:
Let the amount invested in scheme which yields 9% be x and amount invested in scheme which yields 13% be y.
x + y = 180000 --equation 1
0.09x + 0.13y = 18000 --equation 2
Balancing the equations, multiply equation 1 with 0.09 and equation 2 with 1,
0.09x + 0.09y = 16200 -equation 3
0.09x + 0.13y = 18000 --equation4
Subtracting equation 4 from 3,
-0.04y = -1800
y = 45000
Now putting value of y in equation 1,
x + 45000 = 180000
x = 135000
The amount to be invested in scheme which yields 9% = $135,000
The amount to be invested in scheme which yields 13% = $45,000
<span>This is an example of positive reinforcement. Positive reinforcement rewards a person or thing for performing a desired action or behavior. By rewarding the person or thing every time it does the desired action you increases the chances of the action or behavior being done again. It a type of subconscious training.</span>
Answer:
a) Absolute Value Inequality => Absolute(0 + y) < 2
b) -2 < y < 2
Which means, Johnson Family has to live within the range of -2 to +2 from the fire department. Otherwise, they will have to pay 500 USD as increased deductible.
Explanation:
<u><em>Johnson Family has to live within the range of -2 to +2 from the fire department.
</em></u>
<em>a) Absolute Value Equation:</em>
Absolute(0 + y) < 2
where y represent the location of the new house and 0 represents the location of the fire department.
Furthermore,
<em>Absolute(0 + y) < 2 = (0 + x) < 2 when (0 + y) is +ve. </em>
and
<em>Absolute(0+y) <2 = -(0 + x) < 2 when (0 + y) is -ve.
</em>
b) When (0 + y) is +ve,
we have, (0 + y) < 2.
<em>Solving for y and subtracting 0 from both sides. </em>
0-0 + y < 2 - 0
<em>y < 2</em>
and when (0 + y) is -ve,
<em>we have, - (0 + y) < 2.
</em>
Solving for y:
- 0 - y < 2
multiplying negative from both sides
<em>y > - 2</em>
<em>So, we have -2 < y < 2 </em>
<em>Johnson Family has to live within the range of -2 to +2 from the fire department. Otherwise, they will have to pay 500 USD as increased deductible. </em>
