The population is increasing by 1500 each year and starts at 1970 population ( = 4800) so the equation is
y=1500x+4800
Answer:
Fraction: 81/100
Decimal: 0.81
Percentage: 81%
Step-by-step explanation:
The question is complete but the diagram mentioned can be found in
brainly.com/question/12188410
First step is to find the area of the whole square and then the area of the part that was shaded.
From the diagram, there are 100 squares in the whole square. 81 of those squares are shaded.
Area of the whole square = 10 by 10
= 10×10 = 100unit²
Area of shaded region = (10 by 8) + 1
= 80+1 = 81unit²
shaded area expressed as a fraction = 81unit²/100unit²
= 81/100
Shaded area expressed as a decimal = 81/100
You take the number 81 and carry the point by two decimal place from the right
= 0.81
Shaded area expressed as a percent of the whole = (81/100) × 100
= (81×100)/100
= 81%
Answer:
The values of x for which the model is 0 ≤ x ≤ 3
Step-by-step explanation:
The given function for the volume of the shipping box is given as follows;
V = 2·x³ - 19·x² + 39·x
The function will make sense when V ≥ 0, which is given as follows
When V = 0, x = 0
Which gives;
0 = 2·x³ - 19·x² + 39·x
0 = 2·x² - 19·x + 39
0 = x² - 9.5·x + 19.5
From an hint obtained by plotting the function, we have;
0 = (x - 3)·(x - 6.5)
We check for the local maximum as follows;
dV/dx = d(2·x³ - 19·x² + 39·x)/dx = 0
6·x² - 38·x + 39 = 0
x² - 19/3·x + 6.5 = 0
x = (19/3 ±√((19/3)² - 4 × 1 × 6.5))/2
∴ x = 1.288, or 5.045
At x = 1.288, we have;
V = 2·1.288³ - 19·1.288² + 39·1.288 ≈ 22.99
V ≈ 22.99 in.³
When x = 5.045, we have;
V = 2·5.045³ - 19·5.045² + 39·5.045≈ -30.023
Therefore;
V > 0 for 0 < x < 3 and V < 0 for 3 < x < 6.5
The values of x for which the model makes sense and V ≥ 0 is 0 ≤ x ≤ 3.
As we are given with
we are supposed to simplify this expression. which can be done as below
