Think of the question as money. You have 3 dollars and 50 and you want to count by a quarter of much which is 25. Now you find the answer
Given:
Annual population of butterflies after t years is

To find:
The growth rate.
Solution:
The general exponential function is
...(i)
where, a is initial value, t is time and r is growth rate.
We have,

It can be written as
...(ii)
On comparing (i) and (ii), we get
Initial value : 
Growth rate : 
Therefore, the growth rate is 8.5%.
Answer:
The answer is D
Step-by-step explanation:
9(x + -3) + 28 = 4x + -3
Reorder the terms:
9(-3 + x) + 28 = 4x + -3
(-3 * 9 + x * 9) + 28 = 4x + -3
(-27 + 9x) + 28 = 4x + -3
Reorder the terms:
-27 + 28 + 9x = 4x + -3
Combine like terms: -27 + 28 = 1
1 + 9x = 4x + -3
Reorder the terms:
1 + 9x = -3 + 4x
Solving
1 + 9x = -3 + 4x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-4x' to each side of the equation.
1 + 9x + -4x = -3 + 4x + -4x
Combine like terms: 9x + -4x = 5x
1 + 5x = -3 + 4x + -4x
Combine like terms: 4x + -4x = 0
1 + 5x = -3 + 0
1 + 5x = -3
Add '-1' to each side of the equation.
1 + -1 + 5x = -3 + -1
Combine like terms: 1 + -1 = 0
0 + 5x = -3 + -1
5x = -3 + -1
Combine like terms: -3 + -1 = -4
5x = -4
Divide each side by '5'.
x = -0.8
Simplifying
x = -0.8
Label the 3 distinct sides of the box. I arbitrarily chose the letters a, b and c.
Use the info about areas as follows:
ab=54 in^2
ac=90 in^2
bc=60 in^2
Here you have 3 equations in 3 unknowns (a, b and c), which is enough info to use to determine a, b and c. Then the volume of the box is a*b*c.
Example: bc = 90, but c = 60/b. You could subst. 60/b for c in the 2nd and 3rd equation, which will eliminate c completely and leave you with 2 equations in 2 unknowns.
Continuing this procedure, I determined that a=9, b=6 and c=10. Thus, the volume of the box is V = 9*6*10 = 540 cubic inches (answer)
Answer:
e= -5.41
Step-by-step explanation:
Hello!
In linear regression, a residual value is a distance between the observed values and the regression line.
The residual value (e) is calculated as the difference between the observed value (Y) and the predicted value (^Y).
e= Y - ^Y
e= 15.92 - 21.33 = -5.41
I hope it helps!