This is an exponential decay problem.
Using the equation Y = a *(1-rate)^time
where Y is the future value given as 12,000 and a is the starting value given as 13,000.
The rate is also given as 5%.
The equation becomes:
12,000 = 13,000(1-0.05)^x
12,000 = 13,000(0.95)^x
Divide each side by 13000:
12000/13000 = 0.95^x/13000
12/13 = 0.95^x
Use the natural log function:
x = ln(12/13) / ln(0.95)
x = 1.56 years. ( this will equal 12,000
Round to 2 years it will be less than 12000.
3/4 foot is 9 inches, and 4 1/2 feet is 54 inches, so, 54/9 makes exactly 6 pieces of string.
Answer:

Step-by-step explanation:
Take out 8m as a factor from the top side of the equation. You are left with 
Answer:
The answer is below
Step-by-step explanation:
The question is not complete. The complete question is:
The 12 foot long bed of a dump truck loaded with debris must rise an angle of 30 degrees before the debris will spill out. Approximately how high must the front of the bed rise for the debris to spill out.
Solution:
Let x be the height of the front of the bed rise needed to be raised for the debris to spill out. We can find x using trigonometric identities. That is:
sin θ = opposite / hypotenuse
Using trigonometric identities, we can get that:
sin(30) = x / 12
This gives:
0.5 = x / 12
Cross multiplying the terms to get:
x = 12 * 0.5
x = 6 ft
Therefore the front of the bed rise must be raised 6 ft for the debris to spill out.
Answer:
Integer
Step-by-step explanation:
The greatest integer function, F(x)=[[x]], is defined to be the greatest <u>integer that is </u>less than or equal to x.
The Greatest Integer Function is also referred to as the Floor Function.
It is written as F(x)=[[x]]
The value of ⌊x⌋ is the largest or the greatest integer that is less than or equal to x