Answer:
7.487 tons
Step-by-step explanation:
There are 2,000 pounds in one ton, so you divide 14,974 by 2,000 to get your answer.
Answer:
Left: The substance is decreasing by 1/2 every 12 years
Right: The substance is decreasing by 5.61% each year
Step-by-step explanation:
exponential decay
A = P(1-r)ᵇⁿ, where A is the final amount, P is the initial amount, r is the rate decreased each time period, b is the number of years, and n is the number of times compounded each year
let's write each formula in terms of this
left:
f(t) = 600(1/2)^(t/12)
matching values up...
A = P(1-r)ᵇⁿ
A = f(t)
P = 600
1 - r = 1/2 -> r = 1/2
t/12 = bn -> b = number of years = t, so bn = b/12 -> n = 1/12. Thus, it is compounded 1/12 times each year, so it is compounded every t*12 = 12 years. If it was compounded each month, it would be compounded 12 times a year
Thus, this is decreasing by a rate of 1/2 each 12 years
right:
f(t) = 600(1-0.0561)^(t)
matching values up...
A = P(1-r)ᵇⁿ
A = f(t)
P = 600
1 - r = 1 - 0.0561 -> r = 0.0561 = 5.61%
t = bn -> b = number of years = t, so bn = b -> n = 1. Thus, it is compounded annually (1 time each year)
Thus, this is decreasing by a rate of 5.61% each year
3-4z=-5+8z
Add 5 to both sides
8-4z=8z
Add 4z to both sides
8=12z
Divide both sides by 12
z=12/8
Simplify
z=3/2
<span>square root if 54 is 7.35</span>
<h3>
Answer: D) infinitely many solutions</h3>
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Explanation:
Let's solve the first equation for y
4x - 2y = 6
4x-6 = 2y
2y = 4x-6
y = (4x-6)/2
y = (4x/2) - (6/2)
y = 2x - 3
After doing so, we see that 4x-2y = 6 is equivalent to y = 2x-3
Therefore, the original system of equations is effectively listing the same equation twice (one has a different form compared to the other).
Both equations in this system produce the same graph, which leads to infinitely many solutions. All solutions are on the line y = 2x-3.
You can say that all solutions are in the form (x, 2x-3) where x is any real number you want.
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Here's another approach using substitution
4x - 2y = 6 ... start with the first equation
4x - 2( y ) = 6
4x - 2( 2x-3 ) = 6 .... replace y with 2x-3; ie plug in y = 2x-3
4x - 2(2x) - 2(-3) = 6
4x - 4x + 6 = 6
0x + 6 = 6
0 + 6 = 6
6 = 6
We get a true statement. The last equation is always true regardless of what we plug in for x, so this is another way to see how we get to infinitely many solutions.
Side note: the system is considered dependent since one equation depends on the other. The system is also consistent since it has at least one solution.
