The interest on the first monthly payment is ...
I = Prt
I = 110,000*7.5%*(1/12)= 687.50
For the first payment, the interest is
$687.50
_____
The time period for the interest rate calculation is 1/12 year.
Answer:
a) P(μ-k*σ≤ Y ≤ μ+k*σ ) ≥ 0.90
a= μ-3.16*σ , b= μ+3.16*σ
b) P(Y≥ μ+3*σ ) ≥ 0.90
b= μ+3*σ
Step-by-step explanation:
from Chebyshev's inequality for Y
P(| Y - μ|≤ k*σ ) ≥ 1-1/k²
where
Y = the number of fish that need be caught to obtain at least one of each type
μ = expected value of Y
σ = standard deviation of Y
P(| Y - μ|≤ k*σ ) = probability that Y is within k standard deviations from the mean
k= parameter
thus for
P(| Y - μ|≤ k*σ ) ≥ 1-1/k²
P{a≤Y≤b} ≥ 0.90 → 1-1/k² = 0.90 → k = 3.16
then
P(μ-k*σ≤ Y ≤ μ+k*σ ) ≥ 0.90
using one-sided Chebyshev inequality (Cantelli's inequality)
P(Y- μ≥ λ) ≥ 1- σ²/(σ²+λ²)
P{Y≥b} ≥ 0.90 → 1- σ²/(σ²+λ²)= 1- 1/(1+(λ/σ)²)=0.90 → 3= λ/σ → λ= 3*σ
then for
P(Y≥ μ+3*σ ) ≥ 0.90
Answer:
20,944 years
Step-by-step explanation:
The formula you use for this type of decay problem is the one that uses the decay constant as opposed to the half life in years. We are given the k value of .00012. If we don't know how much carbon was in the bones when the person was alive, it would be safer to say that when he was alive he had 100% of his carbon. What's left then is 8.1%. Because the 8.1% is left over from 100% after t years, we don't need to worry about converting that percent into a decimal. We can use the 8.1. Here's the formula:

where N(t) is the amount left over after the decay occurs,
is the initial amount, -k is the constant of decay (it's negative cuz decay is a taking away from as opposed to a giving to) and t is the time in years. Filling in accordingly,

Begin by dividing the 100 on both sides to get

Now take the natural log of both sides. Since the base of a natual log is e, natural logs and e "undo" each other, much like taking the square root of a squared number.
ln(.081)= -.00012t
Take the natual log of .081 on your calculator to get
-2.513306124 = -.00012t
Now divide both sides by -.00012 to get t = 20,944 years
Answer:
10x=10y so x and y are the same or x=y
Step-by-step explanation:
Answer:
The middle slab is 2 cubic feet.
Step-by-step explanation:
The problem presents the information: Mr. Alvarez makes a walkway out of 3 cement slabs.
However, he uses 14 Cubic feet of cement to make the walkway. Each square slab has a volume of 4 cubic feet.
Mr. Alvarez makes the way with 3 cement slabs (NC), each cement slab is 4 cubic feet (UC). It means, the cubic feet for the 3 cement slabs (CS) are:
CS = NC* UC = 3*4 = 12 cubic feet.
It means Mr. Alvarez uses 12 cubic feet with 3 cement slabs.
Mr. Alvarez used in total of 14 cubic feet of cement (TC). At this moment he used 12 cubic feet of cement (CS). It means, there will be a part of the cement slab used (PC).
PC = TC - CS = 14 - 12 = 2 Cubic feet.
Finally, the middle slab is 2 cubic feet of cement.