Answer:
Step-by-step explanation:
You don't say whether this is compound interest or simple interest.
I will assume it's compounding that interests you.
The appropriate formula is
A = P(1 + r)^t, where r is the interest rate as a decimal fraction, t is the time in years, and P is the original amount. Thus:
A = $1000·(1 + 0.05)^t, or A = $1000·(1.05)^t
Please note: There were apparently possible answer choices. Next time, please be sure to list such choices. Thank you.
Subtract the 15 from the 133
you get 118
divide 29.50 from the 118
you get 4
4 people went to the concert
Answer:
the answer is A. $32.23
Step-by-step explanation:
Hi there what you need is lagrange multipliers for constrained minimisation. It works like this,
V(X)=α2σ2X¯1+β2\sigma2X¯2
Now we want to minimise this subject to α+β=1 or α−β−1=0.
We proceed by writing a function of alpha and beta (the paramters you want to change to minimse the variance of X, but we also introduce another parameter that multiplies the sum to zero constraint. Thus we want to minimise
f(α,β,λ)=α2σ2X¯1+β2σ2X¯2+λ(\alpha−β−1).
We partially differentiate this function w.r.t each parameter and set each partial derivative equal to zero. This gives;
∂f∂α=2ασ2X¯1+λ=0
∂f∂β=2βσ2X¯2+λ=0
∂f∂λ=α+β−1=0
Setting the first two partial derivatives equal we get
α=βσ2X¯2σ2X¯1
Substituting 1−α into this expression for beta and re-arranging for alpha gives the result for alpha. Repeating the same steps but isolating beta gives the beta result.
Lagrange multipliers and constrained minimisation crop up often in stats problems. I hope this helps!And gosh that was a lot to type!xd
Answer:
1.3
Step-by-step explanation:
each person gets 1 1/3 of a pie