search the web for a building somewhere in the world that you think shows the power of mathematics and present a small summary

Mathematical modeling is a process whereby a real world problem or situation is described in mathematical language. Research and share a real world problem, situation, phenomenon, or event that can be modeled using a linear equation or inequality. Post the mathematical model describing your application if available.

1) Construct a 2 × 2 examples to prove the following statements:

(a) λ ∈ σ(A) and µ ∈ σ(B) 6=⇒ λ + µ ∈ σ(A + B).

(b) λ ∈ σ(A) and µ ∈ σ(B) 6=⇒ λµ ∈ σ(AB).

how to approach algebra type easy moderate problem and show some tips tecniques and shortcuts formula ..i would give positive response if you help me a little.... thankyou

Question: A set of data has a normal distribution with a mean of 53 and a standard deviation of 6. Find the...

A set of data has a normal distribution with a mean of 53 and a standard deviation of 6. Find the percent of data within each interval...

a. from 47 to 65

b. from 41 to 47

c. greater than 59

d. less than 65

Please show all steps.

Note: a - d are NOT potential answers, they are subquestions. I would like to know the percent of data within each interval in a, b, c, and d.

Please show all the work, including any calculator steps taken. Please do not say "use calculator" - specify what exactly to do with it if you do use it.

. Compare these odds to the odds of being in a car accident, plane crash, struck by lightning, or hit by a meterorite. type please

You want to be able to withdraw $40,000 from your account each year for 15 years after you retire. If you expect to retire in 25 years and your account earns 7.6% interest while saving for retirement and 6.9% interest while retired:
Round your answers to the nearest cent as needed.

a) How much will you need to have when you retire?
$

b) How much will you need to deposit each month until retirement to achieve your retirement goals?
$

c) How much did you deposit into you retirement account?
$

d) How much did you receive in payments during retirement?
$

e) How much of the money you received was interest

Solve the minimum problem using the duality principle.

Minimize subject to

z = 3x + 4y

x + y ≥ 3

2x + y ≥ 4

x ≥ 0, y ≥ 0

1) You wish to accumulate $100,000 through monthly payments of $100. If you can earn interest at an annual rate of 4% compounded monthly, how long (to the nearest year) will it take to accomplish your goal?
________  yr

2)Alonzo plans to retire as soon as he has accumulated $250,000 through quarterly payments of $3,500. If Alonzo invests this money at 5.4% interest, compounded quarterly, how long (to the nearest year) until can he retire?
_____ year

3) Your pension plan is an annuity with a guaranteed return of 4% per year (compounded quarterly). You can afford to put $1,700 per quarter into the fund, and you will work for 40 years before retiring. After you retire, you will be paid a quarterly pension based on a 25-year payout. How much will you receive each quarter? (Round your answer to the nearest cent.)
$ _______

4). You wish to accumulate $100,000 through monthly payments of $100. If you can earn interest at an annual rate of 4% compounded monthly, how long (to the nearest year) will it take to accomplish your goal?
_________ yr

5) Alonzo plans to retire as soon as he has accumulated $250,000 through quarterly payments of $3,500. If Alonzo invests this money at 5.4% interest, compounded quarterly, how long (to the nearest year) until can he retire?
________ yr

PLEASE help ! GBU

The annual interest rate on a credit card is 18% with interest compounded monthly. If a payment of $100 is made at the end of each month, how many months will it take to pay off an unpaid balance of $2,583.56 (assuming no additional purchases are made)?