1. You deposit $3000 each year into an account earning 7% interest compounded annually. How much will you have in the account in 25 years?

2. Suppose you want to have $600,000 for retirement in 25 years. Your account earns 7% interest.

a) How much would you need to deposit in the account each month?

b) How much interest will you earn?

3. You have $400,000 saved for retirement. Your account earns 7% interest. How much will you be able to pull out each month, if you want to be able to take withdrawals for 15 years?

I need mathematical modeling of cancer for PhD thesis. Preferably Colon cancer or Cervical cancer

I need a minimum of 500 words, do not answer one line answers!

1. Reflect on the concept of polynomial and rational functions.

2. What concepts (only the names) did you need to accommodate these concepts in your mind?

3. What are the simplest polynomial and rational function you can imagine?

4. In your day to day, is there any occurring fact that can be interpreted as polynomial and rational functions?

5. What strategy are you using to get the graph of polynomial and rational functions?

Please write it here and not on paper. Do not plagiarize the answers.  

Let X be a metric space and t: X to X be a map that preserves distances: d(t(x), t(y)) = d(x, y). Give an example in whicht is not bijective.

Could let t: x to x+1,x non-negative, but how does this mean t is not surjective?

Any help will be much appreciated!

For the following, A = attractiveness and B=time; same levels. Conduct a two-factor fixed effects ANOVA (alpha=.05).

A₁B₁: 10, 8, 7, 3

A₁ B₂: 15, 12, 21, 13

A₂ B₁: 13, 9, 18, 12

A₂B₂: 20, 22, 24, 25

A₃ B₁: 24, 29, 27, 25

A₃ B₂: 10, 12, 21, 14

A₄ B₁: 30, 26, 29, 28

A₄ B₂: 22, 20, 25, 15

Numerical Linear Algebra:

Please provide a correct detailed solution!!!

Suppose you have the following data: (0, 1.0000), (0.25, 1.2840), (0.50, 1.6487), (0.75, 2.1170) and (1.00, 2.7183) . Using MATLAB, find a polynomial P (x) of degree 2 that fits the data with the minimal approximation error. Calculate this error. Then sketch these discrete points and the graph of the polynomial P(x) in a figure using MATLAB.

3.93 Automobile Depreciation For a random sample of 20 automobile models, we record the value of the model as a new car and the value after the car has been purchased and driven 10 miles.⁴⁷ The difference between these two values is a measure of the depreciation on the car just by driving it off the lot. Depreciation values from our sample of 20 automobile models can be found in the dataset CarDepreciation.

1. Find the mean and standard deviation of the Depreciation amounts in CarDepreciation.
2. Use StatKey or other technology to create a bootstrap distribution of the sample mean of depreciations. Describe the shape, center, and spread of this distribution.
3. Use the standard error obtained in your bootstrap distribution to find and interpret a 95% confidence interval for the mean amount a new car depreciates by driving it off the lot.

Notes: Please solve using Rstudio. show all work, including Rstudio code. Also, You will need to make a bootstrap distribution in this one.

Thank you

2.5xˆ3=cos(x)+13.5 if your initail estimate is x0=1.1

Imagine that you buy a new computer system with independent components including a new desktop computer (with a CPU and a graphics card), new software, and a new monitor. You want to play games on the new system, but it runs games very slowly. You assume that the keyboard and mouse are not creating the problem; so, to figure out what is making the system run so slowly, you experiment with combinations of your old equipment with the new equipment. Here are your experiments and results:

Experiment 1: New computer, new software, and new monitor — and it runs slowly.
Experiment 2: New computer, new software, and old monitor — and it runs slowly.
Experiment 3: New computer, old software, and new monitor — and it runs fast.
Experiment 4: New computer, old software, and old monitor — and it runs fast.
Experiment 5: Old computer, new software, and new monitor — and it runs fast.
Experiment 6: Old computer, new software, and old monitor — and it slowly.
Experiment 7: Old computer, old software, and new monitor — and it runs fast.
Experiment 8: Old computer, old software, and old monitor — and it runs fast.

Based on this data, which experiment shows that the conjunction of the new software and the old monitor is NOT SUFFICIENT for the system to run slowly?

• A. Experiment 1
• B. Experiment 2
• C. Experiment 3
• D. Experiment 4
• E. Experiment 5
• F. Experiment 6
• G. Experiment 7
• H. Experiment 8
• I. None of these experiments

What differential equation is the one-dimensional potential equation? What is the form of the solution of the one-dimensional Dirichlet problem? The one-dimensional Neumann problem?

The instructions for the given integral have two​ parts, one for the trapezoidal rule and one for​ Simpson's rule. Complete the following parts.

Integral from 0 to pi ∫4sint dt

I. Using the trapezoidal rule complete the following.

a. Estimate the integral with n=4 steps and find an upper bound for AbsoluteValueET.

T=?

​(Simplify your answer. Round to four decimal places as​ needed.)

An upper bound for AbsoluteValueET is ?

​(Round to four decimal places as​ needed.)

b. Evaluate the integral directly and find ET.

Integral from 0 to pi ∫4sint dt =?

​(Type an integer or a​ decimal.)

AbsoluteValueET =?

​(Simplify your answer. Round to four decimal places as​ needed.)

c. Use the formula AbsoluteValueET​/(true value)) times ×100 to express AbsoluteValueET as a percentage of the​ integral's true value.

?​%

​(Round to one decimal place as​ needed.)

II. Using​ Simpson's rule complete the following.

a. Estimate the integral with n=4 steps and find an upper bound for AbsoluteValueES.

S=?

​(Simplify your answer. Round to four decimal places as​ needed.)

An upper bound for

AbsoluteValueES is ?

​(Round to four decimal places as​ needed.)

b. Evaluate the integral directly and find AbsoluteValueES.

Integral from 0 to pi 4 ∫4sint dt=?

​(Type an integer or a​ decimal.)

ES=?

​(Round to four decimal places as​ needed.)

c. Use the formula AbsoluteValueES​/(true value)) times ×100

to express AbsoluteValueES as a percentage of the​ integral's true value.

? ​%

​(Round to one decimal place as​ needed.)

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Enter your answer in each of the answer boxes.

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Using the formulas for geometric progression to prove the formulas of growing annuity and growing perpetuity

1. Suppose that New York fire department receives an average of 12 requests for fire engines each hour, and that these requests occur according to a Poisson process. Each request causes a fire engine to be unavailable for an average of 12 minutes. To have at least a 90% chance of being able to respond to a request, how many fire engines should the fire department have?

2. Two one-barber shop sit side by side in New York. Each shop can hold a maximum of 5 people, and any potential customer who finds a shop full will not wait for a haircut. Barber 1 charges $18 per haircut and takes an average of 20 minutes to complete a haircut. Barber 2 charges $13 per haircut and takes 15 minutes to complete a haircut. On average 12 potential customers arrive per hour at each barber shop. Of course, a potential customer become an actual customer only if he or she finds that the shop is not full. Assuming that inter-arrival times and haircut times are exponential, which barber will earn more money?

Determine a lower bound for the radius of convergence of series solutions about each given point x0 for the given differential equation.

(1 + x^3)y'' + 4xy' + 6xy = 0   

x0 = 0. x0 = 4

1. Prove that if the primal minimisation problem is unbounded then the dual maximisation

   problem is infeasible.