Question 1. A soil management specialist was studying the relationship between the average temperature (in ºC) and the yield in bushels per acre for a certain crop. The data is given in Table 1 below.

Table 1

1. Construct a scatter a scatter diagram for the paired data.
2. As temperature increases, does yield appear to increase, decrease, or remain the same?
3. Compute the coefficient of correlation, and interpret it.
4. Compute the coefficient of determination and interpret it.

The “standard” bagel has always been the one obtained by rotating the circle of radius 3/4 inch centered at (3/4 , 0) around the line x = −1.

Recently, a Californian chef created a bagel with the same circle but rotated around the line x = −2.

(a) Physically, what’s the difference between the two bagels?

(b) What are the volumes of the standard and Californian bagels?

Given is a population of wolves (W) and rabbits (R). R[t+1] = R[t]+ g*R[t] * (1 – R[t]/K) - sR[t]W[t] W[t+1] = (1-u)W[t] + vR[t]W[t] Where the carrying capacity of rabbits is 1 million. The growth rate of rabbits is 10% a year and s is equal to 0.00001, v is 0.0000001, and u is equal to 0.01. How many wolves and how many rabbits exist in the equilibrium?

Show that the worst-case number of entries computed by the refined dynamic programming algorithm for the 0-1 Knapsack problem is in Ω(2n). Do this by considering the instance in which W = 2n −2 and wi = 2i−1 for 1 ≤ i ≤ n.

Please answer with clear explanations!!!

Excerpt From: Richard Neapolitan. “Foundations of Algorithms.”

5. Equations of the form y’ = P(x)*y^2 + Q(x)*y + R(x) are called Riccati equations.

i) If we know a solution y = φ(x) of this equation, then any other solution

can be written in the form y(x) = φ(x)+ 1/v(x), where v(x) is an unknown

function which satisfies a certain linear equation. Using the fact that

φ and y both solve the above Riccati equation, find the differential

equation that v satisfies.

ii) Consider the equation 3y’ + y^2 +2/(x^2) = 0. Find one solution of this equation by inspection.

iii) Use the method of part(i) to find the general solution of the equation

in (ii).

Given the following utility matrix, representing the ratings, on a 1–5 star scale, of eight items, a through h, by three users A, B, and C:

After we normalize the matrix by subtracting from each nonblank entry the average value for its user, what is the cosine distance between users A and C ?

One particle travels along the path

p1(t) = <2.666 cos(6.405t + 5.149) + 4.430, 2.666 sin(6.405t + 5.149) − 3.610, 11.18t + 6.633>

and another along the path

p2(t) = <1.084t + 3.125, 3.096t − 5.332, −2.925t + 4.377>.

The paths intersect at two points, one of which is a collision. Find the point where the particles collide and the other point where the paths intersect.

Jennifer is the owner of a video game and entertainment software retail store. She is currently planning to retire in 30 years and wishes to withdraw $11,000/month for 20 years from her retirement account starting at that time. How much must she contribute each month for 30 years into a retirement account earning interest at the rate of 2%/year compounded monthly to meet her retirement goal? (Round your answer to the nearest cent.)

$________

Assignment 1 - IN PDF FORMAT Using R and Rstudio

Pick a database from: data()

Then preview the first 10 rows.

Print the number of rows and columns

- Print the names of the variables

If you have row names, print them - work with the values for a field in your dataset. You can do it by dataset[[xx]] operator with xx can be the index of the field or the nae of the field.

Now use dataset[xx] to get a slice of datframe instead of vector, e.g. df = mtcars[c(‘mpg’, ‘disp’)] - With two scalar arguments (rows,columns), the [] operator can select elements in the dataframe. Try this.

- Subset your data using rules similar to the lectures. For example part of the data that has a characteristics AND/OR another one, etc.

- Write a function that does an operation, for example averaging a property, on your dataset.

- Write a function that works on rows and adds a column to the dataset with the results for each row.

- Using the iris database, explain the following line of code:

data(iris) aggregate(iris["Petal.Length"], by = iris["Species"], FUN=median)

## Species Petal.Length

## 1 setosa 1.50

## 2 versicolor 4.35

## 3 virginica 5.55

For extra credit for my Differential Equation class, I have to come up with a real-world example of a system of linear differential equations (three) such as a population, spring, or circuit and solve it and then write a paper about it. I can write the paper no problem but I need help coming up the equation and then solving it, the equation should be roughly 8-11 steps.

For the example given to us, (WHICH WE CANNOT USE) the person put a resistor circuit into a system of linear equations and then defined ohms law as eq(1) I=V/R then stated the sum as eq(2) then put the ohms and resistors into wronskin determinant and solved for sq(3)&(4) and provided a figure for each or every other one which I should be able to come up with if you cannot.

I need help coming up with the idea and the first couple sets of equations, I can do the research, I just need an idea and an system of equations presented and solved

Expressions and Equations

Think about a scenario when you would use an expression and an equation in a real life application. Discuss each scenario and explain how to write the expression and equation. What is the difference between both of them?

Create two sample equations for your peers to solve.

Please give me an answer ASAP Something new that not already on the Chegg site.

a) Show that if A is a real, non-singular nxn matrix, then A.(A^T) is positive definite.

b) Let H be a real, symmetric nxn matrix. Show that H is positive definite if and only if its eigenvalues are positive.

How are Histograms and Pareto Charts in Excel created? Give an example using sample dataset.