Show that the set of complex numbers ℂ= {x+iy|x and y are real, i²=-1} is a vector space. Verify each of the 10 axioms.

5.52. Potency of a drug. Eli Lilly and Company has developed three methods (G, R1, and R2) for esti- mating the shelf life of its drug products based on potency. One way to compare the three methods is to build a regression model for the dependent variable, estimated shelf life y (as a percentage of true shelf life), with potency of the drug (x1) as a quantitative predictor and method as a qualitative predictor.

(a) Write a first-order, main effects model for E(y) as a function of potency (x1) and method. SAS Output for Exercise 5.51

(b) Interpret the β coefficients of the model, part a.

(c) Write a first-order model for E(y) that will allow the slopes to differ for the three methods.

(d) Refer to part c. For each method, write the slope of the y – x1 line in terms of the β’s.

brief history on Camassa-Holm equation for fun!

find an alternative 
definition of the degree of a vertex of a graph. 
please be detailed as possible thank you

Question 1:

There are 180 primary schools in a country area having an average of 30 or more people under the age of 21 per class. A sample of 30 schools drawn using systematic sampling with an interval of k = 6.

1. Estimate total number of students.
2. Estimate average number of students per farm.
3. The variance of the sample mean of students per farm.
4. 95% confidence interval for the total number of students.

what combinations using only 0, 1,2, then transform that number to base 3, can give 7 when doing modulus division 9. Need a number x in base 10 that when transformed in base 3, where x%9 = 7

Solve the given initial value problem by undetermined coefficients (annihilator approach).

y'' − 4y' + 4y = e^4x + xe^−2x

y(0) = 1

y'(0) = −1

Lab Assignment

Part B - Recurrence Intervals

Data from the chart below was collected at the USGS site and includes the 20 largest discharge events for Sweetwater Creek at station 02337000 from January 1, 2008 through May 1, 2015, excluding the dramatic 2009 flood (we will learn more about that later). In order to create a flood-frequency graph, you must first calculate the recurrence interval (one is calculated below as an example). A recurrence interval refers to the average time period within which a given flood event will be equaled or exceeded once. To calculate it, first evaluate the rank of the flood, with a “1” going to the highest discharge event and a “20” going to the lowest discharge event. Calculate the recurrence interval using the following equation:

RI = (n+1) ÷ m

where, RI = Recurrence Interval (years)

n = number of years of records (in this case, 8)

General Ford produces cars in Los Angeles and Detroit and has a warehouse in Atlanta. The company supplies cars to customers in Houston and Tampa. The costs of shipping a car between various points are listed in the file P05_54.xlsx, where a blank means that a shipment is not allowed. Los Angeles can produce up to 1600 cars, and Detroit can produce up to 3200 cars. Houston must receive 1800 cars, and Tampa must receive 2900 cars. a. Determine how to minimize the cost of meeting demands in Houston and Tampa. b. Modify the answer to part a if no shipments through Atlanta are allowed.

total cost

What are the primary differences among the CF valuation model, asset-based valuation model, and multiples valuation model?

1. Show that if u is harmonic in a domain Ω, then also the derivatives of
u of any order are harmonic in Ω. (Hint: To get the result for any order
you may want to use induction).

Gabriella and Steve have adjusted gross incomes of ​$47 comma 200 and ​$32 comma 700​, respectively. Assume that each person takes one exemption and the standard deduction. Answer parts ​(a) through ​(c) below.

a. Calculate the tax owed by the couple if they delay their marriage until next year so they can each file a tax return at the single tax rate this year.

The couple owes ______

​(Simplify your answer. Round to the nearest dollar as​ needed.)

b. Calculate the tax owed by the couple if they marry before the end of the year and file a joint return.

The couple owes____________

​(Simplify your answer. Round to the nearest dollar as​ needed.)

c. Does the couple face a​ "marriage penalty" if they marry before the end of the​ year?

1. Extend your understanding of place value systems to another base. Imagine you wanted to package truffles into groups of powers of 6. Describe how the B6 Corporation would group quantities. How would B6 record numerals, count, and package large numbers of truffles?
2. The B4 Candy Company prepared the following package of truffles: 2321B4.
   a) How many truffles are being shipped?
   b) There are two 2s in this numeral. What do they represent? Why don’t they have the same value?
3. If you worked at the B6 Candy Corporation, how would you package 1 to 36 truffles? Write the numerals that show which boxes are needed for 1 to 36 truffles in the table below.

The following table lists a portion of Major League Baseball’s (MLB’s) leading pitchers, each pitcher’s salary (In $ millions), and earned run average (ERA) for 2008. Salary ERA J. Santana 17.0 2.28 C. Lee 3.0 2.39 ⋮ ⋮ ⋮ C. Hamels 0.2 3.00 Click here for the Excel Data File a-1. Estimate the model: Salary = β0 + β1ERA + ε. (Negative values should be indicated by a minus sign. Enter your answers, in millions, rounded to 2 decimal places.) Salaryˆ= + ERA a-2. Interpret the coefficient of ERA. A one-unit increase in ERA, predicted salary decreases by $3.20 million. A one-unit increase in ERA, predicted salary increases by $3.20 million. A one-unit increase in ERA, predicted salary decreases by $11.92 million. A one-unit increase in ERA, predicted salary increases by $11.92 million. b. Use the estimated model to predict salary for each player, given his ERA. For example, use the sample regression equation to predict the salary for J. Santana with ERA = 2.28. (Round coefficient estimates to at least 4 decimal places and final answers, in millions, to 2 decimal places.) c. Derive the corresponding residuals. (Negative values should be indicated by a minus sign. Round coefficient estimates to at least 4 decimal places and final answers, in millions, to 2 decimal places.)