Quadratic Equations and Functions

Remember the form of a quadratic equation: ax2+bx+c

You will use: W=-.01×2+100x+c where (-.01×2+100x) represents the store’s variable costs and c is the store’s fixed costs.
So, W is the stores total monthly costs based on the number of items sold, x.
Think about what the variable and fixed costs might be for your fictitious storefront business – and be creative. Start by choosing a fixed cost, c, between $5,000 and $10,000, according to the following class chart:

If your last name starts with the letter Choose a fixed cost between
S-T $8600-$9200
Your monthly cost is then, W = -.01×2+100x+c.
Substitute the c value chosen in the previous step to complete your unique equation predicting your monthly costs.
Next, choose two values of x (number of items sold) between 100 and 200. Again, try to choose different values from classmates.
Plug these values into your model for W and evaluate the monthly business costs given that sales volume

 

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Quadratic Equations and Functions

Typing hint: Type x2 as x^2 (shift 6 on the keyboard will give ^)

1) Solve the following quadratic equation by factoring:

a) x 2 ? 6x ? 27 ? 0

b) Solve the quadratic equation 3×2 + 2x – 16 = 0 using the quadratic formula.

Read the information in the assignment list to learn more about how to type math symbols, such as the square root.

 

2) Use the graph of y = x2 + 4x – 5 to answer the following:

 

a) Without solving the equation or factoring, determine the solution(s) to the

equation,

x 2 ? 4x ? 5 ? 0 , using only the graph.

 

Explain how you obtained your answer(s) by looking at the graph in a brief sentence:

b) Does this function have a maximum or a minimum?
Explain how you obtained your answer by looking at the graph in a brief sentence::

c) What are the coordinates of the vertex in (x, y) form? Answer:

d) What is the equation of the line of symmetry for this parabola? Answer:

 

 

 

 

3) The profit function for Wannamaker Trophies is P(x) = -0.4×2 + fx – m, where f represents the design fee for a customer’s awards and m represents the monthly office rent. Also, P represents the monthly profit in dollars of the small business where x is the number of awards designed in that month.

a) If $80 is charged for a design fee, and the monthly studio rent is $1,600; write an equation for the profit, P, in terms of x.

 

 

 

b) How much is the profit when 50 award designs are sold in a month?

 

c) How many award designs must be sold in order to maximize the profit? Show
your work algebraically. Trial and error is not an appropriate method of solution –

 

d) What is the maximum profit?
4) Graph the equation on the graph by completing the table and plotting the points.
You may use Excel or another web-based graphing utility. a) y = x2 – 6x
Use the values of x provided in the table to find the y values.
x y
0
1
2
3
4
5
6

 

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a) Benchmark Assessment:Integrating Science and Mathematics

Topic  a) Benchmark Assessment:Integrating Science and Mathematics

 

 

a)    Benchmark Assessment:Integrating Science and Mathematics

i)    Create a unit of study integrating science and math content of fractions, decimals, and/or percents.

ii)    Ensure you have listed each of the science (NSES)) and math (NCTM) standards to include learning goals and objectives.

iii)    Create the unit of study to include the following:

(1)    clear-cut objectives that align to standards

(2)    relevantmaterials and resources

(3)    differentiation of instruction to address the diverse needs of students. Name the differentiation strategies for the specific diverse groups.

(4)    problem solving and inquiry strategies

(5)    the twelve science processes

(6)    concrete manipulatives to help develop science and fraction/decimal sense

(7)    informal and/or formal assessment that align with objectives

(8)    authentic, formative and/or summative assessments

(9)    allow for student reflection

iv)    Write a narrativeof 800 -1,000 wordsthat addresses the assignment criteria, gives specific examples from the unit of study, and state your rationale.

 

 

 

 

 

 

solving mathematics problems

Topic: MATH

explain all the rules needed to calculate fractions, (including how to change a fraction into percentage and vice versa) and

equations What are the main rules to know to resolve an equation?

exercice 1 (explain as much as you can how you get the result):
one hundred and six people were stopped in the street and the following information obtained: 62 were born in this country ,

50 were taller than 1.6m and 14 were left-handed.

If 3 people were taller than 1.6m, born n this country and left-handed, how many people were only one of these things?

what percentage of those born in this country were left-handed?

there are 3 people who are left-handed, born in England and taller than 1.6m, 2 people who are left-handed and taller than

1.6m. there are twice as many people who are just eft-handed as are left-handed and born in England. How many people are just

left-handed?

calculate and find x/Y:

3X +2Y=1285

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MATHEMATICS AND ECONOMICS

 TO DO a. Discuss the pros and cons of option 1, and prioritize your thoughts. What are the most positive aspects of this option, and what are the biggest drawbacks? b. Do the same for option 2. c. Which option do you think Sara should recommend to the board and why?  

Question 1 Answer

In order to expand a business, it is necessary for the owners to source for financial resources. Therefore the available resources that can be tapped are divided into two; acquisition of debt and obtaining equity finance. Debt financing will involve obtaining a loan which is repaid plus an interest while equity financing may involve selling a firm’s interests like floating of shares. If Merit decides to use JPMorgan Chase bank to borrow the $4billion in loan and an additional $2 billion, there are advantages and disadvantages accrued to it. The most positive aspect in debt financing is that, it does not temper with the ownership interests of the firm. Merit can remain private and independent. Besides, JPMorgan Chase bank will have no entitlement to future profits of the firm. The bank will only be entitled to repayment of the agreed –upon principal and interest of the loan. Moreover, the principal and interest obligation are normally constant, hence can be planned for except in an incidence where a variable rate has been used. There are no complications in obtaining debt financing since Merit is not expected to conform to various legal regulations or requirement. Merit will also not be required to send mails to a big number of investors and hold regular meetings in order to make certain decisions. Furthermore, Merit can use its tax returns to pay the interests hence reducing the cost of the debt.

However, the major drawback of this option is that debts must be repaid at some point. The numerous installments in interest paid may be too much for Merit; to an extent if it defaults there are grave repercussions which might render the firm bankrupt. Acquiring such a huge debt of $4billion and an additional $2billion of which it will be restricted for the firm is quite demanding. This also limits the growth of the firm as a result of servicing the loan. Besides, cash flows for making interest payment must be planned for which limits the use of the funds for other purposes. Merit might also face restrictions on some ventures that may be profitable but risky, which the bank might consider from the statements as a threat to their funds. In debt financing Merit will be required to pledge assets as collateral for the loan guaranteeing repayment of the loan.

Question 2 Answer

Under option 2 Merit is considering making an initial public offer by floating shares in the market. Through such measures, the company’s major benefit will be, it will not be required to repay the money, indeed it might recover through profits realized out of the investments. In case high profile investors venture into the shares, the firm will be guaranteed of higher business credibility. In most cases the investors will not demand their money to be paid back in an incidence of loss making, since they understand the riskiness involved in venturing into the business hence possibility of Merit running bankrupt.

The main drawbacks in such kind of financing are the dilution of ownership. The firm is no longer independent as it has to incorporate the decisions of investors through numerous meetings. This may be costly and tedious to the firm. As a matter of fact, Merit will be required to act in the interest of the shareholders hence needed to disclose various statements of finance to ascertain its performance of which Merit is not used to.

Question 3 Answer

Though the firm is not used to equity financing Sara should recommend it to the firm to avoid situations of running bankrupt. With debt financing the firm is not assured of making full repayment, of which JP Morgan and its affiliate banks might recall the debts to be paid fully before time. This might put the firm’s finances in a serious fix. Besides, the firm has already a good reputational background which implies floating an initial public offer will be more profitable and less restrictive. Therefore this will be the best decision of financing the expansion strategies. Though investors will want to participate in any stock Merit is offering, the end result will be far better of.

 

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Math Discussion

Discussion 1 – Words 125 Provide an example of at least five ordered pairs that do not model a function. The domain will be any five integers between 0 and 20. The range will be any five integers between -10 and 10. Your example must not be the same as those of other students or the textbook. Why does your example not model a function?
Discussion 2 –  Words 125 What similarities and differences do you see between functions and linear equations studied in Ch. 3 Are all linear equations functions? Is there an instance when a linear equation is not a function? Support your answer. Create an equation of a nonlinear function and provide two inputs for your classmates to evaluate. Provide answers………..

 

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Statistics

RESEARCH PROJECT

The format of the report:

Title Page (1 page)  Body of the report • Introduction/rationale (this will incorporate a reworking of the proposal including the database source) (1-2 pages)  • Abbreviated Literature Review of all three sources/background material on the problem being studied (Use APA style in-text citations) (1-2 pages)  • Graphical and Numerical Summaries (length will vary)  • Hypothesis Testing (1 page)  • Conclusion and Recommendations for further study (1-2 pages)  Reference page (3 literature sources and the database source needed using APA reference style) (1 page)  Appendices: Copies of the three articles from the literature review

The report needs to address the following:

Clearly identify the null and research hypotheses.

Identify the type of data being studied (e.g. ordinal)  Identify the population and the sample and discuss the method of sampling and why this method was chosen.

Discuss limitations resulting from the sampling method chosen or sample size available.  Identify in words what constitutes Type I and Type II errors for this problem.

Descriptive statistics with appropriate means of presentation.

Discussion of the statistical analysis used, why it is chosen, and what the results tell us.

Below are some Databases and Resources you can use (select one topic to complete the project)  1. Internet Statistics: Growth and Usage of the Web and the Internet: https://www.mit.edu/people/mkgray/net/  2. Consumer Price Index: https://stats.bls.gov/news.release/cpi.toc.htm  3. Employment Statistics: https://stats.bls.gov/news.release/empsit.t02.htm  4. Population Estimates For The U.S.: https://www.census.gov/population/estimates/nation/intfile2-1.txt………………

 

 

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