Category: Mathematics

Minimum-cost staffing plan for PharmaPlus

Posted on | by Kelvin

PharmaPlus operates a chain of 30 pharmacies. The pharmacies are staffed by licensed pharmacists and pharmacy technicians. The company currently employs 85 full-time-equivalent pharmacists (combination of full time and part time) and 175 full-time-equivalent technicians. Each spring management reviews current staffing levels and makes hiring plans for the year. A recent forecast of the prescription load for the next year shows that at least 250 full-time-equivalent employees (pharmacists and technicians) will be required to staff the pharmacies. The personnel department expects 10 pharmacists and 30 technicians to leave over the next year. To accommodate the expected attrition and prepare for future growth, management states that at least 15 new pharmacists must be hired. In addition, PharmaPlus’s new service quality guidelines specify no more than two technicians per licensed pharmacist. The average salary for licensed pharmacists is $40 per hour and the average salary for technicians is $10 per hour.
a. Determine a minimum-cost staffing plan for PharmaPlus. How many pharmacists and technicians are needed?
Let P = number of full-time equivalent pharmacists
T = number of full-time equivalent technicians
b. Given current staffing levels and expected attrition, how many new hire (if any)must be made to reach the level of recommended in part (a)? What would be the impact on the payroll?

 

The Effectiveness of Collaboration in a Mastermind Group: A Reflection

Posted on | by Kelvin

 

What OD skills made this collaboration effective? What do you see as the pros and cons to a Mastermind group?
If you have never participated in a Mastermind session before, the experience was likely both helpful and challenging. You may have received beneficial advice as well as some candid critiques. This is precisely the goal of the Mastermind model.
In this weeks Discussion, you review and reflect on your Mastermind group interactions and evaluate the efficacy of this process.
The mastermind group is our current group we will be doing it over the lack of recycling centers around and how this problem is not easy to fix in that most places are over an hour away to drive to which makes it an unreasonable request or action do recycle more even if you wanted to.

Direct Proof: Every odd integer is a difference of two squares

Posted on | by Kelvin

For the following construct a proof for the statements provided. If the statement is false, give a counter example. Unless the question explicitly states a proof technique, feel free to prove by any established means.
1. Using a direct proof, prove the following statement.
Every odd integer is a difference of two squares. (Ex 42 32 = 7)
2. Suppose a Z. If a2 is not divisible by 4, then a is odd.
3. The number log2(3) is rational.
4. If ab is odd, then a3 +b3 is even.
5. Let A and B be sets. Show A B B A = A.
6. IfXAB,thenXAorXB.
7. Prove that 9 | (43n + 8) for every integer n 0.
n
8. Prove for every positive integer n, X k2k = (n 1)2n+1 + 2
k=1
1 1 1 1 1 1 1
9. IfnN,then 12 14 18 116 12n 4+2n+1
(Note we can write this using a product formula: notation. Similar to sigma notation for sums.

 

The Correlation Between Height and 3-Point Accuracy in Miami Heat Players

Posted on | by Kelvin

Two Miami Heat basketball fans are arguing about whether taller players are more skilled in basketball or whether
shorter players have an advantage. One friend thinks that taller players are actually better and that they’re more likely
to make 3 pointers. They decide to look at a correlation to test this out. They look specifically at the correlation
between player’s height (in inches) and the percentage of 3pointers (calculated by the number of 3 point shots made
divided by the number of shots attempted–with a higher score indicating more 3 point shots made).
MIAMI HEAT PLAYER NAME 3 pointer % Height (in inches)
Jimmy Butler 35 79
Bam Adebayo 8.3 81
Tyler Herro 37.8 77
Max Strus 35 77
Kyle Lowry 34.5 72
Victor Oladipo 33 76
Caleb Martin 35.6 77
Gabe Vincent 33.4 74
Kevin Love 29.7 80
Cody Zeller 0 83
Duncan Robinson 32.8 79
Dewayne Dedmon 29.7 82
Nikola Jovic 22.9 82
Jamal Cain 35 78
Omer Yurtseven 42.9 77
Haywood Highsmith 33.9 83
Udonis Haslem 33.3 79
Jamaree Bouyea 40 74
Orlando Robinson 0 82
Dru Smith 16.7 74
Question 1
Now it’s time to calculate the correlation coefficient (Don’t panic! It’s not so bad!). Here is the formula to help you out! If you’re struggling with this, be sure to read over the PowerPoint from this week to help you figure out which values should go where. There is a really helpful table in that PowerPoint that you should use to organize your data. Type your answer in the box below. Round to only three decimal places!
Question 2
Let’s check to make sure you got the steps right for your calculation of r in question 3. In the formula you used to calculate r , what was the value of (∑X)^2
Question 3
Let’s check to make sure you got the steps right for your calculation of rxy in question 3. In the formula you used to calculate rxy,what was the value of ∑XY? Round your answer to one decimal place
Question 4
Let’s check to make sure you got the steps right for your calculation of rxy in question 3. In the formula you used to calculate rxy, what was the value of ∑X∑Y?
Question 5
What does this correlation coefficient represent (in other words, how can you interpret this correlation coefficient)?
A causal relationship between height and 3 pointer accuracy.
No meaningful correlation between height and 3 pointer accuracy.
A strong positive correlation between height and 3 pointer accuracy.`
A strong negative correlation between height and 3 pointer accuracy.
A weak positive correlation between between height and 3 pointer accuracy.
A moderate negative correlation between height and 3 pointer accuracy.
A weak negative correlation between height and 3 pointer accuracy.
A moderate positive correlation between height and 3 pointer accuracy.
Question 6
Interpret this correlation coefficient. Explain what this means. Which friend was right? Do taller players appear to be more accurate in their 3 pointers than shorter players? Why or why not?
Question 7
Come up with a variable that you think might be POSITIVELY correlated with a player’s 3 pointer accuracy. Explain this correlation (what does it mean that the two variables are positively correlated? and why do you believe it is a positive correlation?)

 

 

The Remarkable Element with a Long Half-Life: Technetium-99

Posted on | by Kelvin

The Periodic Table of Elements arranges all chemicals in an informative array. This listing of elements make up all of the materials and compounds that are used in daily life. Each element in the Periodic Table has a unique history, properties, and uses. One unique aspect of each element is its half-life. Defined as the amount of time for the quantity of an element to reduce by %, the half life is an imporant feature of all elements.

1. In the core project for MATH 1314, research .\ and prepare a report on a chosen element from the periodic table of elements having a half-life greater than 1 year. Prepare a 300 word (minimum) report including where your element is found in nature as well as how your element is utililized in your chosen field of study. Include citations.

The Contributions of Isaac Newton to Modern Day Mathematics

Posted on | by Kelvin

 

Write a paper on a famous mathematician and there contributes to todays society

Objective:
• Research a known historical mathematician (Examples: Euler, Newton, Leibniz, Galois, Lorentz)
• Discover the mathematician contributions to modern day mathematics (30pts)
• Explain how this mathematics may have influenced modern day life or how it has effected historical events in the world
• Discover the importance of mathematics

 

The Calculation of Pension for Contributors

Posted on | by Kelvin

 

Q1/ A contributor having a contribution period of 120 months, started in 01/01/1416 H. and left employment on 30/12/1425 II. He reached the age of 60 years. he has 3 dependent and the average salary of his service in the last two years is 10,000 SR What is the amount of his pension? The answer:
Q2i A contributor having a contribution period of 120 months employment on 30/12/1440 11. He reached the age of 60 years. service in the last two years is 7,000 SR What is the amount of The answer:
Q3/ A contributor having a contribution period of 120 months. employment on 30/12/1425 H. He reached the age of 60 years, avenge salary of his service in the last two years is 10.000 SR The answer:
started in 01/01/1431 H. and icji and the average salary of his his pension?
started in 01/01/1416 H. and lsa he has no dependent and the What is the amount of his pension
Q4/ A contributor having a contribution period of 120 months, HEW in 01/01/1417 H. and kil employment on 30/12/1426 H. He reached the age of 60 years, he has 1 dependent and the avenge salary of his service in the last two years is 10,000 SR What is the amount of his pension The answer:
Q5/ A contributor having a contribution period of 120 months, .cursedt in 01/01/1418 H. and kft employment on 30/12/1427 H. He reached the age of 60 years, he has 3 dependent and the average salary of his service in the last two years is 10,000 SR What is the amount of his pension The answer: