Name: Joy Bielenberg

1.  Radioactive decay:  Radioactive decay is determined by understanding and using formulas and calculus.  Although I thought of it last, when viewing a picture of Marie Curie, I chose to list radioactive decay first because it is important to all of us, not just to chemists and physicists.  The radioactive decay equation allows scientists to figure out how many radioactive atoms are left in a sample after any amount of time.  The speed of radioactive decay is proportional to the number of radioactive atoms in the sample.  Each type of radioactive atom is also represented by a decay constant representing the likelihood that any individual atom will decay at any given time.  Atoms that decay faster have larger decay constants. Since the decay rate changes as the number of atoms changes, simple multiplication won’t do.  Curie lost her life to the effects of the radiation she studied.  Humanity is also at risk unless proper storage of radioactive materials and waste are taken seriously.  

2.  Scale drawing:  Chemists who have the opportunity to design their own laboratory will likely make use of a scale drawing.  This will allow multiple approaches to the efficiency of layout for performance and for safety before any hammer is used.  The hood and exhaust must be placed in an area that allows for accessibility without being in the direct line of foot traffic.  Other safety concerns include how to store flammable, combustible, explosive and potentially hazardous materials.  A scale drawing is a place to start to determine how space can and should be allotted.

3.   Research Grant Writing:  Many chemists will be involved in research which may require funding through a grant.  Include an itemized list of each anticipated expense.  Think about laboratory space, specialized instruments, reagents, travel expenses and personnel wages.  The more specific you can be about budget items the more credibility.  Use the funding agencies regulations as a guide to what they will and will not cover.  

4.  Use of numerical information in the Periodic Table:  Each box on the table represents one element. Basic information about the element is included on every periodic table, including the following:

1.       The name of the element

2.       The one- or two-letter atomic symbol

3.       The atomic number, which is the number of protons in the atom's nucleus

4.    The atomic mass in atomic mass units (or AMUs, where one AMU is equal to 1/12th​ the mass of a carbon-12 atom, or about 1.66 x 10 to the minus 27 Kg). (Note: The terms atomic mass and atomic weight are often interchanged, but they do have distinct definitions. Atomic weight is calculated based on the atomic masses and relative abundances of all naturally occurring isotopes of an element.)

For a single atom of an element, the atomic weight would be a whole number, adding the number of protons, neutrons, and electrons together for the atom. However, the value given in the periodic table is an average of the mass of all isotopes of a given element. While the number of electrons does not contribute significant mass to an atom, isotopes have differing numbers of neutrons, which do affect mass.

 

5.  Making solutions:  The mole is useful in chemistry because it is defined such that the mass of Avogadro's number of particles (atoms or molecules) of a substance (the molar mass) is equal to the sum of the numerical values of the atomic masses of its constituent elements.

 

Calculate the molecular mass of CuSO4 · 5 H2O hydrated copper sulphate. Solution: Molecular mass of CuSO4 · 5 H2O = 64 + 32 + (16 × 4) + 5 × ((1 × 2) + 16) = 64 + 32 + 64 + 5 × (2 + 16) = 64 + 32 + 64 + 5 × 18 = 64 + 32 + 64 + 90 = 250

The following steps describe the procedure for making a solution of a specific molarity from a pure, solid substance. First, weigh out the correct mass of solute. Dissolve the solute in water, keeping the volume less than the desired total volume of solution. Dilute the solution to the desired total volume of solution.

6.  Graphing data:  Chemists frequently present the results of experiments.   Plotting data on a graph has the major advantage of making clear trends and patterns that are present, especially to audiences that do not understand mathematical notation.  In experiments there is a control variable that can be changed, and an observed variable that is measured as the control is changed.   All other quantities are kept constant.  When plotting a graph of data, the control variable is plotted along the horizontal (or x) axis and the observed variable along the vertical (or y) axis.  Use of technology can be extremely helpful in producing graphs.

7.  Scientific Notation:  Scientific notation enables simpler order-of-magnitude comparisons. A proton's mass is 0.0000000000000000000000000016726 kg.  If written as 1.6726×10−27 kg, it is easier to compare this mass with that of an electron. The order of magnitude of the ratio of the masses can be obtained by comparing the exponents instead of the more error-prone task of counting the leading zeros. In this case, −27 is larger than −31 and therefore the proton is roughly four orders of magnitude more massive.

8.  pH scale:  The pH scale measures how acidic or basic a substance is. The pH scale ranges from 0 to 14. A pH of 7 is neutral. A pH less than 7 is acidic. A pH greater than 7 is basic.

The pH scale is logarithmic and as a result, each whole pH value below 7 is ten times more acidic than the next higher value. For example, pH 4 is ten times more acidic than pH 5 and 100 times (10 times 10) more acidic than pH 6. The same holds true for pH values above 7, each of which is ten times more alkaline (another way to say basic) than the next lower whole value. For example, pH 10 is ten times more alkaline than pH 9 and 100 times (10 times 10) more alkaline than pH 8.  

 

9. Use of statistics:  Once the study is complete and the observations have been made and recorded the researchers need to analyze the data and draw their conclusions. Typically, data are analyzed using both descriptive and inferential statistics. Descriptive statistics are used to summarize the data and inferential statistics are used to generalize the results from the sample to the population. In turn, inferential statistics are used to make conclusions about whether or not a theory has been supported, refuted, or requires modification.

Statistical analysis 

10.  Conversion of measurements:  Even though, especially in science, the United States has made attempts to convert to the metric system of measurement, many measurements are recorded in the English system.  Scientists must be able to convert from one system to the other.   Conversations are also often needed within a system, say from grams to kilograms.

 

Measurements
Vets use math to track measurements related to animal care. For example, an increased heart size of a certain percentage can be an indication of heart disease, and tracking the measurement of a tumor's growth can help determine how quickly a cancer is progressing. Vets also measure waste and fluid output to assess various conditions. Using mathematical formulas, vets can accurately assess a wide range of health-related issues.

Medication
Appropriate medication dosing requires a keen attention to mathematical formulas. For example, the amount of pain medication or antibiotic given to a horse would be much greater than the dosage given to a kitten or a small dog. Ensuring that all numerical factors are taken into consideration is critical to ensuring that animals receive the appropriate method of care.

Statistics
Many people consider pets to be members of their family, and as such, they want to ensure their pets are happy, healthy, cared for and pain free. Vets may use numbers to help pet owners make the sometimes difficult decisions about medical care. This might involve explaining specific treatment outcomes in terms of percentages, so that pet owners can make informed decisions about treatment options.

Surgery
When an animal must be put under anesthesia for surgery, vets use math to assess the pre-op blood work and to determine the appropriate amount of anesthesia required to keep the animal sedated. Math may also be used to assess approaches to take in treating different medical conditions. For example, if a vet is repairing a torn ligament in a dog's leg, he needs to assess the dog's weight against the strength of various surgical materials so that he can determine the best approach to follow.

Weight Gain or Loss

Vets use math from the moment their patients enter their practice and are weighed. It’s important for a vet to track an animal's weight, as atypical weight gain or loss between examinations can indicate illness. Vets use weight to help track growth and development, as well as to determine body mass index. Changes in weight can also signal concern to general health such as malnourishment, obesity, swelling from infection or weight loss due to dehydration.

Billing
Many vets play an active role in running the business side of the veterinary practice. This can include using math for duties such as internal accounting, paying vendors, handling payroll, office bookkeeping, accounts payable and receivable -- and even tax preparation. As such, a knowledge of and understanding basic math can be an asset to ensuring smooth, accurate business operations.

When you have the cost of an item and its weight in pounds, you're ready to calculate its cost per pound. All you have to do is divide the total cost of the item by the number of pounds it weighs. So if your big bag of candy weighs 5 pounds and costs $13, you'd divide the cost by the weight in pounds: Calculating markup based on cost or selling price.

Markup is the difference between a product's selling price and cost as a percentage of the cost. For example, if a product sells for $125 and costs $100, the additional price increase is ($125 – $100) / $100) x 100 = 25%.

·       Calculating retail sales, gross margin and break-even points.

- Calculating retail sales:

1.    Calculate your cost price.

2.    Calculate your wholesale price, by adding up cost and profit margin.

3.    Calculate your RRP (Recommended Retail Price), by multiplying your wholesale price by 2 or 2.5

- To calculate gross margin subtract Cost of Goods Sold (COGS) from total revenue and dividing that number by total revenue (Gross Margin = (Total Revenue – Cost of Goods Sold)/Total Revenue). The formula to calculate gross margin as a percentage is Gross Margin = (Total Revenue – Cost of Goods Sold)/Total Revenue x 100.

- The components gross margin dollars, gross margin percent, and fixed costs are needed to calculate a break-even situation. In this example, we take ($18,750 − $10,000 = $8,750) / $20,000 = . 4375 or 43.8%. In this example, a retailer would have to generate $57,143 in product sales to break-even.

·       Planning and controlling price/stock reductions (markdowns).

For most companies 80% of their revenue comes from 20% of their stock. While these stats will vary to some degree, this is the theory behind ABC inventory analysis – a model that can be usedReduce inventory with stock classification to categorize your stock. Using ABC analysis, you can classify your inventory items into three groups based on their value to the business. A items are the most important in terms of the value they bring to your company, while C items are the least valuable. You can then prioritize the stock you carry, focusing on your A items to ensure better availability, rather than B and C. This could include reviewing their demand forecasts more frequently or interacting more regularly with suppliers to improve lead times.

·       Developing seasonal budgets.

- Create a baseline of basic expenses.

- Plan a year in advance.

- Don't get derailed from your budget during busy season.

- Track, track, track as much as you can.

- Take advantage of your slow season.

- Build more than one budget.

- Consider an alternative fiscal year.

·       Developing inventory plans (determining stock needs in proportion to forecasted sales).
 

1.    Demand forecast: using historical sales data, KPIs and variables like seasonality, promotions and market predicts to make data-driven forecasts. 

2.    Control costs: considering things like choosing the right suppliers, automating purchase order process, reducing cash tied up in slow-moving products etc.  –

3.    Store efficiently: storing the right amount of products in the right place to optimize your order fulfillment routes if you have multiple inventory locations 
 

·       How to Interpret Your Profit and Loss Statement • 

- Revenue. Revenue is often referred to as the “top line,” because it's the very first line you'll see on your profit and loss statement. ...

- Earnings Before Interest and Tax (EBIT) EBIT reflects the company's productive efficiency, before taking into consideration the tax burden or how the company is financed. ...

- Net Earnings.

·       Evaluating balance sheets (composed of assets, liabilities and equity).

- The balance sheet displays the company's total assets, and how these assets are financed, through either debt or equity. It can also be referred to as a statement of net worth, or a statement of financial position. The balance sheet is based on the fundamental equation: Assets = Liabilities + Equity.

·       Performing ratio analysis. (Comparing items on the balance sheet or income statement with other items on these statements. Reviewing the past year's ratios will pinpoint trends, which can be used to forecast the future.)

- Ratio analysis compares line-item data from a company's financial statements to reveal insights regarding profitability, liquidity, operational efficiency, and solvency. Ratio analysis can mark how a company is performing over time, while comparing a company to another within the same industry or sector. Quick Ratio: In order to calculate the quick ratio, take the Total Current Ratio for 2010 and subtract out Inventory. Divide the result by Total Current Liabilities. You will have: Quick Ratio = 642-393/543 = 0.46X. For 2011, the answer is 0.52X.

·       Forecasting cash flow budgets. (Projecting cash receipts and cash expenses for a period of time into the future, usually done on a monthly basis.)

- Subtract total cash outflows from total cash inflows to determine the net cash flow for each period. Add the net cash flows for each period to check that they equal the total net cash flow for the year.

 

For example: Chef Amber needs to cook enough mac-n-cheese for four people. Her recipe for mac-n-cheese has a portion size of eight people and calls for 1 ⅓ cup of cheddar. In order to cut the recipe in half, she must half the measurements:

1 ⅓ cup => ⅔ cup 

2. CONVERSION- Working with the same recipe, Chef Amber must be familiar with conversions, such as how many tablespoons go into a cup so that she can half the 1 ¾ milk required for the recipe. 

One cup is 16 tablespoons, therefore 12 tablespoons equal ¾ of a cup. If 28 tablespoons equal 1 ¾ cups, then half of that would be 14 tablespoons of milk for Chef Amber’s recipe.

We began the problem with cups and solved the problem with tablespoons. 

3. ESTIMATION- A really good Chef, roughly estimates how much of an ingredient is needed in a recipe. For them to be able to estimate, they must first maintain the basic knowledge of the measurements they are using. 

For example: Chef Amber is recreating a sauce from scratch that she had just thrown together the night before. As she takes a small taste, she realizes it is bitter. She sprinkles in some sugar and estimates that it’s about half a tablespoon. In order to know that, she would have to have the basic knowledge that 3 teaspoons equal 1 tablespoon. 

4. BASIC ADDITION FOR MONEY MAKING- When a chef creates their menu, they must take into account how much money it would cost them to create each dish so that they can charge just enough to profit from their food. 

For example: If the ingredients to create six dishes of lasagna cost them $30, then they would divide that by 6, which would be $5 so each dish cost them $5 to create. In order to profit off the dish, they choose to sell it for $12 a plate of lasagna.

5. BASIC COUNTING- When a chef is serving a restaurant full of people, they must count how many mouths there are to feed and estimate how many dishes to prepare. 

For example: Eight people are seated around a booth. Five of them order the chicken alfredo that creates ten portions per dish. In order to make sure the pasta is made fresh for every guest that orders it, the chef must half the recipe so there is enough for five hungry mouths.

6. TEMPERATURE AND TIME- Being able to tell time and know that sixty seconds equal a minute and sixty minutes equal one hour is necessary for every chef that touches an oven. 

For example: The recipe states that it will take an hour for Chef Amber’s brownies to bake at 350 degrees fahrenheit. If she wants to speed up the process a little bit, she could bake the brownies at 375 degrees fahrenheit for only forty-five minutes.

7. NUTRITIONAL DATA- Calculating the nutritional needs of the targeted guests in a restaurant allows for the chef to great a balanced meal, which will appeal to guest that want to indulge without going off the deep end. Nutritional stats are given in percentages, requiring the chef to be familiar with percentages, decimals, and fractions. 

8. WEIGHT AND MEASUREMENT- When using fresh ingredients, a chef must calculate the edible portion. First they trim away all the parts that they can’t use and then weigh the edible portion and divide it by AP weight, which will give them a percentage. 

For example: Formula (EP weight/AP weight = EP percentage)

Green beans -- 4 lbs. EP/5 lb. AP = 80% EP Yield

9. BASIC MULTIPLICATION AND ADDITION- When a chef is buying ingredients for their dishes, they must add together all of the measurements for each recipe, utilizing multiplication for the recipes that they will need more of. 

For example: Chef Amber is preparing to cook at least twenty portions of her most popular dish: ravioli, which requires 2 cups of mozzarella for eight portions. In order to make sure she prepares enough ingredients for twenty portions, she needs (2 x 3 = 6) 6 cups of mozzarella. 

10. BUDGETING- When purchasing food to prepare, a chef must calculate the prices of each ingredient and ensure that it does not go over their budget spending for that week. 

For example: Chef Amber’s budget for the week was $300 and she spent $250 alone on groceries, which means that she has $50 left for emergency store runs if she runs out of ingredients or forgot one.

1. Basic Arithmetic: There are several types of math that pilots use in their career and throughout their training including basic arithmetic, algebra, geometry, mental math and more. Basic arithmetic are the basics: addition, subtraction, multiplication, and division. A typical example of this for a pilot may be magnetic compass deviation and variation. So adjusting a compass for deviation may be as simple as adding 7 degrees to a heading of 172. 172 + 7 = 179.

 

2. Multiplication: Other typical calculations may be simple multiplication. For example, aviation gas weighs 6lbs per gallon. If you have a fuel tank of 15 gallons, when full how much weight are you carrying? 6 x 15 = 90lbs.

 

3. Algebra: This is when you need to solve for some unknown variable “x” based on other relationships and factors that you already know and have. For a pilot, this might be a simple formula like if you are travelling at 60 miles per hour, and your destination is 90 miles away, how long will it take you to get there? It would take 1hr 30min to your destination. 

Being able to do basic quick mental math in your heard is a great skill to have as a pilot. An example of this would be listing the three basic steps needed to plan your descent. Count down to yourself or co-pilot the steps needed. 

 

Step 1) 

Step 2) 

Step 3) 

Pilots must use geometry to calculate angles for taking off and landing. Planes have recommended angles for takeoff and landing. If a pilot descends or climbs at an angle that is too steep, it can lead to a tail strike, resulting in the plane’s tail hitting the runway. Speed, altitude and distance from the destination are factors pilots use when determining the angle of descent and the angle of climb.

 

Begin by determining how many pounds of fuel are needed.

-omit last 0, divide by 1/2,

-add both to get gallons needed.

Example:  you need 3000 lbs = 3000, omit last 0 = 300, add 1/2 of
that = 300+150 = 450 gallons needed. 

Weight calculations use the basic arithmetic skills of addition and subtraction. For an airplane to fly, it cannot weigh more than the amount of lift it generates. 

Example:  2,810 pound takeoff weight – 1,650 empty weight = 1,160 pounds useful load.  Useful load is the weight of people, baggage, useable fuel and drainable fuel on a flight. If the useful load is miscalculated it can cause problems for take off and cause poor performance of the airplane. 

 

Fuel calculations also use basic addition and subtraction skills. In this case, 13 gallons per hour x 2 hours = 26 gallons. This shows that the pilot would need 26 gallons for an in-flight of two hours. 

9. Crosswind component calculations: 
When you are landing or taking off, if there is a wind which is perpendicular to the runway, this is referred to as a crosswind. Too strong a crosswind can be dangerous, so it is important to calculate the crosswind and determine if it is safe to takeoff or land under the conditions. 

 

Crosswind component = Wind speed x cosine of angle between the wind and runway

10. Interpolation
Interpolation is the mathematical term for making an educated estimation based on surrounding data. This technique uses basic arithmetic skills as well as algebraic skills since the unknown variable you are solving for, “x,” must be determined based on its relationship to the data you do have.

Example: A straight line passes through two points of known value 9 and 10. You can estimate the point of unknown value because it appears to be midway between the other two points. The interpolated value of the middle point could be 9.5.