Developed a partial worksheet, but you need to enter the formulas to calculate the regular pay, overtime pay, gross pay, taxable pay, withholding tax, FICA, and net pay. Include total pay columns and calculate some basic statistics.

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Metropolitan_Zoo_Gift_Shop_Weekly_Payroll

Project Description:

As manager of the gift shop at the Metropolitan Zoo, you are responsible for managing the weekly payroll. Your assistant developed a partial worksheet, but you need to enter the formulas to calculate the regular pay, overtime pay, gross pay, taxable pay, withholding tax, FICA, and net pay. In addition, you want to include total pay columns and calculate some basic statistics. As you construct formulas, make sure you use absolute and relative cell references correctly in formulas.

Use Goal Seek to determine an estimate of the total finished square footage they can afford. Provide more flexibility in their decision-making, you will create a data table listing various finished square footages and their effects on the base house cost and total cost. Create another data table showing combinations of square footages and lot prices to identify total costs.

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Housing Cost

 Project Description:

Your friends, Elijah and Valerie Foglesong, want to build their dream house. They identified tentative costs, but they cannot afford the $414,717 estimated cost. You will use Goal Seek to determine an estimate of the total finished square footage they can afford. To help provide more flexibility in their decision-making, you will create a data table listing various finished square footages and their effects on the base house cost and total cost. Finally, you will create another data table showing combinations of square footages and lot prices to identify total costs.

Convert your mpg into gallons per 100 miles driven for both highway and city. Cells have been created (B7 & B8) for the number of highway and city miles you drive each year. Compute how many gallons of gas each car will use for the year. 

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Math 154 Cars Project

(10 pts) You are buying a car and wish to do a cost/benefit analysis on buying a more expensive Toyota Prius, which gets better mileage, or a cheaper Ford Focus.  Research the price of these two vehicles (2020 standard model) and put their price in B2 and C2.  Find the MPG Highway and City for both vehicles and put that in B4,B5 and C4,C5.  Cite the website(s) you used here:                                            

a.) (20 pts)  Convert your mpg into gallons per 100 miles driven for both highway and city.

b.) (15 pts)   Cells have been created (B7 & B8) for the number of highway and city miles you drive each year. Compute how many gallons of gas each car will use for the year.

c.) (15 pts)   Add the current cost of regular gas (in our area/Fredericksburg) in B9, and with that price per gallon of gas, compute the total cost of gas for each car.

d.) (20 pts)   In the given cells compute how much more you spend on gas each year for Focus versus Prius, and compute how much more the Prius costs initially versus the Focus. (Round to 2 decimals)

e.) (15pts)  Finally determine how long it will take the gas savings per year to make up for the extra cost of the Prius. (Round to 1 decimal)

f.) (5 pts)  If the cost of gas goes up will it take more or less time to recoup the extra cost of the Prius?  Answer should be more or less.

Calculate the slope of the trend line. Choose a “calories from fat” value that is not in your collected data set and that is at least 10 fat calories away from any collected value. Use the equation calculated in step V to predict the number of fat grams in an item having that number of fat calories.

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Project: Data Analysis

Do you ever think about the number of calories in your favorite foods? Maybe ice cream is better for you than a hamburger. One way to find out would be to figure out how many calories and grams of saturated fat are in both foods. Typically, foods have nutritional information like this on the packaging. Or if you eat out, many fast food places will provide this information. Once you have collected the data, you can begin to analyze it.

OBJECTIVES

Collect, organize, and analyze data.
Make predictions based on data.
According to the U.S. Food and Drug Administration, 30% of daily calories should come from fats and only 10% from saturated fats. Based on a 2,000-calorie-a-day intake, this translates to about 600 calories from fat and 20 grams of saturated fat.

By knowing the number of fat calories in a fast food item, can you predict the number of grams of saturated fat?

Your task:

I. Collect data from several fast food chains on the number of fat calories and grams of saturated fat in menu items. Record at least 12 ordered pairs of (fat calories, grams of saturated fat). Organize your data in a table.

II. Make a scatter plot of the data on graph paper. Be sure to label the axes and use an appropriate title for the graph.
You may wish to use a graphing calculator, spread sheet, or other technology resource (such as the graphing utility link below) to aid you in graphing.

Create a Graph

III. Draw a trend line for the scatter plot. Use the following scatter plot of the ordered pairs (fat grams, total calories) as an example.

IV. Calculate the slope of the trend line. (Choose two points on the line and find vertical change over horizontal change.)

Note: Graphing calculators and spread sheets have features with which to draw trend lines and determine the equation. You may choose to use one of these options. If you use technology, indicate what steps were taken to arrive at your equation.

V. Using the slope and y-intercept, write the equation of the trend line ( y = mx + b).

VI. Choose a “calories from fat” value that is not in your collected data set and that is at least 10 fat calories away from any collected value. Use the equation calculated in step V to predict the number of fat grams in an item having that number of fat calories. Be sure to show your work.

VII. Search for an item in a fast food menu having the same number of fat calories as the one you chose above. (If you cannot find the exact value, get as close as you can.) Compare the calculated value from step VI to this actual value. Explain why (or why not) you would have expected your prediction (calculated value) to be close to the actual value.

Given the length of two segments, a and b, construct a line segment, x, whose length is the geometric mean between segments a and b.

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GEOMETRIC MEAN

In this assessment, you will be given the length of two segments, a and b. Your task will be to construct a line segment, x, whose length is the geometric mean between segments a and b.

Written instructions for constructing a segment whose length is the geometric mean between the lengths of the given segments

Constructing: The Geometric Mean

You have learned how to construct a geometric mean with a compass and a straight edge- now we are going to put that knowledge into practice. For this example, we will utilize those techniques to construct a segment with a length of the square root of 6, when we are given a segment labeled PQ whose length is 6.

Recall that in a geometric mean problem, the means of the proportion must be the same. If we cross-multiply, we get x-squared equals a times b and x equals the square root of a b.

[a over x = x over b
x squared = a b
x = square root of a b]

We know that we are looking for a segment that has the square root of 6 as its length. We can substitute the 6 into the last equation to get x equals the square root of 6. Squaring both sides gives us x-squared equals 6. Putting this information back into proportion form gives us 6 over x equals x over 1. Notice that we are not using 2 times 3 because the length of segment PQ is 6.

[x = square root of 6, x squared = 6, 1 over x = x over 6]

To make the construction we need to add the lengths of the extremes to have a single segment that is 7 units long and label it P R. Next, we will construct the perpendicular bisector of segment P R and use the point of intersection as the middle of our circle. Now, place the point of the compass on the intersection of our perpendicular and the segment P R. Extend the compass to either points P or R and draw the circle.

[Line P R. Point Q is on the line, and is 1 away from R. A circle is drawn intersecting points P and R.]

Lastly, we create a perpendicular at point Q and label the intersection with the circle S. The length of this perpendicular is the square root of 6. If we overlay the triangle P Q S, it is easy to see that the segment Q S is the geometric mean.

Come up with a real-life situation that models each of the four types of inequalities listed above. Provide a written description of the situation. Express the situation using the appropriate inequality and the correct units.

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Discussion 2

Review the assigned reading to prepare for this discussion.

Linear inequalities come in one of the following basic forms:
a < x < b
x < b
x > a
x < a or x > b

Note: The “<” (less than) can be replaced with “≤” (equal to or less than), and “>” (greater than) can be replaced with “≥” (equal to or less than) in any of these cases, depending on the context of the problem or situation.

On a daily basis, you are likely to come across situations in which inequalities are alluded to (e.g. “less than”, “more”, “at least”, or “between”) without realizing the connection to math.

Example:
Perhaps you ordered furniture from a local department store and were given a delivery time window between 10 am and 2 pm on a certain day. This situation can be modeled using one of the four inequalities listed above. Additionally, the situation can be modeled graphically and with interval notation, as shown below.

Description: The furniture I ordered will be delivered between 10 am and 2 pm.
Inequality: 10am ≤ x ≤ 2pm
Interval notation: [10:00am, 2:00pm]
Graph:

Inequality Graph with inequality 10am ≤ x ≤ 2pm and interval notation 10:00am, 2:00pm

Respond
Come up with a real-life situation that models each of the four types of inequalities listed above.
Provide a written description of the situation.
Express the situation using the appropriate inequality and the correct units (time, money, weight, etc), if applicable.
Express the situation using interval notation.

Is there a title that explains what the graph is displaying? Are numbers on the axis spaced out proportionally or have they been varied to create a dramatic impression? Is the graph too loud? Does it have too many components that it distracts from content?

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Misleading Graphs

Initial Post Instructions

After exploring different types of graphs this week, it is unfortunate to learn that there are sometimes misleading graphs used in the news, politics, medicine, etc. in order to sway a decision or belief. Some items to watch out for in graphs are—

Is there a title that explains what the graph is displaying?
Are numbers on the axis spaced out proportionally or have they been varied to create a dramatic impression?
Is the graph too loud? Does it have too many components that it distracts from content?
Are there sources cited to know where the data came from?
Use the internet to find a misleading graph. Key Terms to Search: Misleading Graphs

Provide a screenshot of the graph
Cite the Source
Explain why the graph is misleading
Analysis

Explain how you would fix the graph so it is not misleading.
Explain why the creator of the misleading graph would want to create the graph in the first place.

For y = 3x + 1, where does the line cross the y axis? For y = 3x + 1, plotting a point when x is 1 yields what y? What does the equation y = 3 look like when graphed?

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1)For y = 3x + 1, where does the line cross the y axis?

0

1

3

2)For y = 3x + 1, plotting a point when x is 1 yields what y?

3

4

3)For y = 3x + 1, the y-intercept is 1, so a point can be drawn at x = 0 and y = 1, namely up 1 on the y axis. A second point can be drawn by going to the right 1 and going up .

1

3

4)For y = -2x + 3, what is the slope?

-2

2

3

5)

What does the equation y = 3 look like when graphed?

A vertical line

A horizontal line

What was the equation for the total cost of the with-phone contract?Shay chose to plot points for x = 10 and x = 20 because those values were round numbers and so a bit easier to calculate and draw. For the no-phone contract, what did Shay determine as the y value when x was 10?

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PARTICIPATION ACTIVITY

2.4.2: Comparing cell phone plans.

1) What was the equation for the total cost of the with-phone contract?

2) Shay chose to plot points for x = 10 and x = 20 because those values were round numbers and so a bit easier to calculate and draw. For the no-phone contract, what did Shay determine as the y value when x was 10?

3) The graph of both contracts shows the with-phone contract to be how much cheaper at the start, when months is 0?

4)The breakeven point, where the no-phone contract’s total cost becomes cheaper, is at how many months?

5)The graphs not only show the breakeven point (15 months), but give a person a quick way to see the cost difference for any number of months. At 24 months, a person might visually see the blue line at about 1200 and the purple line at about 1000. What is the overall savings for the no-phone contract after 24 months?

In an organized table, record your 25 or more observed numbers in order, state where you observed that number, and classify it as an integer, a rational number that is not an integer, or a real number that is not a rational number. Write a paragraph that explains the importance of each of those three number sets. Your paragraph should explain why each number set is used, and its limitations that require the use of another set.

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Principals of math

Throughout this course, you explored various mathematical topics, investigated their importance, and learned to work with them. In this culminating assignment, you will complete four (4) tasks that assess your expertise in the course material.

Task 1: Principles of Mathematics
Consider the number sets integers, rational numbers, and real numbers. In one day, record at least 25 different numbers that you encounter in your everyday life. Your observations must include at least one of each set: integers, rational numbers that are not integers, and real numbers that are not rational numbers.

Part A: in an organized table, record your 25 or more observed numbers in order, state where you observed that number, and classify it as an integer, a rational number that is not an integer, or a real number that is not a rational number.

Part B: Write a paragraph that explains the importance of each of those three number sets. Your paragraph should explain why each number set is used, and its limitations that require the use of another set.

Part C: Consider a person from a culture that counts in base-6. Assume that they use the number symbols 0: 17 2, 3, 4, and 5. Write a paragraph to them that explains our base-10 system.