Bunker Hill Community College Math 093 Foundations Of Mathem

Bunker Hill Community College Mat 093 Foundations Of Mathematics1nam

Bunker Hill Community College Mat 093 Foundations Of Mathematics1nam

Provide solutions to the following math and reasoning questions based on the provided scenarios and data. Show all work clearly and organize your answers with proper explanations where appropriate. The questions involve basic statistics, geometry, proportions, percentage calculations, and numerical reasoning applied to real-life situations, including airline passenger estimates, land subdivision, snowfall averages, painting calculations, renewable energy output, map scales, discounts, cost comparisons, and loan interest. Additionally, analyze preferences in car color choices, convert units for recipes, calculate area and volume for construction materials, and interpret survey data. A bonus question involves unit conversion involving acres and square miles. Furthermore, improve the clarity and professionalism of a given informal email by removing redundant language and unnecessary phrases. All responses should be comprehensive, accurate, and demonstrate critical thinking and comprehension of mathematical applications in everyday contexts.

Paper For Above instruction

Question 1: Green Way Airlines expects 4.2% of its customers to be “no-shows” when they sell 260 seats. To estimate the expected number of no-shows, multiply 260 by 0.042:

Expected no-shows = 260 × 0.042 = 10.92 ≈ 11 people.

Since the airplane can hold 254 passengers, determine if all passengers who show up can be accommodated. The expected number of passengers who show up is 260 - 11 = 249. Since 249

Question 2: JK Builders has 35 acres of land, gives 1.75 acres to the city, leaving 35 - 1.75 = 33.25 acres. The remaining land is subdivided into lots of 0.875 acres each. To find the number of lots:

Number of lots = 33.25 ÷ 0.875 = 38 lots.

Question 3: Compute mean and median snowfall amounts for Burlington, Vermont:

  • Mean: (6.6 + 18.1 + 18.8 + 16.8 + 12.4) / 5 = 72.7 / 5 = 14.54 inches.
  • Median: Arrange data in order: 6.6, 12.4, 16.8, 18.1, 18.8; median is the middle value, 16.8 inches.

Question 4: To find gallons of paint required for 16 walls, each measuring 14 ft. by 14 ft.:

Area per wall = 14 × 14 = 196 sq. ft.

Total area = 16 × 196 = 3,136 sq. ft.

Gallons needed = 3,136 / 400 ≈ 7.84, rounded up to 8 gallons.

Cost = 8 × $27.95 = $223.60.

Question 5: Wind-generated electricity: 17.8 billion kWh out of 4450 billion kWh total.

Percentage = (17.8 / 4450) × 100 ≈ 0.4%.

Question 6: Map scale: 1 inch = 9 miles, so 1/8 inch = (1/8) × 9 = 1.125 miles.

Question 7: Sale price after 3/4 off: marked price = $156.

Discount = 156 × 3/4 = 117; sale price = 156 - 117 = $39.

Question 8: Cost per ounce:

  • Ounces in 16 oz. container cost $3.49.
  • Ounces in 33 oz. container cost $6.99.

Price per ounce: 16 oz. = $3.49 / 16 ≈ $0.218 per oz.; 33 oz. = $6.99 / 33 ≈ $0.212 per oz. Thus, the 33 oz. container is a better buy.

Question 9: Price increase from $3.24 to $4.05 per gallon:

Percent increase = ((4.05 - 3.24) / 3.24) × 100 ≈ 25%.

Question 10: Material cost: 2.75 yards at $4.80 each = 2.75 × 4.80 = $13.20; sales tax = $0.87.

Total cost = $13.20 + $0.87 = $14.07.

Question 11: Ruth’s order:

  • 2 turtlenecks: 2 × $35 = $70.
  • 2 pants: 2 × $45 = $90.
  • 1 jacket = $130.
  • 3 belts: 3 × $25 = $75.
  • Shipping: $15.

Total = $70 + $90 + $130 + $75 + $15 = $380.

Question 12: Wedding punch calls for 12 quarts. Each bottle contains 4/5 quart. Number of bottles:

Number of bottles = 12 / (4/5) = 12 × (5/4) = 15 bottles.

Question 13: Comparing two car loans:

  • First bank: Principal = $5800; rate = 7%; time = 4 years; interest = 5800 × 0.07 × 4 = $1624; total cost = $5800 + $1624 + $45 = $7469.
  • Second bank: Principal = $5800; rate = 8%; interest = 5800 × 0.08 × 4 = $1856; total cost = $5800 + $1856 = $7656.

Thus, the first bank has lower total loan costs.

Question 14: Area of the concrete slab:

  • Circle with radius r = 20 ft: Area = 3.14 × 20² = 3.14 × 400 = 1256 sq. ft.
  • Rectangle area = 70 ft. × 30 ft. = 2100 sq. ft.
  • Total area = 1256 + 2100 = 3356 sq. ft.

Volume of cement slab = area × thickness. Thickness = 6 inches = 0.5 ft.

Volume = 3356 × 0.5 = 1678 cubic feet.

Question 15: Preference for silver cars:

  • Men: 20/63 ≈ 31.75%; women: 16/49 ≈ 32.65%. The percentage is slightly higher for women, so women have a marginally stronger preference.

Bonus Question:

Number of acres in 1 square mile:

1 mile = 5280 ft., so 1 sq. mile = 5280 × 5280 = 27,878,400 sq. ft.

Since 1 acre = 43,560 sq. ft., number of acres in 1 sq. mile = 27,878,400 / 43,560 ≈ 640 acres.

Effective Email Revision:

Subject: Request for Innovative Ideas to Increase Store Traffic

Dear MAXX Sports Team,

I am committed to taking our business to the next level. Recently, I asked managers across all stores to propose new strategies to attract more customers.

While some common ideas like coupons, clearance sales, rewards programs, sidewalk sales, and store redesigns have been suggested, I find them to be unoriginal and insufficient. We need fresh, innovative approaches that genuinely excite our customers and reflect the passion MAXX Sports is known for.

Therefore, I invite every employee, from warehouse staff to executives, to contribute ideas that could help us draw more shoppers back into our stores. Please email your suggestions to me, or visit my office if you'd prefer to discuss them in person.

Thank you for your dedication and creativity in helping to revitalize our business.

Sincerely,

Maxine Profit

Owner, MAXX SPORTS

References

  • EPA. (2020). Renewable energy in the United States. Environmental Protection Agency.
  • GIS Geography. (2021). Map scales explained. https://gisgeography.com/map-scale-explained/
  • Investopedia. (2022). Simple interest definition and calculation. https://www.investopedia.com/terms/s/simpleinterest.asp
  • National Oceanic and Atmospheric Administration. (2023). Burlington snowfall data. NOAA.
  • U.S. Geological Survey. (2021). Land measurement conversions. USGS.
  • U.S. Department of Agriculture. (2023). Acreage and land measurements. USDA.
  • Statistics Canada. (2020). Housing land subdivision statistics. Statistics Canada.
  • Weather.com. (2023). Vermont winter snow averages. The Weather Channel.
  • Wolfram Alpha. (2023). Mathematical calculations and unit conversions.
  • WindEurope. (2022). Wind energy statistics in the United States. WindEurope.

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