Section 4.1.H: Homework
- Page ID
- 216976
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Section 4.1: Percents - Homework Exercises
- Express each decimal as a percent.
- 0.03
- 0.1
- 0.27
- 8
- 0.00025
- 2.59
- 1
- 0.98765
- Answer
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- 3%
- 10%
- 27%
- 800%
- 0.025%
- 259%
- 100%
- 98.765%
- Express each percent as a decimal.
- 55%
- 4.5%
- 0.025%
- 5\(\frac{1}{4}\)%
- 150%
- 8%
- 1.3%
- 12\(\frac{7}{8}\)%
- Answer
-
- 0.55
- 0.045
- 0.00025
- 0.0525
- 1.5
- 0.08
- 0.013
- 0.12875
As of 2026, the most expensive consumer-grade and prosumer drones often exceed $15,000–$20,000, with specialized industrial systems costing even more. Top contenders include the DJI Inspire 3 (approx. $16,000+) and professional mapping hexacopters like the Freefly Alta 8 ($17,495+), which offer high-end, interchangeable cameras for cinema production. What is the tax on a Freely Alta 8, if the sale price was $17,495? Assume the sales tax rate is 8.75%.
- Answer
-
Sales tax = $1,530.81
A newlywed couple decides to go to Maggiano's Little Italy in Costa Mesa, CA. on Valentine's Day. The bill for dinner cost $114.00 before tax.
- Find the total cost of the dinner including tax. The tax rate in Costa Mesa is 7.75%.
- Many people rely on the suggested tip amounts printed at the bottom of a receipt. However, those suggested percentages are not always calculated the same way. Sometimes they’re based on the pre‑tax total, and other times on the post‑tax total. In some cases, the listed tip amounts have even been rounded incorrectly or calculated inaccurately. So the question becomes: What should the correct tip amounts be when calculating 18%, 20%, and 22% based on the price before tax? What would be the total cost be including tax and tip for each rate?
- In part b, what should the correct tip amounts be when calculating 18%, 20%, and 22% based on the price after tax? What would be the total cost be including tax and tip for each rate?
- Answer
-
- Tax = $8.84; Total cost without tip = $122.84
- 18% tip on $114 = $20.52; 20% tip on $114 = $22.80; 22% tip on $114 = $25.08;
- For 18%: $114 + $8.84 + $20.52 = $143.36
- For 20%: $114 + $8.84 + $22.80 = $145.64
- For 22%: $114 + $8.84 + $25.08 = $147.92
- 18% tip on $122.84 = $22.11; 20% tip on $122.84 = $24.57; 22% tip on $122.84 = $27.02;
- For 18%: $114 + $8.84 + $22.11 = $144.95
- For 20%: $114 + $8.84 + $24.57 = $147.41
- For 22%: $114 + $8.84 + $27.02 = $149.86
Private Mortgage Insurance (PMI) is a required, non-owner-protective fee for conventional loans with less than a 20% down payment, typically costing 0.46%–1.5% of the loan amount annually. It protects the lender if the buyer defaults. A 2,650 square foot, 4 bedroom, 3.5 bath beach-front house in Newport Beach, CA on the Balboa Peninsula was just listed on Realtor.com. The asking price is $10,995,000. What would one have to pay as a down payment to avoid paying PMI? What would be the balance after the down payment?
- Answer
-
Down payment = $2,199,000; Balance after payment = $8,796,000
Car salespeople typically earn a commission ranging from 15% to 40% of the front-end gross profit on a vehicle sale, with 20% to 30% (often around 25%) being the most common rate. Rather than a percentage of the total car price, they are paid based on the profit margin, plus potential bonuses for financing, warranties, and reaching volume targets. Based on early 2026 model year pricing, the gross profit built into the MSRP for a 2026 Dodge Charger is approximately 7%. At Premier Chrysler Dodge Jeep Ram in Buena Park, a new 2026 Dodge Charger 4-Door R/T With Navigation & AWD has an MSRP of $61,200. What is the gross profit on this vehicle if using a 7% rate? Based off that amount, what would be the earned commission for a car saleswomen, if she was to earn a 25% commission on the sale of the 2026 Dodge Charger?
- Answer
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Gross profit = $4,284; Commission = $1,071