4.4.1: Practice Problems Corequisite N.4
- Page ID
- 148605
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The following headlines all refer to change. Identify the change as absolute or relative.
(1) “Enrollments at Northeastern University are expected to increase by 1,000!”
(i) Absolute change
(ii) Relative change
(2) “Another $3,000 tuition increase is expected.”
(i) Absolute change
(ii) Relative change
(3) “A new proposal has sales tax rates dropping from 5% to 1%, a drop of only 4%.”
(i) Absolute change
(ii) Relative change
(4) “A new proposal has sales tax rates dropping from 3% to 1%, a 67% drop!”
(i) Absolute change
(ii) Relative change
Let's say the following tax cut was applied to U.S. taxpayers who earned up to $50,000 per year. On average, these taxpayers retained 4% more of their income than before the cuts. The tax cut also gave these taxpayers a separate $900 credit on their federal tax return.
(5) How much extra money did a typical person earning $50,000 receive due to the federal tax cuts?
(6) This extra money represents what percent of the typical person’s salary? Round to the nearest tenth of a percent.
Let's say the following tax cut was applied to U.S. taxpayers earning $450,000 per year. They were taxed at a lower rate on the first $97,800 they earned, saving them 4% of this portion of their salary. The same taxpayers also received $12,750 more on their federal tax return. Fill in the blank to complete the statement below.
(7) A person earning $450,000 a year received $_________ more of their income. Round to the nearest dollar.
(8) A person earning $450,000 a year received $16,662 more or _______ % more of their income. Round to the nearest tenth of a percent.
The tables below give the dimensions of four different rectangles sets.
(9) Are the four rectangles in this set “Proportional” or “Not Proportional”?
| Width | Length | |
| Rectangle 1 | 17 | 110.5 |
| Rectangle 2 | 23.4 | 152.1 |
| Rectangle 3 | 33 | 214.5 |
| Rectangle 4 | 52.2 | 339.3 |
(10) Are the four rectangles in this set “Proportional” or “Not Proportional”?
| Width | Length | |
| Rectangle 1 | 7.4 | 15.5 |
| Rectangle 2 | 17 | 40.8 |
| Rectangle 3 | 23.4 | 68.5 |
| Rectangle 4 | 33 | 72.6 |
Let's say the United States used 22,691,000 barrels of oil a day, and worldwide, people used around 42,799,000 barrels of oil per day. This includes oil used for (among other things) fuel and manufacturing.
(11) If there were 330 million people in the United States in 2020, what was the daily consumption rate per capita (barrels per person) in the United States? Round to the nearest hundredth of a barrel.
(12) If there were 7.82 billion people in the world in 2020, which of the following statements would be correct? The U.S. rate of oil consumption per capita was about:
(i) 2 times the world rate.
(ii) 5 times the world rate.
(iii) 10 times the world rate.
(iv) 50 times the world rate.
(13) There are 42 gallons in a barrel of oil. Which of the following statements is true? The average American is responsible for about:
(i) 0.5 gallons of oil use per day.
(ii) 3 gallons of oil use per day.
(iii) 5 gallons of oil use per day.
(iv) 30 gallons of oil use per day.