Math 107 Flashcards

Hotel Room Puzzle

• Guests paid ​$45 collectively for a room that cost ​$40.
• Desk clerk gave $5 to return; bellhop kept $2, giving $1 back to each guest.
• Total computed wrongly as $42 (each guest $14) plus $2 = $44, creating a misleading 'missing dollar' narrative.

Appeal to Popularity

• Commonly used deceptive argument claiming that widespread reading of Shakespeare proves his likability.
• Assumes popularity equates to quality or appreciation.

Communication Majors

• The logic questioning if half of a class of communication majors is male, claiming a quarter are male communication majors lacks basis.

Valid Arguments

• Argument example: All hills are steep; El Mound is a hill; therefore, El Mound is steep. It's valid but not sound if the premises are incorrect.

Ambiguity in Statistics

• A statement about two jumbo jets with "more than 350 people" is ambiguous. Clarification on whether the number refers to each jet or combined is needed.

Transactions and Gains

• A woman's series of buying and selling a dining table indicates she gained $800 in total across transactions.

Deductive Reasoning

• An instance of deductive reasoning is observed when inferring that a baseball coach must know baseball due to their profession.

Logical Propositions

• Logical propositions must be declarative statements, not questions, making certain statements nonsensical.

Accuracy in Statements

• A statement discussing a fund's return indicates a previous rate of 10% if the current return is 15% after a 50% increase.

Retail Pricing Calculations

• If a TV's retail price is 40% more than its wholesale price, it can be concluded that the retail cost is 1.40 times the wholesale cost.

Screening Machines Accuracy

• Baggage screening machine accuracy does not guarantee that flagged bags indeed contain banned materials; true positive rates must be considered.

Price Trends Over Time

• Contradictory price trend statements about milk's price in different year's dollars indicate a misunderstanding of inflation.

Water Consumption Estimation

• An estimate of annual water intake per person is 180 gallons based on a daily average of 4 pints.

Measurement Precision

• It's nonsensical to measure a kitchen's length using a yardstick with micrometer precision due to the measuring tool's limitations.

Economic Claims and Real Terms

• A rise in median household income can be misleading if inflation surpasses income growth, resulting in decreased purchasing power.

Sources of Measurement Error

• Discusses potential inaccuracies in car sales reporting; suggests skepticism about the reported figures due to human errors.

Price Adjustments Over Time

• To calculate historical price equivalent, an $8.50 movie ticket in 2007 equals about $2.33 in 1976 dollars, with adjustments based on CPI.

Death Rate Statistics

• Country A's annual death count approximated at 2.1 million translates to roughly 4 deaths per minute.

Federal Debt Context

• The concept of personal allocation of federal debt being greater than a new car's price aligns logically in fiscal discussions.

Credit Card Payment Strategy

• Relying on minimum payments on credit cards prolongs debt with increased interest payments, presenting a strategy flaw.

Interest Rate Confusion

• Discrepancy between an account's APR of 3% and an APY of 3.1% can make sense due to variations in interest rate calculations.

Efficiency of Appliances

• A new dryer costing $10 monthly will take about 69 months to pay off a $690 cost, factoring in operational savings.

Investment Claims Scrutiny

• Claims of high returns with no risk in investments are misleading; high returns typically correlate with higher risks.

Daily Spending Patterns

• Regular expenditures exceeding $1700 per year indicates an average daily cost of roughly $5 for lunch items.

Social Security Tax Implications

• Assuming Social Security is off-budget does not justify tax cuts' impacts on federal budgets, contradicting logical budgetary frameworks.

Tax Calculation Assumptions

• Two individuals with identical gross incomes may face different tax liabilities due to variations in their adjusted gross income.

Stock Investment Assumptions

• Though historically high returns, stocks remain a high-risk investment, challenging the claim that they are superior without risk.

Loan Payment Dynamics

• Student loan payments initially favor interest, aligning with typical amortization schedules over the loan term.

Correlation Analysis in Crime

• Increasing crime rates in correlation with taxi numbers in tourist areas suggest a common cause linked to increased tourism.

Random Sampling in Polling

• A simple random sample of voters is employed to predict election outcomes, emphasizing unbiased representation.

Portfolio Risk Assessment

• Portfolios with fewer stocks showcase higher risk (greater standard deviation), whereas diversifying lowers risk through a reduced standard deviation.

Distribution of Pregnancy Terms

• Approximately 68% of births will occur within one standard deviation of the mean length of pregnancy in a normally distributed dataset.

Data Visualization Techniques

• The differences between ordinary and exponential scales in graphing subscription data serve various analytical purposes, offering distinct insights.

Experimental Design Validity

• A controlled experiment illustrates the effectiveness of a treatment (like ginkgo biloba) compared to a placebo group in evaluating medical efficacy.

Margin of Error Calculation

• A survey claiming 32% dog ownership among Americans has a margin of error of 3%, leading to a confidence interval ranging from 29% to 35%.

Measurement of Radioactive Decay

• A toxic substance with a half-life of 20 years exhibits a past density of 33.3 mg/cm², demonstrating how decay impacts detected levels.

Population Growth Mathematics

• Given 8-hour doubling periods, the population of flies would experience significant growth over set time frames, demonstrating exponential growth principles.

Water Volume and pH Misconceptions

• Doubling water volume does not double its pH; acidity relates to hydrogen ion concentration rather than sheer volume.

Dimensional Analysis of Objects

• A closed book exists in three dimensions; its surfaces in two dimensions, edges in one dimension, and corners represent zero-dimensional points.

Comparison of Scale Models

• Using a scale factor of 25 for models influences surface area comparisons significantly, as area scales with the square of the linear dimension factor.

This quiz explores a classic math riddle involving a hotel bill. Understand the logic behind the seemingly missing dollar as you solve the problem of how much each guest actually paid. Great for reviewing concepts in mathematics and logical reasoning.