Questions and Answers
What is the function for the depreciated value of the washing machine as it varies with time?
V = 400 - 80t
When does the depreciated value of the washing machine reach $0?
5 years
Is the price of the computer component decreasing in a linear or exponential manner?
What will the computer component cost in three years if it costs $60 today?
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What is the length of the longer piece of a divided line segment that is 15 inches long, in the ratio of the golden ratio?
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How many dimensions are needed to describe a closed book?
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How many dimensions describe the surface (cover) of the book?
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How many dimensions describe an edge of the book?
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What represents zero dimensions in the context of the book?
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How does the surface area of the actual concert hall compare to the surface area of a scale model built with a scale factor of 25?
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What are the latitude and longitude of the location on Earth opposite of a town at latitude 42° S, longitude 128° W?
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Identify all of the symmetries in a circle.
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What is the frequency of a note six half-steps above middle C, starting at a frequency of 260 cps?
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What is the total amount paid by each guest for the room?
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What is the term for the fallacy that assumes popularity equals truth?
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It follows that one quarter of the class is male communication majors.
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All hills are steep.
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What is ambiguous about the quote regarding two jumbo jets?
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How much did the woman gain from her transactions?
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Identify whether the argument is inductive or deductive: 'Every coach must know his sport well. Marty Wright is a baseball coach, so Marty Wright knows baseball well.'
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My logical proposition is a question that you must answer.
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The statement 'The rate of return on our fund increased by 50%, to 15%' makes sense.
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The retail cost of a TV is 40% more than its wholesale cost. Therefore, the retail cost is ____ times the wholesale cost.
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Baggage screening machines are 98% accurate in identifying bags that contain banned materials.
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The statement 'When we chart the price of milk in 1995 dollars we find it has become slightly more expensive' makes sense.
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Estimate the amount of water the average person drinks in a year.
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Wilma used a yard stick to measure the length of her kitchen to the nearest micrometer.
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What explains how both gubernatorial candidates can be right about the economy?
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Discuss possible sources of error in the car sales measurements.
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What was the price of movie admission in 1976 dollars if it cost $8.50 in 2007?
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Express 2.1 million deaths per year as deaths per minute.
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The statement 'My share of the federal government's debt is greater than the cost of a new car' makes sense.
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Making only minimum payments on a credit card is a good financial strategy.
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An annual interest rate (APR) of 3.0% resulting in a 3.1% growth is logical.
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How long will it take for the new efficient dryer to pay for itself compared to the old dryer?
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The statement about a highly-risky stock fund offering no risk is logical.
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The claim about spending over $1700 per year on pizza and soda is plausible.
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The statement regarding Social Security not impacting the federal budget makes sense.
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Two individuals with the same gross income must pay the same taxes.
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The assertion that stocks will always outperform other investments is valid.
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The statement that over half of student loan payments go towards interest is accurate.
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The relationship between crime rates and the number of taxi cabs can be correlated.
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What is the definition of simple random sampling?
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Explain the risk measures by standard deviations for portfolios with single and multiple stocks.
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What percentage of births is expected to occur within 16 days of the mean pregnancy length?
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Discuss which graph of cell phone subscriptions is more useful.
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Match the following types of studies with their descriptions:
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Calculate the margin of error and confidence interval from the poll results.
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Your ability to create a bar chart is limited by data type.
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What is the selection bias in surveying college students?
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What kind of distribution is seen in the geyser eruption times?
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Estimate the probability of getting married in the next 3 years.
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The probability statement regarding last names makes sense.
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The statement about tossing coins and their outcomes makes sense.
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Your life expectancy determines how long you live.
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What is the expected waiting time for a bus arriving every 80 minutes?
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What is the probability of randomly selecting a four-person committee consisting entirely of women?
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How many permutations are there of the letters in the word 'CHARGES'?
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The likelihood of HTHT being a more likely outcome than HHHH in a coin toss is valid.
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Doubling the amount of water will also double the pH.
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What does the function relating height to shoe size indicate?
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How much money will the girl have after 22 nights if the number of pennies doubles?
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Create an exponential function for growth with given parameters.
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How many times greater is sound intensity from 1 meter compared to 14 meters?
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What is the depreciation rate for a washing machine in a laundromat?
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Study Notes
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.
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Description
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.
