Questions and Answers
What is the average?
What is a weighted average?
What is the percentage increase formula?
(1+increase)x(original amount)
What percent discount was given if pants originally cost $80.00 but were sold for $60.00?
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If a pair of shoes costs $40 after a 40% discount, what was the original price?
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In a class of 30 kids, with a boys to girls ratio of 2:3, how many boys are there?
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What is the speed formula?
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How many meters did Kyle run per second if he ran 5 kilometers in 15 minutes?
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What is the return of investment formula?
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What is the profit margin formula?
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If a computer costs $2500, the charger costs 8% of that, and the case costs 10% of the charger, how much do all the items cost together?
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What is the famous order of operations acronym?
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Solve for x in the equation (70-20)4/250=x/8.
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In this equation, what operation is done first based on the rules of PEMDAS: ((4-5)3)(4.9+7)?
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In the equation (9x8)50, do the parentheses make a difference?
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Who gets to work first based on their commutes and speeds?
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What’s the sixth term in the arithmetic sequence 1, 7, 13, 19, 25?
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What’s the fifth term of the arithmetic sequence 2, 6, 18, 54?
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What is the best description that matches the synonyms of leaving: desert and abandon?
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What is the percent decrease formula?
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What is the work formula?
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What are fixed costs?
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What are variable costs?
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If a kickboxing studio's rent is $3000/month, with $2 on average for equipment per boxer per week, and $500 per instructor per month, how much is the monthly cost if there are 100 boxers and 4 instructors?
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After a warehouse fire, if 18% of a company’s 145,050 water bottles were destroyed or damaged, how many bottles are left intact?
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Study Notes
Basic Concepts of Averages and Formulas
- Average: Represents the central value of a set of numbers, calculated to summarize data.
- Weighted Average: Similar to average but assigns different importance (weights) to each value or group of values.
Key Mathematical Formulas
- Percentage Increase Formula: Used to calculate any increase in percentage based on an original amount: ( (1 + \text{increase}) \times \text{original amount} ).
- Return on Investment Formula: Helps evaluate the profitability of an investment: ( \frac{(\text{gain} - \text{cost})}{\text{cost}} \times 100 ).
- Profit Margin Formula: Measures how much profit is made from sales: ( \frac{\text{gross profit}}{\text{total revenue}} ).
- Distance Formula: Connects speed, time, and distance: ( \text{distance} = \text{velocity} \times \text{time} ).
Practical Applications
- Percentage Discount: For a pair of pants originally priced at $80 but sold for $60, the discount percentage is 25%.
- Calculating Original Prices: After a 40% discount, a $40 pair of shoes indicates the original price was $66.67.
- Ratio Problems: In a class of 30 children with a boys to girls ratio of 2:3, there are 12 boys.
Arithmetic and Sequences
- Arithmetic Sequences: The sixth term in the sequence 1, 7, 13, 19, 25 is 31. The fifth term of 2, 6, 18, 54 is 162.
Order of Operations
- PEMDAS: Provides the sequence of operations to follow in mathematics: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
- Examples of PEMDAS: In the expression ( (70 - 20) \cdot 4 / 250 = x / 8 ), ( x ) equals 6.4.
Costs and Economics
- Fixed Costs: Consistent expenses that do not fluctuate over time for businesses.
- Variable Costs: Expenses that vary based on a company's production levels.
- Monthly Costs Calculation: For a kickboxing studio with several costs, the total monthly cost sums to $5,800.
Bottle Inventory Post-Fire
- Bottle Loss Calculation: After an 18% destruction due to a fire, a company initially holding 145,050 water bottles has 118,941 bottles remaining.
Commute Comparison
- Commute Timing: Given Bob's 15-mile commute at 40 mph versus Joe's 20-mile commute at 50 mph, calculate arrival times to determine who arrives first.
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Description
Explore key concepts in educational development through Jake's flashcards. This quiz covers definitions of average, weighted average, and percentage increase formulas, providing essential insights for students. Perfect for those studying mathematics or general education principles.
