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Questions and Answers
Consider circle A with radius 1 unit. If $θ=60°$, what is the length, in radians, of arc BC?
Consider circle A with radius 1 unit. If $θ=60°$, what is the length, in radians, of arc BC?
1/3
How can the collector correct his mistake in the expression for the coin's value?
How can the collector correct his mistake in the expression for the coin's value?
The base of the simplified expression should be 1.05, and the exponent should be 2x + y.
What is the value of sin θ if cos θ = 39/89?
What is the value of sin θ if cos θ = 39/89?
-80/89
What is the equation that represents the sound wave producing the note A on a piano?
What is the equation that represents the sound wave producing the note A on a piano?
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Which of the following intervals has the smallest average rate of change in the function y=2x+2?
Which of the following intervals has the smallest average rate of change in the function y=2x+2?
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How many hours will it take for the number of bacteria to reach 1,000,000?
How many hours will it take for the number of bacteria to reach 1,000,000?
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What is the average rate of change for the interval 5-10 days for a radioactive substance?
What is the average rate of change for the interval 5-10 days for a radioactive substance?
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What is the likely purpose of the survey conducted at the rock concert?
What is the likely purpose of the survey conducted at the rock concert?
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What values of x will result in f(x)=g(x) for the equations f(x)=2x−1 and g(x)=38x?
What values of x will result in f(x)=g(x) for the equations f(x)=2x−1 and g(x)=38x?
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What is the inverse of f(x)=−3x+12/4?
What is the inverse of f(x)=−3x+12/4?
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The distribution in the number of seeds per apple is approximately normal.
The distribution in the number of seeds per apple is approximately normal.
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Which graph represents the equation y=−2(3)x−4?
Which graph represents the equation y=−2(3)x−4?
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What is the average rate of change for the interval 10-15 days?
What is the average rate of change for the interval 10-15 days?
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Match the following sampling techniques with their descriptions:
Match the following sampling techniques with their descriptions:
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Study Notes
Arc Length and Circles
- For circle A with a radius of 1 unit and an angle θ of 60°, the length of arc BC is calculated as 1/3 radians.
Growth and Investments
- A rare coin purchased for $100 grows in value at 10.25% annually for x years and then at 5% for y years.
- The correct expression for the coin's value, after x+y years, is 1.1025^x * 1.05^y, where the collector originally miscalculated the exponent.
Trigonometric Values
- For an angle θ in Quadrant IV where cos θ = 39/89, the value of sin θ = -80/89 and tan θ = -80/39.
Sound Waves
- A sound wave that produces the piano note A is represented by the function y = sin(880πx), where time is on the horizontal axis.
Average Rate of Change
- The smallest average rate of change for the linear function y = 2x + 2 occurs in the interval 6 ≤ x ≤ 8.
Bacterial Growth Model
- An initial bacterial culture of 200 doubles every 33 hours, modeled as A = P(2)^(t/3). It will take approximately 37 hours to reach 1,000,000 bacteria.
Sampling Techniques
- Amanda’s simple random sample of 60 students needs to reflect the high school's social media usage accurately; various sampling methods were evaluated with yes/no answers regarding their effectiveness.
Experimentation with Fertilizers
- In a study comparing two fertilizers, Fertilizer A showed a mean radish radius of 0.52 inches smaller than Fertilizer B. A simulation indicated this difference might be due to chance, showing a probability of 0.52 for such a difference.
Exponential Growth
- Josie's text messages follow the equation t = 5 * 3^(d - 1), where t is the number of messages each day after the first.
Radioactive Substance Decay
- The average rate of change in the decay of a radioactive substance over specific intervals results in a consistent decrease per day.
Investor Survey Results
- The survey conducted revealed 82% positive impressions of the performer's song, aiming to estimate overall fan sentiments.
Logarithmic Functions
- The equation g(x) = log(x + 5) and h(x) = -x - 6 leads to a solution x = -4.9.
Intersection of Functions
- The intersection of functions f(x) = 2x - 1 and g(x) = 38x results in x-values of 0 and -2.
Function Inverses
- The inverse of f(x) = (−3x + 12)/4 is f⁻¹(x) = -4x/3 + 4.
Normal Distribution of Seeds
- Approximately 19% of apples have between 5 and 11 seeds based on a normal distribution of seed counts per apple in Hayley’s orchard.
Confidence Intervals
- The mean amount spent on oral hygiene products falls within a 95% confidence level with values including $128.30, $203.36, $206.04, and $189.85.
Graphical Representation
- The graph of the equation y = -2(3)^x − 4 can be visualized at a provided link.
Unit Circle and Angles
- On the unit circle, an angle rotation to point B corresponds to π/2 radians, indicating a quarter rotation.
Fertilizer Growth Simulation
- After testing two fertilizers, the simulation showed Fertilizer A's performance might also be influenced by the characteristics of the assigned seeds.
Exponential Decay Modeling
- Juanita’s savings account model J(t) = 500(1.015)^t has a domain representing whole numbers, as partial years are not applicable.
Comparative Growth Analysis
- The equations f(x) = 240(12)^x suggest rapid growth with particular behaviors as x approaches infinity in both directions.
Tiger Population Projections
- The equation for wild tigers in Nepal projects a population modeled by p = 121(2)^x, with future population figures requiring logarithmic transformations.
Musical Note Periodicity
- The note "A" modeled by f(x) = sin(880πx) has a period of 1/440 seconds and 880 intercepts in the interval (0, 1].
Graphical Changes and Shifts
- Analyzing the graphs of transformations shows the function 5f(x) is shifted upward compared to f(x).
Fairness of Dice Game
- Maggie's and Joe's dice game plan is biased, as results show sums greater than 6 occurring more than 50% of the time, favoring Joe.
Exponential Function Properties
- The properties of a specific exponential graph include a y-intercept at 3 and the graph's behavior indicating it is always decreasing.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge with these flashcards for the Algebra 2b final exam. Covering topics from circle geometry to exponential growth, these cards provide a quick review of essential concepts. Perfect for students preparing for their finals!
