Podcast
Questions and Answers
Which of the following shows the extraneous solution to the logarithmic equation below? $2 ext{log}_5(x+1)=2$
Which of the following shows the extraneous solution to the logarithmic equation below? $2 ext{log}_5(x+1)=2$
What is the formula for margin of error?
What is the formula for margin of error?
What was the missing data value if it was exactly 3 standard deviations away from the mean $u=120$ and $o=9$?
What was the missing data value if it was exactly 3 standard deviations away from the mean $u=120$ and $o=9$?
147
What is the range of the function $y=e^{x}+1$?
What is the range of the function $y=e^{x}+1$?
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What is the probability that the gymnast scores a 9 or 9.5?
What is the probability that the gymnast scores a 9 or 9.5?
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Which system of equations can be graphed to find the solutions to $4x^2 = x^2 - 7$?
Which system of equations can be graphed to find the solutions to $4x^2 = x^2 - 7$?
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What is the intensity in decibels when $l=10^{32}(l_0)$?
What is the intensity in decibels when $l=10^{32}(l_0)$?
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Is the study by the utility company biased?
Is the study by the utility company biased?
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What is the domain of the function $y= ext{ln}(x+2)$?
What is the domain of the function $y= ext{ln}(x+2)$?
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What are the solutions to $log_6(x^2 +8)= 1 + log_6(x)$?
What are the solutions to $log_6(x^2 +8)= 1 + log_6(x)$?
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Which fraction represents the decimal 0.8888...?
Which fraction represents the decimal 0.8888...?
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What is the probability that a randomly chosen person receives the newspaper at least one day per week?
What is the probability that a randomly chosen person receives the newspaper at least one day per week?
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What is the minimum value of $C = 7x + 8y$ given the constraints $2x+y > 8$, $x+4 > 6$, $x > 0$, $y > 0$?
What is the minimum value of $C = 7x + 8y$ given the constraints $2x+y > 8$, $x+4 > 6$, $x > 0$, $y > 0$?
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What is the correct system of equations and solution for $log_2x + log_2 (x-2) = 3$?
What is the correct system of equations and solution for $log_2x + log_2 (x-2) = 3$?
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What system of equations can be used to determine how much of product A and product B were bought?
What system of equations can be used to determine how much of product A and product B were bought?
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What conclusion can be derived from the two-tailed hypothesis test with the teacher's data?
What conclusion can be derived from the two-tailed hypothesis test with the teacher's data?
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What percentage of the runners have times less than 14.4 seconds?
What percentage of the runners have times less than 14.4 seconds?
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Which function is shown in the graph below?
Which function is shown in the graph below?
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What is the probability that at most 4 students have taken chemistry?
What is the probability that at most 4 students have taken chemistry?
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Which graph shows the solution set of the compound inequality $1.5x - 1 > 6.5$ or $7x + 3 < -25$?
Which graph shows the solution set of the compound inequality $1.5x - 1 > 6.5$ or $7x + 3 < -25$?
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What is the completely factored form of $12xy - 9x - 8y + 6$?
What is the completely factored form of $12xy - 9x - 8y + 6$?
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What are the vertices of the feasible region for the problem $4x + 3y = 0$?
What are the vertices of the feasible region for the problem $4x + 3y = 0$?
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Which graph represents the same relation as the set {(-3, 2),(5, 5),(3, 3),(3, -2)}?
Which graph represents the same relation as the set {(-3, 2),(5, 5),(3, 3),(3, -2)}?
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What is the value of $i^{20+1}$?
What is the value of $i^{20+1}$?
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For which pairs of functions is $(f°g)(x) = 12x$?
For which pairs of functions is $(f°g)(x) = 12x$?
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If the discriminant of a quadratic equation is 4, which statement describes the roots?
If the discriminant of a quadratic equation is 4, which statement describes the roots?
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Which set of population data is the least dispersed from its mean?
Which set of population data is the least dispersed from its mean?
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Which angle measures are coterminal with a 95° angle?
Which angle measures are coterminal with a 95° angle?
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Study Notes
Logarithmic Equations
- Extraneous solution example: For (2\log_5(x+1) = 2), the extraneous solution is (x = -6).
Margin of Error
- Formula: (ME = z \cdot s / \sqrt{n}).
Statistics and Data Analysis
- For a data set with mean (\mu = 120) and standard deviation (\sigma = 9), if a missing value is 3 standard deviations from the mean, the value is (147).
- Solutions for (\log_6(x^2 + 8) = 1 + \log_6(x)) are (x = 2) and (x = 4).
Functions and Ranges
- The range of (y = e^{x} + 1) is (y > 1).
- For (f(x) = -2(6^x) + 3), the range is ((-∞, 3)).
- The domain for (y = \ln(x + 2)) is (x > -2).
Probability and Statistics
- Probability of gymnast scoring 9 or 9.5 is (0.14).
- Survey on electric bills could be biased if residents do not want to respond.
- A probability of at most 4 students taking chemistry out of 12 surveyed is approximately (0.438).
- Probability that a sample of registered voters has a proportion between (0.37) and (0.39) is (17%).
Graphing and Systems of Equations
- To find solutions for (4x^2 = x^2 - 7), graph (y = 4x^2) and (y = x^2 - 7).
- For (log_2(x) + log_2(x-2) = 3), correct system is (y_1 = \frac{\log x}{\log 2} + \frac{\log(x-2)}{\log 2}, y_2 = 3) with (x = 4).
Real-world Applications
- Shipping cost equation for products: (x + y = 4,000) and (0.1x + 0.04y = 352).
- Cost analysis of yoga classes shows gym option cheaper after seven classes.
Geometry and Measurement
- Volume of a cube with side length (s = 3x + 2y) is given by (V = s^3 = 27x^3 + 54x^2y + 36xy^2 + 8y^3).
Normal Distribution and Z-scores
- For Thanh's grade with a z-score of (-2.5), it indicates the grade is (2.5) standard deviations below the mean.
- Percentage of 15-year-olds running less than (14.4) seconds in a race is (0.15%).
Angle and Coterminal Angles
- A (95)° angle has a coterminal angle expressed as (95° - (1080n)°).
- The angle equivalent to (-865°) is (215°) when adjusted within (0°) to (360°).
Quadratic Equations and Discriminants
- If the discriminant of a quadratic equation is (4), there are two real roots.
Factorization and Rational Expressions
- The completely factored form of (12xy - 9x - 8y + 6) is ((3x - 2)(4y - 3)).
- The rational expression for a player's free throw percentage after (x) successful attempts is (\frac{13+x}{20+x}).
Transportation and Cost Minimization
- Minimum transportation cost for field trip with constraints is (1700) dollars using large and small buses.
Dispersion of Data
- The least dispersed set of population data is (6, 2, 2, 2).
Complex Numbers
- The value of (i^{20} + 1) is (i).
Studying That Suits You
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Description
Test your knowledge with this comprehensive Algebra Cumulative Exam Review. Covering key concepts, including logarithmic equations and the margin of error, these flashcards will help reinforce your understanding of algebraic principles. Perfect for last-minute preparation before the exam!
