Algebra Cumulative Exam Review

Questions and Answers

Which of the following shows the extraneous solution to the logarithmic equation below? $2 ext{log}_5(x+1)=2$

x=2

x=0

x=3

x=-6 (correct)

What is the formula for margin of error?

ME = z*s/sqr(n) (correct)

ME = z*sqr(n)

ME = z/(s*n)

ME = z/n

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 $y=e^{x}+1$?

y > 1 Signup and view all the answers

What is the probability that the gymnast scores a 9 or 9.5?

0.14 Signup and view all the answers

Which system of equations can be graphed to find the solutions to $4x^2 = x^2 - 7$?

y=4x^2; y=x^2-7 Signup and view all the answers

What is the intensity in decibels when $l=10^{32}(l_0)$?

320 Signup and view all the answers

Is the study by the utility company biased?

Yes, it is biased. Signup and view all the answers

What is the domain of the function $y= ext{ln}(x+2)$?

x > -2 Signup and view all the answers

What are the solutions to $log_6(x^2 +8)= 1 + log_6(x)$?

x=2 and x=4 Signup and view all the answers

Which fraction represents the decimal 0.8888...?

8/9 Signup and view all the answers

What is the probability that a randomly chosen person receives the newspaper at least one day per week?

83% Signup and view all the answers

What is the minimum value of $C = 7x + 8y$ given the constraints $2x+y > 8$, $x+4 > 6$, $x > 0$, $y > 0$?

42 Signup and view all the answers

What is the correct system of equations and solution for $log_2x + log_2 (x-2) = 3$?

y1 = log x/log 2 + log(x-2)/log2, y2 = 3; x=4 Signup and view all the answers

What system of equations can be used to determine how much of product A and product B were bought?

x + y = 4000; 0.1x + 0.04y = 352 Signup and view all the answers

What conclusion can be derived from the two-tailed hypothesis test with the teacher's data?

Her students, on average, do not take 30 minutes on the quiz, contrary to what the textbook company stated. Signup and view all the answers

What percentage of the runners have times less than 14.4 seconds?

0.15% Signup and view all the answers

Which function is shown in the graph below?

y=2^x+2 +3 Signup and view all the answers

What is the probability that at most 4 students have taken chemistry?

0.438 Signup and view all the answers

Which graph shows the solution set of the compound inequality $1.5x - 1 > 6.5$ or $7x + 3 < -25$?

Graph B Signup and view all the answers

What is the completely factored form of $12xy - 9x - 8y + 6$?

(3x - 2)(4y - 3) Signup and view all the answers

What are the vertices of the feasible region for the problem $4x + 3y = 0$?

(0, 0), (0, 2.5), (1.5, 2), (3, 0) Signup and view all the answers

Which graph represents the same relation as the set {(-3, 2),(5, 5),(3, 3),(3, -2)}?

Graph B Signup and view all the answers

What is the value of $i^{20+1}$?

i Signup and view all the answers

For which pairs of functions is $(f°g)(x) = 12x$?

f(x) = 4x and g(x) = 3x Signup and view all the answers

If the discriminant of a quadratic equation is 4, which statement describes the roots?

There are two real roots. Signup and view all the answers

Which set of population data is the least dispersed from its mean?

6, 2, 2, 2 Signup and view all the answers

Which angle measures are coterminal with a 95° angle?

95° - (1080n)°, for any integer n Signup and view all the answers

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).

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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!