End of Semester Algebra 2B Quiz and Flashcards

Questions and Answers

Which equation can be used to find the number of weeks, x, after which the balance of the fund will reach 1,280?

5(2)^x = 1,280

How many weeks will it take to reach the class goal of $1,280?

x = 8

The value of Sam's car after one year is represented by 17,930(0.81)^x.

False

Which expressions are equivalent to log10(20x^5) - 1?

log10(20x^5) - 1 = log10(10x) Signup and view all the answers

Match each logarithmic equation to its corresponding x-value:

log5x=4 = 625 log4x=2 = 16 log10x=3 = 1,000 log2x=5 = 32 Signup and view all the answers

What value of x satisfies the equation 1.5(4)^(2x) = 12?

0.75 Signup and view all the answers

What is the approximate solution to the equation 4ln(x) - 8 = 12?

x ≈ 148.4 Signup and view all the answers

What is the equation of the transformed function g in terms of f(x) = e^x?

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

What is the range of function g if g(x) = -2f(x) + 1?

(-infinity, 1) Signup and view all the answers

The graph of function f has a range of {y| -infinity < x < infinity}.

True Signup and view all the answers

Match each transformation of function f with a feature of the transformed function:

j(x) = f(x) - 1/2 = vertical asymptote of x = 0 h(x) = f(x - 1/2) = y-intercept at (0, -1/2) g(x) = -1/2f(x - 2) = function decreases as x increases Signup and view all the answers

What is the explicit function that describes the sequence 16, 24, 36, 54...?

f(n) = 16(3/2)^(n - 1) Signup and view all the answers

Select all functions that can be used to find the number of miles Natalie drives in a month.

f(1) = 800 Signup and view all the answers

What is the total profit Jessica earned in 5 years?

$7,776 Signup and view all the answers

Match each series with the equivalent series written in sigma notation:

3 + 12 + 48 + 192 + 768 = 3(4) 4 + 32 + 256 + 2,048 + 16,384 = 4(8) 2 + 6 + 18 + 54 + 162 = 2(3) 3 + 15 + 75 + 375 + 1,875 = 3(5) Signup and view all the answers

What does the function h(x) look like?

h(x) = {-6, -9 for -4 < x < -3, 1 for -2 < x < 2, 4 for 2 < x < 8} Signup and view all the answers

Function g is continuous.

True Signup and view all the answers

What should Ronald do with the functions regarding the height of the chest?

Multiply functions + sqrt(x) Signup and view all the answers

Which expression is equal to f(x) * g(x)?

x-2/x+6 Signup and view all the answers

As x approaches positive infinity, f(x) approaches _ and g(x) approaches _.

[positive infinity] and [negative infinity] Signup and view all the answers

What did Jane record about her marigold sapling?

The function is increasing, but the average rate of change is decreasing. Signup and view all the answers

What is the approximate value for the solution to the equation f(x) = g(x)?

7/8 Signup and view all the answers

Using a table of values, what is the approximate solution to the equation f(x) = g(x) to the nearest quarter of a unit?

x ≈ -2.25 Signup and view all the answers

To keep producing a specific shirt style, the company must make a profit of at least $5,000.

[meets] Signup and view all the answers

What are the two equations that represent Leo's savings plans?

400(1.02)^x and 400e^(0.02x) Signup and view all the answers

Which statements are true about the measure of angle 0 being 7x/4?

The reference angle is 45° Signup and view all the answers

If cos(0) = -3/10 and 0 is in quadrant II, what is the value of tan(0)?

-sqrt(91)/3 Signup and view all the answers

When a graph is symmetric about the origin, it is an ___ function.

[odd] Signup and view all the answers

When a graph is symmetric about the y-axis, it is an ___ function.

[even] Signup and view all the answers

A function is considered even if f(-x) = f(x).

True Signup and view all the answers

A function is considered odd if f(-x) = -f(x).

True Signup and view all the answers

What is true about the function y=1/2cos(2x)-1?

The midline of the function is y = -1 Signup and view all the answers

To create function d, what transformations occur?

Frequency [increases by a factor of 2] Signup and view all the answers

Which equation matches the function shown in the graph?

y = sin(x + pi/2) Signup and view all the answers

How long does it take for a friend in the left seat to move upward and back to the initial position?

4 seconds Signup and view all the answers

What function could represent the price tag's height relative to the table top after t seconds?

h(t) = -2cos(5x/2t)+2 Signup and view all the answers

What is the sample mean number of trees per block if there must be at least 18 trees?

21.3 Signup and view all the answers

Which statement is true about the survey of coffee and tea preferences?

The population proportion is not necessarily equal to the sample proportion Signup and view all the answers

What is the difference between the experimental probability and the theoretical probability in tire manufacturing?

0.4% Signup and view all the answers

If a soccer team wins 65% of matches, how many matches is it expected to lose out of 20?

4 Signup and view all the answers

What generalization can be made from the results of the grocery store study?

Twice as many shoppers select apples Signup and view all the answers

What kind of statistical study did Thad conduct when evaluating window cleaners?

Experiment Signup and view all the answers

Complete the missing values in the table and statement about positive and negative results below.

[Negative result], [Positive result] Signup and view all the answers

Which of the following situations are fair?

To decide which citizens will be asked to participate Signup and view all the answers

What is the mean midday temperature recorded in June in a city in Southern California?

36°C Signup and view all the answers

Summarize the normal distribution of tomatoes sold weekly by a grocery store.

There is an 84% chance that the grocery sells more than 390 tomatoes in a week Signup and view all the answers

The standard error of the mean of the sample is ____ hours.

[0.13] Signup and view all the answers

By the central limit theorem, which interval can the branch manager be 95% certain that the sample mean will fall within?

$44.87 and $46.93 Signup and view all the answers

What is the 90% confidence interval for the true proportion of club members who use compost?

[0.45] ± [0.05] Signup and view all the answers

What is the margin of error assuming a 95% confidence level in the restaurant's server study?

0.171 Signup and view all the answers

Which statements are true about the marketing department's fabrics?

Fabric B must be a medium-duty fabric Signup and view all the answers

What factor is most relevant when evaluating the report from the technology research group on game development?

28% of the respondents worked for game development companies Signup and view all the answers

Study Notes

Fundraising and Exponential Growth

Ms. Walker's class aims to raise $1,280, starting with a $5 deposit.
Weekly, the fund doubles, modeled by the equation 5(2)^x = 1,280; it takes 8 weeks to reach the goal.

Depreciation of Assets

Sam's car, valued at $17,930, depreciates at 19% annually.

Logarithmic Expressions

Equivalent expressions: log10(20x^5) - 1 simplifies to log10(10x).

Logarithmic Equations and Their Values

Corresponding values for logarithmic equations:
- log5x=4 → x = 625
- log4x=2 → x = 16
- log10x=3 → x = 1,000
- log2x=5 → x = 32

Solving Equations

Solve 1.5(4)^2x = 12 to find x ≈ 0.75.
Approximate solution for 4Inx - 8 = 12: x ≈ 148.4.

Transformations of Exponential Functions

Transformed function g(x) = 3f(x) where f(x) is the parent exponential function f(x) = e^x.
For g(x) = -2f(x) + 1 derived from f(x) = 10^x, the range is (-∞, 1).

Characteristics of Function Graphs

Function f has a range of all real numbers and decreases as x approaches 0.
Transformations of f(x) = ln x provide varying features, such as vertical asymptote and intercept changes.

Sequence Representation

Explicit form of the sequence 16, 24, 36, 54 is f(n) = 16(3/2)^(n - 1).

Planning and Profit Analysis

Natalie drives approximately 900 miles each month, starting at 800 miles.
Jessica's five-year total profit calculation remains unclear, initially posing a profit of $3,125 in the first year.

Sigma Notation

Conversions to sigma notation for series:
- 3 + 12 + 48 + 192 + 768 → 3(4)
- 4 + 32 + 256 + 2,048 + 16,384 → 4(8)

Graphical Transformations and Functions

Midline for function y = 1/2cos(2x) - 1 is at y = -1.
Graph transformations include shifts and frequency adjustments.

Angles and Trigonometry

Angle 0 = 7x/4 gives tan(0) = -1, with the reference angle being 45°.
For cos(0) = -3/10 in quadrant II, tan(0) value equals -√91/3.

Probability and Statistics

Function g exhibits continuity, with limits approaching positive infinity as x increases.
A factory's tire molding machine has a 0.2% failure rate, with actual faults at a 0.4% difference from theoretical.

Sampling and Confidence Intervals

A sample of 1,000 students reveals a 59% preference for coffee; the population proportion may differ.
The city council mandates at least 18 trees per block, averaging 21.3 trees, ensuring environmental standards.

Effectiveness of Products

Analysis concludes Fabric B as more durable than Fabric A based on double rub ratings, affirming its medium-duty classification.

Experimental Studies

Thad conducted an experiment to compare window cleaners by washing half the windows with each brand, demonstrating a practical study approach.

Growth Measurement in Gardening

Jane's marigold sapling grows at an increasing rate with decreasing average change over time.

Studying That Suits You

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Description

This quiz includes practice flashcards for Ms. Walker's Algebra 2B class. It focuses on exponential growth and solving equations related to a fundraising scenario. Test your understanding of functions and their applications in real-world problems.

Algebra 2B End of Semester Test

Questions and Answers

Which equation can be used to find the number of weeks, x, after which the balance of the fund will reach 1,280?

How many weeks will it take to reach the class goal of $1,280?

The value of Sam's car after one year is represented by 17,930(0.81)^x.

Which expressions are equivalent to log10(20x^5) - 1?

Match each logarithmic equation to its corresponding x-value:

What value of x satisfies the equation 1.5(4)^(2x) = 12?

What is the approximate solution to the equation 4ln(x) - 8 = 12?

What is the equation of the transformed function g in terms of f(x) = e^x?

What is the range of function g if g(x) = -2f(x) + 1?

The graph of function f has a range of {y| -infinity < x < infinity}.

Match each transformation of function f with a feature of the transformed function:

What is the explicit function that describes the sequence 16, 24, 36, 54...?

Select all functions that can be used to find the number of miles Natalie drives in a month.

What is the total profit Jessica earned in 5 years?

Match each series with the equivalent series written in sigma notation:

What does the function h(x) look like?

Function g is continuous.

What should Ronald do with the functions regarding the height of the chest?

Which expression is equal to f(x) * g(x)?

As x approaches positive infinity, f(x) approaches ___ and g(x) approaches ___.

What did Jane record about her marigold sapling?

What is the approximate value for the solution to the equation f(x) = g(x)?

Using a table of values, what is the approximate solution to the equation f(x) = g(x) to the nearest quarter of a unit?

To keep producing a specific shirt style, the company must make a profit of at least $5,000.

What are the two equations that represent Leo's savings plans?

Which statements are true about the measure of angle 0 being 7x/4?

If cos(0) = -3/10 and 0 is in quadrant II, what is the value of tan(0)?

When a graph is symmetric about the origin, it is an ___ function.

When a graph is symmetric about the y-axis, it is an ___ function.

A function is considered even if f(-x) = f(x).

A function is considered odd if f(-x) = -f(x).

What is true about the function y=1/2cos(2x)-1?

To create function d, what transformations occur?

Which equation matches the function shown in the graph?

How long does it take for a friend in the left seat to move upward and back to the initial position?

What function could represent the price tag's height relative to the table top after t seconds?

What is the sample mean number of trees per block if there must be at least 18 trees?

Which statement is true about the survey of coffee and tea preferences?

What is the difference between the experimental probability and the theoretical probability in tire manufacturing?

If a soccer team wins 65% of matches, how many matches is it expected to lose out of 20?

What generalization can be made from the results of the grocery store study?

What kind of statistical study did Thad conduct when evaluating window cleaners?

Complete the missing values in the table and statement about positive and negative results below.

Which of the following situations are fair?

What is the mean midday temperature recorded in June in a city in Southern California?

Summarize the normal distribution of tomatoes sold weekly by a grocery store.

The standard error of the mean of the sample is ____ hours.

By the central limit theorem, which interval can the branch manager be 95% certain that the sample mean will fall within?

What is the 90% confidence interval for the true proportion of club members who use compost?

What is the margin of error assuming a 95% confidence level in the restaurant's server study?

Which statements are true about the marketing department's fabrics?

What factor is most relevant when evaluating the report from the technology research group on game development?

Study Notes

Fundraising and Exponential Growth

Depreciation of Assets

Logarithmic Expressions

Logarithmic Equations and Their Values

Solving Equations

Transformations of Exponential Functions

Characteristics of Function Graphs

Sequence Representation

Planning and Profit Analysis

Sigma Notation

Graphical Transformations and Functions

Angles and Trigonometry

Probability and Statistics

Sampling and Confidence Intervals

Effectiveness of Products

Experimental Studies

Growth Measurement in Gardening

Studying That Suits You

Description

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