Business Math Quiz on Profit and Teams
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Questions and Answers

What is the profit function relationship when the club sells shirts?

  • y = \frac{2}{5}x + 5
  • y = \frac{5}{2}x - 5
  • y = \frac{5}{2}x + 4
  • y = \frac{2}{5}x + \frac{38}{5} (correct)
  • How many different 2-person teams can be formed from 19 students?

  • 38
  • 342 (correct)
  • 171
  • 9
  • What is the profit when the club sells 10 shirts?

  • $25
  • $10
  • $20 (correct)
  • $15
  • What is the maximum possible profit increase per shirt sold based on the information provided?

    <p>$2 (C)</p> Signup and view all the answers

    How many different teams can be chosen from a group of 10 students?

    <p>45 (C)</p> Signup and view all the answers

    What was the main reason plastic owls and floating balloons were used?

    <p>To deter flickers from occupying the area. (A)</p> Signup and view all the answers

    What impact did the flickers have on the Discovery's launch schedule?

    <p>The launch was delayed for five weeks. (C)</p> Signup and view all the answers

    Which option best describes the essay's primary focus?

    <p>The identification of wildlife interferences before a launch. (A)</p> Signup and view all the answers

    What is the consequence of focusing specifically on flickers in the essay?

    <p>It diverts attention from the technical aspects of the launch. (A)</p> Signup and view all the answers

    How might the primary purpose of the essay change if it aimed to describe a typical space shuttle launch?

    <p>It would include more technical specifications of the shuttle. (D)</p> Signup and view all the answers

    What does the reference to 'the unique nesting habits of the northern flicker' imply about the essay's content?

    <p>It introduces a critical interference in space operations. (C)</p> Signup and view all the answers

    What can be inferred about the use of the word 'incidentally' in the context?

    <p>It implies a minor relationship between the flickers and the launch. (D)</p> Signup and view all the answers

    Why would deleting the section about the flickers be considered?

    <p>It would make the paragraph more focused. (C)</p> Signup and view all the answers

    Which phrase best describes the atmosphere of the mural depicting workers?

    <p>motionless amidst movement (D)</p> Signup and view all the answers

    What emotional reaction does Yueming experience towards the figures in the mural?

    <p>Surprise at their incongruity (A)</p> Signup and view all the answers

    What is the significant detail regarding the child in the mural?

    <p>They are tugging at a kite (D)</p> Signup and view all the answers

    What does the phrase 'incongruous as they were' imply about the figures in the mural?

    <p>They seem out of place in the setting (C)</p> Signup and view all the answers

    What aspect of the city is highlighted by the mention of 'the Vine Street Expressway'?

    <p>The busy urban traffic (A)</p> Signup and view all the answers

    Which part of South Philadelphia is depicted in the mural?

    <p>Railroad construction (C)</p> Signup and view all the answers

    What can be inferred about the graduation referenced in the content?

    <p>It's the culmination of hard work (A)</p> Signup and view all the answers

    What does the term 'caught up in' imply about the workers in the mural?

    <p>They are focused intensely on their tasks (D)</p> Signup and view all the answers

    What was Pina Bausch's perspective on choreography?

    <p>She viewed dance as an expression of emotion. (B)</p> Signup and view all the answers

    What style did Bausch follow when she began her dance education?

    <p>Expressionism (C)</p> Signup and view all the answers

    Which of the following themes did Bausch NOT tackle in her work?

    <p>Joy (D)</p> Signup and view all the answers

    During which time period did German art flourish before WWII?

    <p>1920s (D)</p> Signup and view all the answers

    How did Bausch's works generally portray emotional feelings?

    <p>Through expressive and sometimes violent movements (D)</p> Signup and view all the answers

    What was the main focus of Expressionism in the artistic realm?

    <p>Exploring abstract concepts and emotions (B)</p> Signup and view all the answers

    What distinguishes Bausch's Tanztheater style from traditional ballet?

    <p>Focus on raw emotional expression instead of technical precision (B)</p> Signup and view all the answers

    How many small prisms have the same volume as the large prism if the volume of the large prism can be expressed as $3z$?

    <p>06 (B)</p> Signup and view all the answers

    When an octahedron is tossed, what is the probability that the number landing down is a prime or even number?

    <p>7/8 (C)</p> Signup and view all the answers

    What is the total profit from the sale of grass seeds on Friday and Saturday, given the profit per bag in matrix B?

    <p>$110.50 (B)</p> Signup and view all the answers

    Based on the relationship between red and white rods, which equation must hold true?

    <p>3R = 5W (A)</p> Signup and view all the answers

    What is the result of calculating (2 + 2i)²?

    <p>04 + 4i (B)</p> Signup and view all the answers

    If the equation $1/3 = 2^{x}$ holds true, what is the value of $x$?

    <p>-3 (D)</p> Signup and view all the answers

    In a geometric scenario involving prisms, how do you determine the ratio of the volumes of two prisms?

    <p>By multiplying base area and height for both (C)</p> Signup and view all the answers

    For all θ where cos(θ) and sin(θ) are not equal to zero, which expression equals to sec(θ) × tan(θ)?

    <p>1 (C)</p> Signup and view all the answers

    Which pair of villages indicates a valid starting and ending point for the mail carrier's route?

    <p>Ripley to Willa (C)</p> Signup and view all the answers

    What is the range of the function f(x) = 3 + (x² + 5x - 6)/(2x - 5x + 6)?

    <p>[−3, ∞) (D)</p> Signup and view all the answers

    What is the probability of rolling an even number on a fair 12-sided die?

    <p>1/2 (C)</p> Signup and view all the answers

    Which of the following represents a solution for the equation 2x - 3 = 7?

    <p>x = 5 (B)</p> Signup and view all the answers

    What outcome is impossible when rolling a fair 12-sided die?

    <p>Rolling a number greater than 12 (B)</p> Signup and view all the answers

    What was Pina Bausch's view of her role in the world of dance?

    <p>She identified more as a director than a choreographer. (A)</p> Signup and view all the answers

    Which style did Bausch follow at the beginning of her dance education?

    <p>Expressionism (D)</p> Signup and view all the answers

    What themes did Bausch explore in her dance pieces?

    <p>Identity and alienation (D)</p> Signup and view all the answers

    What aspect of Bausch's Tanztheater style was notable?

    <p>It emphasized raw emotional expression. (B)</p> Signup and view all the answers

    In which era did the Expressionism movement primarily flourish in German art?

    <p>In the 1920s up to World War II (A)</p> Signup and view all the answers

    What characterized the movements depicted in Bausch's work?

    <p>They often involved violent expressions. (D)</p> Signup and view all the answers

    How did Bausch's works differ from typical traditional ballet?

    <p>They emphasized emotional rather than technical expression. (C)</p> Signup and view all the answers

    What was an essential goal of Bausch's Tanztheater?

    <p>To explore the psychological motivations of movement. (B)</p> Signup and view all the answers

    Flashcards

    Expressionism

    A style of art that expresses strong inner emotions and often uses distorted figures and bold colors. It emerged around the early 20th century, influenced by the tumultuous period of World War I.

    Tanztheater

    A type of dance theatre developed by Pina Bausch, characterized by expressive, unconventional movements and emotional themes, blurring the lines between dance and theatre.

    What moves people, not how they move

    Pina Bausch's approach to dance, focusing on the underlying emotions and motivations behind movement rather than just technique.

    Deterrent strategies

    A strategy that discourages birds from settling in a particular location.

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    Plastic owls

    A device used to deter birds, resembling a predatory owl.

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    Floating balloons

    A lightweight object inflated with air, used for deterring birds.

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    Birds leaving for new territory

    Moving to a new area in search of food, shelter, or other resources.

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    Launch delay

    The delay of a scheduled event.

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    Fuel tank

    A part of a rocket or spacecraft that holds fuel.

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    Repairing the fuel tank

    The act of repairing something that is broken or damaged.

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    Focus of a paragraph

    To focus on one specific aspect or subject.

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    Solving an equation

    The process of finding the solutions (values of the variable) that make an equation true.

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    Equation

    A mathematical statement that expresses the equality of two expressions. It typically includes variables, coefficients, and constants.

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    R

    The number that represents the length of the red rod.

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    W

    The number that represents the length of the white rod.

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    Equivalent expressions

    Two expressions are equivalent if they represent the same value for all possible input values.

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    Algebraic equation

    A statement that expresses the equality of two different expressions involving variables.

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    Problem solving

    A process of understanding and applying mathematical relationships to solve real-world problems.

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    Range of a function

    The range of a function is the set of all possible output values.

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    Volume Ratio

    The number of small prisms that fit inside the large prism is equal to the ratio of their volumes. To find the volume of each prism, multiply the length, width, and height.

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    Solving exponential equations

    To solve for x, you need to isolate it. Remember that 64 is the same as 2^6. Then, use the rule of exponents that (a^m)^n = a^(m*n) to simplify the left side of the equation.

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    Probability of Prime or Even

    Each face of the octahedron has an equal chance of landing down. Prime numbers are numbers only divisible by 1 and itself(e.g., 2, 3, 5, 7, 11, 13, 17). Even numbers are divisible by 2. Count the favorable outcomes (prime or even numbers) and divide by the total number of outcomes.

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    Angle Bisector & Triangle Sum

    An angle bisector divides an angle into two equal angles. The sum of the angles inside a triangle is 180 degrees.

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    Matrix Multiplication for Profit

    Matrix multiplication involves multiplying corresponding entries of each row of the first matrix with corresponding columns of the second matrix. Multiply the price per bag by the number of bags sold for each type of seed and add the results to find the total profit.

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    Solving for x

    To solve the equation 36x-1 = 6, isolate the variable x. First, add 1 to both sides. Then, divide both sides by 36 to get x by itself.

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    Quadrilateral Angle Sum

    The sum of interior angles in any quadrilateral is 360 degrees. To find the missing angle, subtract the sum of the known angles from 360.

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    Solving for x

    To solve the equation 36x − 1 = 6, perform operations on both sides to isolate x. First, add 1 to both sides, then divide both sides by 36.

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    Finding Linear Equations From Data Points

    The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. To find the equation representing the relationship between the number of shirts sold (x) and the profit (y), we need to determine the slope (m) and the y-intercept (b).

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    Slope Formula

    The slope of a line passing through two points is defined by the difference in the y-coordinates divided by the difference in the x-coordinates.

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    Y-intercept Definition

    The y-intercept is the point where the line crosses the y-axis. In the slope-intercept form, the y-intercept is represented by 'b'.

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    Solving Systems of Equations

    To solve a system of equations, we need to find values for the variables that satisfy both equations simultaneously. One common method is elimination, where we manipulate the equations to eliminate one variable and solve for the other.

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    Combinations Formula

    The number of ways to choose a group of r objects from a set of n objects is given by the combination formula, denoted by nCr or (n choose r). The formula is n! / (r! * (n-r)!).

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    Quadratic Equation

    A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants with a ≠ 0. The roots of the quadratic equation are the values of x that satisfy the equation.

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    Discriminant of a Quadratic Equation

    The discriminant of a quadratic equation ax^2 + bx + c = 0 is given by b^2 - 4ac. The sign of the discriminant determines the nature of the roots: positive means two real roots, negative means two complex roots, and zero means one real root (a double root).

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    Real Roots of a Quadratic Equation

    A quadratic equation will have real roots if and only if the discriminant (b^2 - 4ac) is greater than or equal to zero.

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    What does 'incongruous' mean in this passage?

    In this context, "incongruous" means that something feels out of place or doesn't fit in with its surroundings. The mural's figures are frozen in time, while the real world continues to move around them.

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    What effect does the sentence "motionless—with the rush of Philadelphia’s urban city traffic heading for the Vine Street Expressway" have on the reader?

    The sentence describes the mural's figures as "motionless" even though they're depicted working, implying that they're trapped in a frozen moment in time. This creates a contrast with the dynamic, busy atmosphere of Philadelphia's traffic.

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    What is the main contrast being presented between the mural's depiction and the real world?

    The passage describes how the mural's figures, such as the immigrant workers and the child with a kite, are "incongruous" in relation to the bustling cityscape. This suggests that the mural is trying to show how these figures are both a part of and also stand apart from the city's life.

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    What does the phrase "caught up" signify in the sentence "others caught up in railroad construction"?

    The phrase "caught up" in the context of "others caught up in railroad construction" implies that the workers are actively engaged and involved in the process of building railroads. It suggests a sense of energy and focused effort.

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    What is the significance of the giant figure's gaze in the mural?

    The sentence describes a giant figure in the mural whose gaze is fixed on a passerby, indicating a watchful presence. This suggests that the mural might be trying to convey a sense of observation or surveillance.

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    What insight does the passage provide into the lives of the Chinese immigrant workers?

    The phrase "their jobs, one bent over a clothes iron" implies that the mural depicts people working and highlights their everyday tasks and livelihoods. It also emphasizes the hard work and dedication these individuals put into their labor.

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    Why is the child with a kite in the mural significant?

    The reference to the child playing with a kite in a schoolyard is meant to highlight the innocence and joy of childhood. This contrasts with the harsh realities of immigrant life and the toil of the railroad workers, creating a sense of balance in the mural's portrayal.

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    What is the purpose of mentioning the 'schoolyard' in the passage?

    The detail about the "schoolyard" suggests a familiar and safe space associated with youth and education, creating a sense of contrast with the harsh environment the immigrants are depicted in. This might be symbolic of the struggles faced by these individuals as they navigate a new country.

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    Study Notes

    ACT Form E26 Study Notes

    • Test Information Booklet: Contains test questions, scoring keys, and conversion tables for determining ACT scores.
    • Answer Report: Includes a record of each answer, correctness, and the correct answer for incorrect responses.
    • Copyright Restrictions: The test materials are protected by copyright and may not be copied or distributed without permission. Violators are subject to penalties.
    • Test Format: Tests are in English, mathematics, reading, and science.
    • Calculator Use: Calculators are allowed only on the mathematics test.
    • Answering Directions: Carefully read the directions for each section
    • Answering Procedure: Follow the process for each question: Identify the correct answer choice in each row, ensure to fill in the corresponding oval on the answer document completely, and use a soft lead pencil.
    • Testing Procedure: Work only when directed, use remaining time to review unanswered questions in that section, and do not move to a different test section unless told to do so. If you do move to a different section before time is called, the test result will be voided.
    • Penalties: No penalty for guessing, answer every question even if you must guess.
    • Answer Document: Only responses marked on the answer document will be scored.
    • Time Limits: Be aware of time limits for each test.

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    June 2022 Act1 Test PDF

    Description

    This quiz covers key concepts in business mathematics, focusing on profit functions and combinatorial calculations related to team formations. Test your understanding of how profit varies with shirt sales and the different ways to form teams from a group of students.

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