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Calculate (in a simplified fraction) the probability of choosing a green marble. Solve for y in the following diagram: Consider the diagram alongside. Write down (with reason) the value of x:

Mathematics

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3 parts
2.1

110\frac{1}{10}

3.1

60∘60^\circ

3.2

75∘75^\circ

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Part 2

Part 2.1

110\frac{1}{10}

Calculate (in a simplified fraction) the probability of choosing a green marble.

  1. Identify the number of green marbles and the total number of marbles.

    Number of green marbles = 4
    Total number of marbles = 40

  2. Write the probability as a fraction.

    P(Green)=Number of green marblesTotal number of marbles=440P(\text{Green}) = \frac{\text{Number of green marbles}}{\text{Total number of marbles}} = \frac{4}{40}
  3. Simplify the fraction.

    Divide both the numerator and the denominator by their greatest common divisor, which is 4.

    P(Green)=4÷440÷4=110P(\text{Green}) = \frac{4 \div 4}{40 \div 4} = \frac{1}{10}

    The probability of choosing a green marble is: 110\boxed{\frac{1}{10}}

Part 3

Part 3.1

60∘60^\circ

Solve for yy in the following diagram

  1. Identify the relationship between the angles 2y2y and yy.

    The angles 2y2y and yy are adjacent angles on a straight line. Angles on a straight line sum to 180∘180^\circ.

  2. Set up the equation and solve for yy.

    2y+y=180∘2y + y = 180^\circ 3y=180∘3y = 180^\circ y=180∘3y = \frac{180^\circ}{3} y=60∘y = 60^\circ

    The value of yy is: 60∘\boxed{60^\circ}

Part 3.2

75∘75^\circ

Consider the diagram alongside. Write down (with reason) the value of xx

  1. Identify the relationship between the angle 75∘75^\circ and angle xx.

    The angles 75∘75^\circ and xx are vertically opposite angles.

  2. State the value of xx and the reason.

    Vertically opposite angles are equal.
    Therefore, x=75∘x = 75^\circ.
    The value of xx is: 75∘\boxed{75^\circ} (Reason: Vertically opposite angles are equal)

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