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Siphe makes 6 paper flowers in 2/3 of an hour. If she spent the same amount of time on each flower, how long does it take her to make one flower?

Mathematics

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Answer

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Step-by-step solution

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Part 2.5· 1 step

Siphe makes 6 paper flowers in 23\frac{2}{3} of an hour. If she spent the same amount of time on each flower, how long does it take her to make one flower?

  1. Divide the total time by the number of flowers to find the time per flower.

    Time per flower=Total timeNumber of flowers\text{Time per flower} = \frac{\text{Total time}}{\text{Number of flowers}} Time per flower=23 hour÷6\text{Time per flower} = \frac{2}{3} \text{ hour} \div 6 Time per flower=23×16\text{Time per flower} = \frac{2}{3} \times \frac{1}{6} Time per flower=218\text{Time per flower} = \frac{2}{18} Time per flower=19 hour\text{Time per flower} = \frac{1}{9} \text{ hour}

    The correct option is a).

    • a) 19 of an hour\boxed{\text{a) } \frac{1}{9} \text{ of an hour}}

Part 2.6· 2 steps

The ratio of Daniela's age to her brother's age is 2:3. If Daniela is 12 years old now, how old was her brother 4 years ago?

  1. Determine the brother's current age using the given ratio.

    Let Daniela's current age be DD and her brother's current age be BB.
    The ratio D:B=2:3D:B = 2:3.
    Given D=12D = 12 years.

    DB=23\frac{D}{B} = \frac{2}{3} 12B=23\frac{12}{B} = \frac{2}{3} 2B=12×32B = 12 \times 3 2B=362B = 36 B=362B = \frac{36}{2} B=18 years oldB = 18 \text{ years old}

  2. Calculate the brother's age 4 years ago.

    Brother’s age 4 years ago=Current age−4\text{Brother's age 4 years ago} = \text{Current age} - 4 Brother’s age 4 years ago=18−4\text{Brother's age 4 years ago} = 18 - 4 Brother’s age 4 years ago=14 years old\text{Brother's age 4 years ago} = 14 \text{ years old}

    The correct option is a).

    • a) 14 years old\boxed{\text{a) } 14 \text{ years old}}

Part 2.7· 2 steps

Which one of the following is the diameter?

  1. Recall the definition of a diameter.

    A diameter is a straight line segment that passes through the center of a circle and has its endpoints on the circumference.

  2. Examine the options based on the definition and the provided diagram.

Part a

OA: This is a radius (from center O to point A on circumference).

Part b

OB: This is a radius (from center O to point B on circumference).

Part c

AC: This is a chord (connects two points on the circumference but does not pass through the center).

Part d

AB: This is a line segment connecting points A and B on the circumference and passing through the center O. This matches the definition of a diameter.

The correct option is d).

  • d) AB\boxed{\text{d) AB}}

Part 2.8· 2 steps

A cube has a volume of 64 cm364 \text{ cm}^3, what is the length of one of its sides?

  1. Write down the formula for the volume of a cube.

    The volume VV of a cube with side length ss is given by:

    V=s3V = s^3

  2. Substitute the given volume and solve for the side length ss.

    64 cm3=s364 \text{ cm}^3 = s^3

    To find ss, take the cube root of both sides:

    s=64 cm33s = \sqrt[3]{64 \text{ cm}^3} s=4 cms = 4 \text{ cm}

    The correct option is a).

    • a) 4 cm\boxed{\text{a) } 4 \text{ cm}}
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