Question

17 the wheels on a bicycle each have a diameter of 670 mm.
the wheels turn 10 times.
approximately how many metres has the bicycle travelled?
10 m
21 m
42 m
352 m

18 which expression is equivalent to 3x^2 - 9x + x^3?
3(x^2 - 3x + x^3)
3x(x - 3 + x^2)
x^3(3x^2 - 9x + x^3)
x(3x - 9 + x^2)

19 jenny asked 35 people whether they work, go to school, do both or do neither.
the venn diagram shows the results.
what is the probability that a person randomly selected from the group goes to school and works, rounded to three decimal places?
0.943
0.100
0.091
0.086
0.057

Explanation:

Calculate distance traveled by the bicycle

Using the Geometric Formulas and Unit Conversion knowledge points:

1. The diameter of each wheel is \(d = 670\text{ mm}\).
2. The circumference \(C\) of a wheel represents the distance traveled in one full turn:

$$C = \pi \cdot d = \pi \cdot 670\text{ mm} \approx 2104.87\text{ mm}$$

1. For 10 turns, the total distance is:

$$\text{Distance} = 10 \cdot C \approx 21048.7\text{ mm}$$

1. Convert millimeters to meters:

$$\text{Distance in meters} = \frac{21048.7\text{ mm}}{1000\text{ mm/m}} \approx 21.05\text{ m}$$

This rounds to approximately \(21\text{ m}\).

Factor the algebraic expression

To find which expression is equivalent to \(3x^2 - 9x + x^3\):

1. Identify the greatest common factor (GCF) of the terms \(3x^2\), \(-9x\), and \(x^3\). The GCF is \(x\).
2. Factor out \(x\) from each term:

$$3x^2 - 9x + x^3 = x(3x - 9 + x^2)$$

1. Comparing this with the options, it matches \(x(3x - 9 + x^2)\).

Calculate the probability from the Venn diagram

Using the Theoretical Probability knowledge point:

1. The total number of people surveyed is \(N = 35\).
2. The number of people who both go to school and work is represented by the intersection of the two sets in the Venn diagram, which is \(3\).
3. The probability \(P\) of randomly selecting a person who does both is:

$$P = \frac{3}{35} \approx 0.08571$$

1. Rounding to three decimal places gives \(0.086\).

Answer:

Question 17

• 10 m
• 21 m (Correct answer)
• 42 m
• 352 m

Question 18

• \(3(x^2 - 3x + x^3)\)
• \(3x(x - 3 + x^2)\)
• \(x^3(3x^2 - 9x + x^3)\)
• \(x(3x - 9 + x^2)\) (Correct answer)

Question 19

• 0.943
• 0.100
• 0.091
• 0.086 (Correct answer)
• 0.057