Sure, let’s break down the two parts of the question step-by-step to provide detailed solutions.
### Part 1:
Question: The mass of which one of the following is usually measured in tones?
- (a) a parcel
- (b) a packet of sugar
- (c) a person's body
- (d) a packet of biscuits
- (e) A lorry's load
Solution:
1. Parcel: Generally, the mass of parcels varies widely, but they are typically measured in grams or kilograms, not tones.
2. Packet of Sugar: Sugar packets are usually quite small, typically measured in grams or kilograms.
3. Person's Body: Body weights are commonly measured in kilograms.
4. Packet of Biscuits: Similar to sugar packets, these are usually measured in grams or kilograms.
5. A Lorry's Load: Lorry (truck) loads can be extremely heavy and are often measured in large units such as tones.
Correct Answer: The mass of a lorry’s load is usually measured in tones. Thus, the answer is (e) A lorry's load.
### Part 2:
Question: The mean of three numbers is 6. The mode of the three numbers is the lowest of the 3 numbers.
- (a) 2
- (b) 3
- (c) 6
Solution:
1. Calculate the Sum of the Numbers:
- The mean of three numbers is given as 6.
- If we denote the three numbers as [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]:
[tex]\[
\frac{a + b + c}{3} = 6
\][/tex]
- Multiply both sides by 3:
[tex]\[
a + b + c = 18
\][/tex]
2. Determine the Mode:
- Mode is the most frequent number in a set.
- Given condition: The mode of the three numbers is the lowest number among the three.
3. Considering Different Number Patterns:
- Let’s assume that the lowest number is [tex]\(a\)[/tex] and it appears at least twice for it to be the mode.
- For [tex]\(a\)[/tex] to be the mode and the lowest number, consider the following scenarios:
1. [tex]\(a, a, x\)[/tex]
2. All numbers could be the same, i.e., [tex]\(a = b = c\)[/tex]
4. Trial values:
- Suppose all three numbers are equal:
[tex]\[
\frac{a + a + a}{3} = 6 \implies 3a = 18 \implies a = 6
\][/tex]
This makes all numbers 6, and the mode is also 6. But we are asked for the smallest mode other than 6.
- Let’s now consider the numbers [tex]\(a, a, x\)[/tex]:
[tex]\[
2a + x = 18
\][/tex]
If [tex]\(a\)[/tex] is the lowest of the two repeated:
[tex]\[
a = 2
\][/tex]
Then calculate [tex]\(x\)[/tex]:
[tex]\[
2(2) + x = 18 \implies 4 + x = 18 \implies x = 14
\][/tex]
Here, 2 is the lowest and is the mode because it appears twice.
Correct Answer: Thus, considering the modes and the conditions given, the lowest number (mode) is 2. So, the answer is (a) 2.
### Final Answers:
1. The mass of a lorry's load is usually measured in tones: (e) A lorry's load
2. The mode of the three numbers, considering the lowest value: (a) 2
