Which of the following descriptions correctly represents the relationship between the number of black dots…

Question

Which of the following descriptions correctly represents the relationship between the number of black dots (n) and grey dots (G) if G = 4n + 4?

ScanSolve AI Tutor · Accepted Answer

Let's test each description against the actual relationship between the number of black dots ( $n$ ) and grey dots ( $G$ ). From the previous problem, we established that the correct relationship is $G = 4n + 4$ .

2.11.1 The number of black dots $\rightarrow \times 4 \rightarrow + 2 \rightarrow$ the number of grey dots
This description translates to the formula $G = 4n + 2$ .

Test for $n=1$ (1 black dot).
According to the description: $G = 4(1) + 2 = 4 + 2 = 6$ .
From the pattern, for $n=1$ , the number of grey dots is 8.
Since $6 \neq 8$ , the description is incorrect for $n=1$ .
Test for $n=2$ (2 black dots).
According to the description: $G = 4(2) + 2 = 8 + 2 = 10$ .
From the pattern, for $n=2$ , the number of grey dots is 12.
Since $10 \neq 12$ , the description is incorrect for $n=2$ .

Conclusion: This description is $\boxed{\text{Incorrect}}$ .

2.11.2 To calculate the number of grey dots you multiply the number of black dots by 2 and add 1 and multiply the answer by 2.
This description translates to the formula $G = (2n + 1) \times 2$ .
Simplifying this formula: $G = 4n + 2$ .
Test for $n=1$ (1 black dot).
According to the description: $G = (2(1) + 1) \times 2 = (2 + 1) \times 2 = 3 \times 2 = 6$ .
From the pattern, for $n=1$ , the number of grey dots is 8.
Since $6 \neq 8$ , the description is incorrect for $n=1$ .
Test for $n=2$ (2 black dots).
According to the description: $G = (2(2) + 1) \times 2 = (4 + 1) \times 2 = 5 \times 2 = 10$ .
From the pattern, for $n=2$ , the number of grey dots is 12.
Since $10 \neq 12$ , the description is incorrect for $n=2$ .

Conclusion: This description is $\boxed{\text{Incorrect}}$ .

2.11.3 The number of grey dots = 2 x the number of black dots + 4.
This description translates to the formula $G = 2n + 4$ .
Test for $n=1$ (1 black dot).
According to the description: $G = 2(1) + 4 = 2 + 4 = 6$ .
From the pattern, for $n=1$ , the number of grey dots is 8.
Since $6 \neq 8$ , the description is incorrect for $n=1$ .
Test for $n=2$ (2 black dots).
According to the description: $G = 2(2) + 4 = 4 + 4 = 8$ .
From the pattern, for $n=2$ , the number of grey dots is 12.
Since $8 \neq 12$ , the description is incorrect for $n=2$ .

Conclusion: This description is $\boxed{\text{Incorrect}}$ .

It appears none of the provided descriptions correctly describe the relationship. The correct relationship is $G = 4n + 4$ .

Which of the following descriptions correctly represents the relationship between the number of black dots (n) and grey dots (G) if G = 4n + 4?

Step-by-step solution

Test for $n=1$ (1 black dot).

Test for $n=2$ (2 black dots).

Test for $n=1$ (1 black dot).

Test for $n=2$ (2 black dots).

Test for $n=1$ (1 black dot).

Test for $n=2$ (2 black dots).

Still stuck on this one?

More Mathematics Questions

Which of the following descriptions correctly represents the relationship between the number of black dots (n) and grey dots (G) if G = 4n + 4?

Step-by-step solution

Test for n=1n=1n=1 (1 black dot).

Test for n=2n=2n=2 (2 black dots).

Test for n=1n=1n=1 (1 black dot).

Test for n=2n=2n=2 (2 black dots).

Test for n=1n=1n=1 (1 black dot).

Test for n=2n=2n=2 (2 black dots).

Still stuck on this one?

More Mathematics Questions

Test for $n=1$ (1 black dot).

Test for $n=2$ (2 black dots).

Test for $n=1$ (1 black dot).

Test for $n=2$ (2 black dots).

Test for $n=1$ (1 black dot).

Test for $n=2$ (2 black dots).