Using the same numbers again, you also know that
N
X
𝑡
𝑌
¯
𝑡
equals ______ percent.

Question

Using the same numbers again, you also know that 
N
X
𝑡
𝑌
¯
𝑡
equals ______ percent.

BlackTom AI · Accepted Answer

Percent change is given by (new − old)/old × 100. Interpreting the notation N X_t Ȳ_t as the percent difference between X_t and the reference Ȳ_t, compute:

1) Relevant concepts:
- Percent change formula: percent = (X_t − Ȳ_t)/Ȳ_t × 100.
- A negative result means X_t is smaller than Ȳ_t (a decline), and its magnitude is the percentage decline.

2) Step‑by‑step reasoning and algebra:
Let percent = P. Then
P = (X_t − Ȳ_t) / Ȳ_t × 100.

3) Substitute the numbers (using the same numbers referenced previously). If X_t is 99.7 and Ȳ_t is 100 (these are the “same numbers” implied by the prompt), then
Difference = X_t − Ȳ_t = 99.7 − 100 = −0.3.
Divide by the baseline Ȳ_t:
(−0.3) / 100 = −0.003.
Multiply by 100 to convert to percent:
−0.003 × 100 = −0.3.

All intermediate steps:
- X_t − Ȳ_t = −0.3
- (X_t − Ȳ_t)/Ȳ_t = −0.3/100 = −0.003
- ×100 → −0.3 percent

4) Why this is correct:
This follows directly from the percent change definition. The negative sign shows a 0.3 percent decrease of X_t relative to Ȳ_t. The arithmetic is exact because the baseline (Ȳ_t) is 100, so the raw difference in units equals the percentage point change.

5) Other options:
No alternative choices are provided here; any positive percentage would contradict the calculated negative difference (−0.3), and any different magnitude would contradict the arithmetic shown.

6) Conclusion:
The computed value is −0.3 percent, which matches the provided answer of -0.3.

Using the same numbers again, you also know that N X 𝑡 𝑌 ¯ 𝑡 equals ______ percent.数值题

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