The solution is x = 6
Step-by-step explanation:
Let us revise some rules of the exponents
- If
, then n = m 
∵ 
∵ 9 = 3 × 3
∴ 9 = 3²
- Substitute 9 by 3² in the equation above
∴ 
- Use the second rule above for the left hand side
∵ 
∴ 
∴ 
- By using the first rule above
∴ 2x + 30 = 7x
- Subtract 2x from both sides
∴ 30 = 5x
- Divide both sides by 5
∴ 6 = x
The solution is x = 6
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Answer:
None of the above
Step-by-step explanation:
According to the divergence test, if the limit of a sequence as n approaches infinity does not equal 0, then the series diverges. (Notice that if the limit does equal 0, the series doesn't necessarily converge).
According to the geometric series test, a geometric series converges if -1 < r < 1, and diverges otherwise.
The first series is a geometric series with r = -5/3. So it diverges.
The second series is also a geometric series:
3ⁿ⁻¹ / 2ⁿ = ⅓ (3ⁿ / 2ⁿ) = ⅓ (3/2)ⁿ
r = 3/2, so it diverges.
For the third series, the limit as n approaches infinity equals 1. This fails the divergence test, so this series also diverges.
For the fourth series, the limit as n approaches infinity equals 1. This fails the divergence test, so this series also diverges.
Answer:
A
Step-by-step explanation:
Answer:
Step-by-step explanation:
Since the population standard deviation 
, is known, we use the z confidence interval for the mean.
This is given by:
For a 95% confidence interval we use 
.
It was also given that: 
, 
and 
Let us substitute the values to get:
<u>Interpretation:</u>
We can say with 95% confidence that the interval between 1463.3 and 1580.7 SAT scores contains the population mean based on the sample 125 SAT scores.
