PLEASE SOMEBODY HELP. I NEED ANSWERS . HOMEWORK IS DUE TODAY!!!!

Mathematics

1 answer:

Semmy [17]3 years ago

7 0

Step-by-step explanation:

hint: anthing with a 0 on top is always equal to 1

example: 3⁰ = 1, 4⁰ = 1

1 16⁰ = 1

2. 4^-2 = 8

3. 3⁻³= -3 x -3 x -3 = -27

4. 8⁻⁴ = -8 x -8 x -8 x -8 = 4,096

5. 1/ 2³ = 2³ = 8

6. 4/ ⁻³ = 2²/2⁻⁶ = 2⁸

7. 3 x 8⁰ = 3 x 1 = 3

8. 2 x 2⁻² = 2⁻¹ = 1/2 or 0.5 0r 2⁻¹

9. (-7)⁻² = 1/49

10. 9⁰ = 1

11. 2/2⁻¹ = 4

12. 8⁻²/ 80 = 2⁻⁶ or 1/64

13. 5 x 6⁰ = 5 because 6⁰ = 1 and 5 x 1 = 5

14. (-4.9)⁰ = 1

15. 7⁻²/7⁻¹ = 1/7 or 7⁻¹

16. x⁻⁸ = 1/ x⁸

17. xy⁻³ = X/y³

18. a⁻⁸b = b/a⁸

19. m²n⁻⁹ = m²/ n⁹

20. 1/x⁻⁷ = x⁷

21. 3/ a⁻⁴ = 3a⁴

22. 5/d⁻³ = 5d³

23. 6/ r-8s⁻¹ = 6s/ rs-8

24. 8a⁻³b²c⁻² = 8b²/a³c²

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A researcher reports survey results by stating that the standard error of the mean is 25 the population standard deviation is 40

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Answer:

a) A sample of 256 was used in this survey.

b) 45.14% probability that the point estimate was within ±15 of the population mean

Step-by-step explanation:

This question is solved using the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .