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arsen [322]
3 years ago
11

All of the following are equal except___. 1/4^3 4^5/4^ 4^-3 4^2/4^5

Mathematics
1 answer:
Mariulka [41]3 years ago
5 0

Answer:

\frac{4^{5}}{4^{2}}\\

Step-by-step explanation:

\frac{1}{4^{3}} =4^{-3}\\\\4^{-3}\\\\\frac{4^{2}}{4^{5}}=4^{2-5}=4^{-3}

But 4^5/4^{2} = 4^3

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Answer:

a. (29526.192 , 32155.808)

b. (29673.9301 , 32008.0699)

Step-by-step explanation:

on calculation, we find that sample mean = 30843 and sample standard deviation = 3018.504, and n=20

1)

Sample Mean = 30841

SD = 3000

Sample Size (n) = 20

Standard Error (SE) = SD/root(n) = 670.8204

alpha (a) = 1 - 0.95 = 0.05

z critical value for 95% confidence interval:

z(a/2) = z(0.025) = 1.96

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95% confidence interval is given by:

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2)when std dev of population is not known, we use sample's, but we have to use t instead of z

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SD = 3018.504

Sample Size (n) = 20

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alpha (a) = 1-0.9 = 0.1

we use t-distribution as population standard deviation is unknown

t(a/2, n-1 ) = 1.7291

Margin of Error (ME) = t(a/2,n-1)x SE = 1167.0699

90% confidence interval is given by:

Sample Mean +/- (Margin of Error)

30841 +/- 1167.0699 = (29673.9301 , 32008.0699)

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