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Brums [2.3K]
3 years ago
10

Use the identity a^3+b^3=(a+b)^3−3ab(a+b) to determine the sum of the cubes of two numbers if the sum of the two numbers is 4 an

d the product of the two numbers is 1.
Mathematics
1 answer:
Butoxors [25]3 years ago
5 0

a^3+b^3=(a+b)^3-3ab(a+b)\\\\a+b=4,\ ab=1\\\\\text{Substitute:}\\\\a^3+b^3=(4)^3-3(1)(4)=64-12=52

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A random sample of 121 automobiles traveling on an interstate showed an average speed of 65 mph. From past information, it is kn
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Answer:

95 percent confidence interval for μ is determined by

(60.688 ,  69.312)

a) be the same

Step-by-step explanation:

<u>Step (i)</u>:-

Given data a random sample of 121 automobiles traveling on an interstate showed an average speed of 65 mph.

The sample size is n= 121

The mean of the sample x⁻ = 65mph.

The standard deviation of the population is 22 mph

σ = 22mph

<u>Step (ii) :</u>-

Given  The 95 percent confidence interval for μ is determined as

(61.08, 68.92)

we are to reduce the sample size to 100 (other factors remain unchanged) so

given The sample size is n= 100

The mean of the sample x⁻ = 65mph.

The standard deviation of the population is 22 mph

σ = 22mph

<u>Step (iii)</u>:-

95 percent confidence interval for μ is determined by

(x^{-} - 1.96\frac{S.D}{\sqrt{n} } , x^{-} + 1.96 \frac{S.D}{\sqrt{n} } )

(65 - 1.96\frac{22}{\sqrt{100} } , 65 + 1.96 \frac{22}{\sqrt{100} } )

(65 - 4.312 ,65 +4.312)

(60.688 ,  69.312) ≅(61 ,69)

This is similar to (61.08, 68.92) ≅(61 ,69)

<u>Conclusion</u>:-

it become same as (61.08, 68.92)

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