Consider sampling heights from the population of all female college soccer players in the United States. Assume the mean height

Answer: CI = (0, 8)

Step-by-step explanation: The confidence interval for the difference in means is given as

Lower limit

= (x1 - x2) + margin of error

Upper limit

= (x1 - x2) - margin of error

Where x1 - x2 = 8 and the margin of error = 8

For the lower limit,

= 8 - 8 = 0

For the upper limit

= 8 + 8 = 16

Thus, CI = (0, 8)

Detailed explanation:

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Answer:

  (1/10)∛100 ≈ 0.4642

Step-by-step explanation:

For a cubic shape with volume V, the edge length is defined as...

  s = ∛V

and the surface area is given by...

  A = 6s² = 6V^(2/3)

The area-to-volume ratio is therefore...

  r1 = A/V = 6V^(2/3)/V = 6V^(-1/3)

When the volume V is increased by a factor of 10, the new area-to-volume ratio becomes...

  r2 = 6(10V)^(-1/3)

Consequently, the change factor for the ratio is...

  r2/r1 = (6(10V)^(-1/3))/(6V^(-1/3)) = 10^(-1/3) = (1/10)∛100

The change in surface area per unit volume results in a factor of (∛100)/10.

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Example

For a cube with side length 2, the corresponding volume equals 2³ = 8, with a surface area of 6·2² = 24. The resulting area-to-volume ratio is 24/8 = 3.

The area-to-volume ratio changed by a factor of (0.3∛100)/3 = (∛100)/10, as previously noted.

Answer:

Detailed steps:

y – 4 = –1 (x – 2)

y – 7 = –1 (x + 1)

y = –x + 6

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