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Elina [12.6K]
3 years ago
14

The volume (in m3) of water in my (large) bathtub when I pull out the plug is given by f(t)=4−t2 (t is in minutes). This formula

is only valid for the two minutes it takes my bath to drain.
(a) Find the average rate the water leaves my tub between t=1 and t=2

(b) Find the average rate the water leaves my tub between t=1 and t=1.1

(c) What would you guess is the exact rate water leaves my tub at t=1

(d) In this bit h is a very small number. Find the average rate the water leaves my tub between t=1 and t=1+h (simplify as much as possible)

(e)

What do you get if you put in h=0 in the answer to (d)?
Mathematics
1 answer:
maks197457 [2]3 years ago
8 0
The answer is EEEEEE
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The thicknesses of 81 randomly selected aluminum sheets were found to have a variance of 3.23. Construct the 98% confidence inte
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Answer:

The confidence interval for the population variance of the thicknesses of all aluminum sheets in this factory is Lower limit = 2.30, Upper limit = 4.83.

Step-by-step explanation:

The confidence interval for population variance is given as below:

[(n - 1)\times S^{2}  /  X^{2}  \alpha/2, n-1 ] < \alpha < [(n- 1)\times S^{2}  / X^{2} 1- \alpha/2, n- 1 ]

We are given

Confidence level = 98%

Sample size = n = 81

Degrees of freedom = n – 1 = 80

Sample Variance = S^2 = 3.23

X^{2}_{[\alpha/2, n - 1]}   = 112.3288\\\X^{2} _{1 -\alpha/2,n- 1} = 53.5401

(By using chi-square table)

[(n – 1)*S^2 / X^2 α/2, n– 1 ] < σ^2 < [(n – 1)*S^2 / X^2 1 -α/2, n– 1 ]

[(81 – 1)* 3.23 / 112.3288] < σ^2 < [(81 – 1)* 3.23/ 53.5401]

2.3004 < σ^2 < 4.8263

Lower limit = 2.30

Upper limit = 4.83.

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Which of the following expressions simplifies to a negative number? Select all that apply.
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Step-by-step explanation:

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