Find the dimensions of the closed rectangular box with maximum volume that can be inscribed in the unit sphere.

Response: Using the Pythagorean theorem, we can set up the equation as 14^2=9^2+x^2

                                     -9^2    -9^2

Thus, our equation simplifies to

x^2=14^2-9^2

Answer: F(x) > 0 in the ranges (-0.7, 0.76) and (0.76, ∞).

I hope this is useful:)

Answer:

Step-by-step explanation:

Step 1

Calculate the slope of the dashed line

The slope between two points is computed with the formula:

We consider

(-3,1) and (0,3)

and substitute into it:

Step 2

Determine the equation of the dashed line in slope-intercept form:

The equation we established is:

---> associated problem

Substituting yields:

Step 3

Establish the inequality corresponding to the graph

Given that it is represented by a dashed line, the area to the left of this line is shaded.

Thus,

Refer to the attached diagram for enhanced understanding of the problem.

a) The hypothesis states that the mean is different from 0.5025 and has been rejected. b) The p-value computed is 0. c) A confidence interval is established as 0.50456 < u < 0.50464. The hypothesis testing is based on a given standard deviation (s.d.) of 0.0001, a sample mean of x = 0.5046 from a sample size of n = 25. The two-sided alternative and significance level of 0.05 were assumed. A Z-score was calculated to show that the hypothesis is rejected since the mean differs from 0.5025.

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