Answer the statistical measures and create a box and whiskers plot for the following set of data. 4,4,5,5, 6, 6, 8, 10, 11, 11,
12, 14 Min: Q1: Med: Q3: Max: Create the box plot by dragging the lines: 2 3 4 b 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 answer:
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Answer:
1) , 2) The domain of S is
. The range of S is
, 3)
, 4)
, 5)
Step-by-step explanation:
1) The function of the box is:
2) The maximum cutout is:
The domain of S is . The range of S is
3) The surface area when a 1'' x 1'' square is cut out is:
4) The size is found by solving the following second-order polynomial:
5) The equation of the box volume is:
The first derivative of the function is:
The critical points are determined by equalizing the derivative to zero:
The second derivative is found afterwards:
After evaluating each critical point, it follows that is an absolute minimum and
is an absolute maximum. Hence, the value of the cutoff so that volume is maximized is:
The surface area of the box is: