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Answer:
1242.81
Step-by-step explanation:
Answer:
(364.595 ; 391.405)
Step-by-step explanation:
Given the sample data:
406, 385, 389, 383, 352, 379, 388, 343, 368, 387
Using calculator :
Sample mean, xbar = 378
Standard deviation, s = 18.74
Confidence interval :
Xbar ± Margin of error
Margin of Error = Tcritical * s/√n
TCritical at df = 24 ; 0.05 = 2.262
Margin of Error = 2.262 * 18.74/√10 = 13.405
Lower boundary = (378 - 13.405) = 364.595
Upper boundary = (378 + 13.405) = 391.405
(364.595 ; 391.405)
Answer:
Step-by-step explanation:
The the area of the rectangular pen be A = LW
L is the length
W is the width
Given
A = 3136ft²
3136 = LW..........1
Given the perimeter P = 2L+2W....... 2
From 1; L = 3136/W
Substitute into 2
P = 2(3136/W)+2W
P = 6272/W + 2W
In order to minimize the amount of material needed, then dP/dW = 0
dP/dW = -6272/W² + 2
0 = -6272/W² + 2
6272/W² = 2
cross multiply
6272 = 2W²
W² = 3136
W = √3136
W = 56ft
Since A = LW
3136 = 56L
L = 3136/56
L = 56ft
Hence the dimensions of the rectangular pen that minimize the amount of material needed is 56ft by 56ft
