Using Lagrange multipliers, we have the Lagrangian
with partial derivatives (set equal to 0)
Substituting the first three equations into the fourth allows us to solve for
:
For each possible value of
, we get two corresponding critical points at
.
At these points, respectively, we get a maximum value of
and a minimum value of
.
Answer:
D) 2p+14/p
Step-by-step explanation:
Y = 2/3x
it's the best answer
Given:
Total length of tape in roll = 16.8 meters
Length of each piece = 1.125 meters
Number of pieces = 8
To find:
The remaining tape.
Solution:
We have,
Length of 1 piece = 1.125 meters
Length of 8 piece = 8 × 1.125 meters
= 9 meters
Total length of tape in roll = 16.8 meters
Remaining tape = Total length of tape in roll - Length of 8 piece
= 16.8 - 9 meters
= 7.8 meters
Therefore, the length of remaining tape is 7.8 meters.
a. The standard error is equal to the standard deviation divided by the square root of the sample size:
SE = (23 ppm)/√18 ≈ 5.42 ppm
b. The t statistic is given by the difference between the true and sample means, divided by the standard error:
t = (192 ppm - 180 ppm)/SE ≈ 2.21
c. The p-value is approximately 0.0204.
d. Since p < 0.05, the difference is significantly different, so we reject the null hypothesis.
e. A type I error might have occurred, since it's possible that the null hypothesis was true, but we ended up rejecting it.
