If a multiple choice test consists of questions, each of which with of which only 1 is correct, (a) in how many different way
1 answer:
Answer:
Step-by-step explanation:
From the given information.
suppose a multiple choice test consists of 5 questions, each with 4 possible answers of which 1 is correct.:
So, we can now suggest that a person can answer each question in 4 different ways given that there are 5 different questions.
Thus, the students can check off one answer to each question in
= 4 × 34 × 4 × 4 × 4
= 1024 different ways.
From the 4 possible answers, since 1 will be correct, definitely 3 other answers will be incorrect.
Thus, the number of ways a student can check off one answer to each question and get all the answers wrong is = 3⁵
= 3 × 3 × 3 × 3 × 3
= 243 ways
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Answer:
Saddle point:
Local minimum:
Local maxima: ,
Step-by-step explanation:
The function is:
The partial derivatives of the function are included below:
Local minima, local maxima and saddle points are determined by equalizing both partial derivatives to zero.
It is quite evident that one point is (0,0). Another point is found by solving the following system of linear equations:
The solution of the system is (3/8, -3/8).
Let assume that y = 0, the nonlinear system is reduced to a sole expression:
Another solution is (9/8,0).
Now, let consider that x = 0, the nonlinear system is now reduced to this:
Another solution is (0, -9/8).
The next step is to determine whether point is a local maximum, a local minimum or a saddle point. The second derivative test:
The second derivatives of the function are:
Then, the expression is simplified to this and each point is tested:
S1: (0,0)
(Saddle Point)
S2: (3/8,-3/8)
(Local maximum or minimum)
S3: (9/8, 0)
(Local maximum or minimum)
S4: (0, - 9/8)
(Local maximum or minimum)
Unfortunately, the second derivative test associated with the function does offer an effective method to distinguish between local maximum and local minimums. A more direct approach is used to make a fair classification:
S2: (3/8,-3/8)
(Local minimum)
S3: (9/8, 0)
(Local maximum)
S4: (0, - 9/8)
(Local maximum)
Saddle point:
Local minimum:
Local maxima: ,