Ami is having a pizza party on Saturday night. She ordered 8 pizzas. If the average person eats 1/3 of a pizza, how many persons
2 answers:
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Answer:
Standard form of
Step-by-step explanation:
Here, the given expression is
Now, simplifying the above expression in parts, we get
hence, combining both parts:
=
The above expression is of the STANDARD FORM:
Hence, the standard form of
Answer:
So the value of height that separates the bottom 35% of data from the top 65% (Or the 35 percentile) is 146.7.
Step-by-step explanation:
1) Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
2) Solution to the problem
Let X the random variable that represent the scores on the LSAT of a population, and for this case we know the distribution for X is given by:
Where and
We want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.35 of the area on the left and 0.65 of the area on the right it's z=-0.385. On this case P(Z<-0.385)=0.35 and P(Z>-0.385)=0.65
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 35% of data from the top 65% (Or the 35 percentile) is 146.7.
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: ,