Answer:
the lines are perpendicular
Answer:
Step-by-step explanation:
top = 120sq m
middle = 17sq cm
bottom = 102 sq feet
Answer:
9x
Step-by-step explanation:
3y +2x-3y +7x
Combine like terms
2x+7x +3y-3y
(2+7)x +(3-3)y
9x +0y
9x
Solution:
There is no saddle point (DNE). However, there is local maximum at (1, 1/2) for the given function.
Explanation:
we have function of two variables f(x,y)= 9-2x+4y-x^2-4y^2
we will find the values by partial derivative with respect to x,y,xy
= -2 -2x
= 4 -8y
to find the saddle point we should first find the critical points so equate
-2 -2x=0 and 4 -8y=0
we get x= 1 and y =1/2 so, critical points are (1,1/2)
to find local maximum or minimum we have to find
,
and
formula is
*
-
=0
= -2
= -8
=0
putting values in formula
(-2)*(-8) -0 =16 > 0, and
< 0 and
<0
so, here we have local maximum
we have no saddle point for this function by using the same formula we used to find extrema.
Answer:

And using the normal atandard table or excel we got:

Step-by-step explanation:
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".
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Solution to the problem
Let X the random variable that represent the length of the tape of a population, and for this case we know the following parameters
Where
and
We sselect a sample size of n =78>30. From the central limit theorem we know that the distribution for the sample mean
is given by:
And we want to find this probability:

And using the normal atandard table or excel we got:
