Share £747 in the ratio 2:7 between Tom and Ben
1 answer:
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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:
The expected combined weight of the child's lollipop and two chocolate bars is 5.5 oz.
Step-by-step explanation:
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Addition of normal variables:
The mean is the sum of the means.
Find the expected combined weight of the child's lollipop and two chocolate bars.
Child lollipop: Mean 1.5 oz
Chocolate bars: Mean 2 oz
One lollipop and 2 bars combined
The mean will be 1.5 + 2*2 = 5.5 oz
The expected combined weight of the child's lollipop and two chocolate bars is 5.5 oz.
They would have to buy 32 cans and would have 24 ounces left.
