Elena spent 45 minutes at the library, half an hour at the grocery store, 20 minutes visiting a friend, and arrived home at 4:10
1 answer:
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Answer:
B. Larger sample size and lower confidence level
Step-by-step explanation:
The margin of error of a confidence interval is given by the following formula:
In which is the standard deviation of the population and n is the size of the sample.
z is related to the confidence level. The higher the confidence level, the higher the value of Z.
So, the margin of error is direct proportion to the confidence level and inverse proportional to the sample size.
We want to decrease the margin of error.
So the correct answer is:
B. Larger sample size and lower confidence level
Answer:
The maximum value= 36
Minimum value = - 36
Step-by-step explanation:
Given that
f(x, y, z) = 8 x + 8 y + 4 z
h(x,y,z)=4 x² + 4 y² + 4 z² - 36
From Lagrange multipliers
Δf = λ Δh
Δf = < 8 ,8 , 4>
Δh = < 8 x ,8 y , 8 z>
Δf = λ Δh
So
< 8 ,8 , 4> = < 8 λ x ,8 λ y , 8 λ z>
8 = 8 λ x -------------1
8 = 8 λ y ---- ------2
4 = 8 λ z ----------------3
From equation 1 ,2 and 3
Now by putting the value of x,y and z in the following equation
4 x² + 4 y² + 4 z² = 36
So the value of λ is
When λ = 1/2
x = 1 / λ , y=1 / λ , z= 1 /2 λ
x= 2 , y = 2 , z=1
So
f(x, y, z) = 8 x + 8 y + 4 z
f(2, 2, 1) = 8 x 2 + 8 x 2 + 4 x 1
f(2, 2, 1) =36
When λ = - 1/2
x = 1 / λ , y=1 / λ , z= 1 /2 λ
x= - 2 , y = - 2 , z= - 1
So
f(x, y, z) = 8 x + 8 y + 4 z
f(-2, -2, -1) = 8 x (-2) + 8 x (-2) + 4 x (-1)
f(-2, -2, -1) = - 36
The maximum value= 36
Minimum value = - 36