Answer:
1 apple
Step-by-step explanation:
2 apples - 1 apple would equal 1 apple
Answer:
x=pi/3 + 2pi*k
x=2pi/3+2pi*k
Step-by-step explanation:
sin(x)=sqrt(3)/2
This happens twice in the first rotation on our unit circle.
It happens in the first quadrant and in the second quadrant. Third and fourth quadrants are negative for sine.
So we are looking for when the y-coordinate on the unit circle is sqrt(3)/2.
This is at pi/3 and 2pi/3.
So we can get all the solutions by adding +2pi*k to both of those. This gives us a full rotation about the circle any number of k times. k is an integer.
So the solutions are
x=pi/3 + 2pi*k
x=2pi/3+2pi*k
Looks like the given curve is
5<em>xy</em> + <em>z</em>⁴<em>x</em> - 3<em>yz</em> = 3
Differentiate both sides with respect to <em>x</em> :
5<em>y</em> + 4<em>z</em>³<em>x</em> ∂<em>z</em>/∂<em>x</em> + <em>z</em>⁴ - 3<em>y</em> ∂<em>z</em>/∂<em>x</em> = 0
Solve for ∂<em>z</em>/∂<em>x</em> :
(4<em>z</em>³<em>x</em> - 3<em>y</em>) ∂<em>z</em>/∂<em>x</em> = - (5<em>y</em> + <em>z</em>⁴)
∂<em>z</em>/∂<em>x</em> = - (5<em>y</em> + <em>z</em>⁴) / (4<em>z</em>³<em>x</em> - 3<em>y</em>)
At the point (1, 1, 1), this derivative is
∂<em>z</em>/∂<em>x</em> (1, 1, 1) = - (5 + 1) / (4 - 3) = -6
Answer:
The 99% confidence level for the proportion of all American youngsters who are seriously overweight is (0.137, 0.163)
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of 
, and a confidence level of 
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of 
.
For this problem, we have that:
99% confidence level
So 
, z is the value of Z that has a pvalue of 
, so 
.
The lower limit of this interval is:
The upper limit of this interval is:
The 99% confidence level for the proportion of all American youngsters who are seriously overweight is (0.137, 0.163)
