First let as solve all unit pirce
whistles 21.25 / 25 = $ 0.85 per unit
36 / 50 = $ 0.72 per unit
60 / 80 = $ 0.75 per unit
kazoos
10 / 25 = $ 0.4 per unit
18.50 / 50 = $ 0.37 per unit
27.20 / 80 = $ 0.34 per unit
a.) $ 0.85 - $ 0.72 = $ 0.13
b.) 10 / 25 = $ 0.4 per unit
c.) he must order 80 kazoos she should
order
Answer:
The answer to the question is
μx + (σx/4)
Step-by-step explanation:
The sample mean that is one standard deviations above the population mean is given by
value = μx + (Number of standard deviations)
(σx/√n)
value = μx + 1 (σx/√16)=
= μx + (σx/4) =
Where
μx = Population mean
σx = Population standard deviation
n = Sample size
The standard error of the mean is
σ/√n =σ/√16 = σ/4
The standard of error is an indication of the expected error in the mean of a sample from the mean of the population.
The above statements is based on the central limit theorem, which states that, in particular instances the normalized sum of independent random variables becomes closer and closer to those of normal distribution regardless of the variation in the sample of the variables
The feasible region is shown in the picture above. The horizontal axis is the X axis.
If you now draw a family of lines parallel to 
through the region, increasing $C$, that is, the X-intercept, we will have the maximum value of $C$ when the line passes through the endpoint $(-2,6)$ .
Hence, $C=5(-2)+4(6)=14$
Solve cos(4x)-cos(2x)=0 ∀ 0<=x<=2pi ..............(0)
Normal solution:
1. use the double angle formula to decompose, and recall cos^2(x)+sin^2(x)=1
cos(4x)=cos^2(2x)-sin^2(2x)=2cos^2(2x)-1 .................(1)
2. substitute (1) in (0)
2cos^2(2x)-1-cos(2x)=0
3. substitute u=cos(2x)
2u^2-u-1=0
4. Solve for x
factor
(u-1)(u+1/2)=0
=> u=1 or u=-1/2
However, since cos(x) is an even function, so solutions to
{cos(2x)=1, cos(-2x)=1, cos(2x)=-1/2 and cos(-2x)} ...........(2)
are all solutions.
5. The cosine function is symmetrical about pi, therefore
cos(-2x)=cos(2*pi-2x),
solution (2) above becomes
{cos(2x)=1, cos(2pi-2x)=1, cos(2x)=-1/2, cos(2pi-2x)=-1/2}
6. Solve each case
cos(2x)=1 => x=0
cos(2pi-2x)=1 => cos(2pi-0)=1 => x=pi
cos(2x)=-1/2 => 2x=2pi/3 or 2x=4pi/3 => x=pi/3 or 2pi/3
cos(2pi-2x)=-1/2 => 2pi-2x=2pi/3 or 2pi-2x=4pi/3 => x=2pi/3 or x=4pi/3
Summing up,
x={0,pi/3, 2pi/3, pi, 4pi/3}
