Answer: 
Step-by-step explanation:
This is a <em>homogeneous linear third-order differential equation</em>
z′′′+2z′′−4z′−8z=0 so the
FIRST STEP is to find the characteristic equation and its roots
<em>
</em>
Using the method of finding roots of a polynomial (using m = 2) would provide the solution below
(m-2)(m+2)(m+2)=0; m = 2 and m = -2 (repeated twice)
SECOND STEP is to write the general solution with the arbitrary constants.
The general solution based on the roots and the using x as the independent variable would provide
<em>*It should be noted that when the characteristic equation has a repeated root, the general equation form becomes similar to the last part of the answer*</em>
Answer:
H0 : p = 0.028
H1: p > 0.028
We conclude that there is not enough evidence to support the school counselor's claim they the use of electronic cigarettes in high school is higher Than 2.8%
Type 11 error
Step-by-step explanation:
H0 : p = 0.028
H1: p > 0.028
If null should not be rejected then;
We conclude that there is not enough evidence to support the school counselor's claim they the use of electronic cigarettes in high school is higher Than 2.8%
3.)
If the actual proportion is 0.034, which means 3.4%, this means it is actually higher. For failing to reject a false Null, then a type 11 error has been committed
Answer: see proof below
<u>Step-by-step explanation:</u>
Use the following Half-Angle Identities: tan (A/2) = (sinA)/(1 + cosA)
cot (A/2) = (sinA)/(1 - cosA)
Use the Pythagorean Identity: cos²A + sin²B = 1
Use Unit Circle to evaluate: cos 45° = sin 45° = 
<u>Proof LHS → RHS</u>
Given: 
Rewrite Fraction: 
Half-Angle Identity: 
Substitute: 
Simplify: 
= 2
LHS = RHS: 2 = 2 
The correct answer is B-It has to be less than 100.
What is the measure of arc ADB?
The measure of the arc for this case is given by the following angle:
theta = 360-90
theta = 270 degrees
What is the length of arc ADB?
The arc length is given by:
s = R * theta
Substituting values:
s = 15 * (270 * (pi / 180))
s = 70.69 m
What is the area of the shaded region?
The area of the shaded region is:
A = (s' / s) * (pi) * (r ^ 2)
Substituting values:
A = (270/360) * (3.14) * (15 ^ 2)
A = 529,875 m ^ 2
