Answer:
(c) 43.
Step-by-step explanation:
Given:
Margin of error (E) = 2
Sample variance
= 44
Confidence level = 95%
The z- value at 95% confidence level is 1.96.
The sample using the provided information can be calculated as:

Hence, the correct option is (c) 43.
Answer:

Step-by-step explanation:
Given
See attachment for diagram
Required
The equation to find x
First, calculate the area of the big rectangle using:

So:

The smaller rectangle

The difference between this areas give the area of the shaded region.
So:


Open brackets

Collect like terms


<em>The above equation can be used to solve for x</em>
Answer:

Step-by-step explanation:
P, A, and R are collinear.
PR = 54


To solve for the numerical length of PR, let's generate an equation to find the value of x.
According to the segment addition postulate:

(substitution)
Solve for x

Combine like terms


Add 2 to both sides


Divide both sides by 7



Plug in the value of x into the equation


Answer:
A=L*W
Let w be width
L=(w+6)
40=(w+6)*w
40= w^{2} +6w
w^{2} +6w-40=0
w^{2}+10w-4w-40=0
w(w+10)-4(w+10)=0
(w-4)(w+10)=0
w=4
Length= 10 units
Width=4 units
Step-by-step explanation: