Answer:
Length = 5p + 3
Perimeter = 26p + 6
Step-by-step explanation:
Given
Area = 40p² + 24p
Width = 8p
Solving for the length of deck
Given that the deck is rectangular in shape.
The area will be calculated as thus;
Area = Length * Width
Substitute 40p² + 24p and 8p for Area and Width respectively
The formula becomes
40p² + 24p = Length * 8p
Factorize both sides
p(40p + 24) = Length * 8 * p
Divide both sides by P
40p + 24 = Length * 8
Factorize both sides, again
8(5p + 3) = Length * 8
Multiply both sides by ⅛
⅛ * 8(5p + 3) = Length * 8 * ⅛
5p + 3 = Length
Length = 5p + 3
Solving for the perimeter of the deck
The perimeter of the deck is calculated as thus
Perimeter = 2(Length + Width)
Substitute 5p + 3 and 8p for Length and Width, respectively.
Perimeter = 2(5p + 3 + 8p)
Perimeter = 2(5p + 8p + 3)
Perimeter = 2(13p + 3)
Open bracket
Perimeter = 2 * 13p + 2 * 3
Perimeter = 26p + 6
Correct answer is third option ---C in edge
Using the z-distribution, it is found that the 90% confidence interval is given by: (0.6350, 0.6984).
<h3>What is a confidence interval of proportions?</h3>
A confidence interval of proportions is given by:
In which:
is the sample proportion.
In this problem, we have a 90% confidence level, hence
, z is the value of Z that has a p-value of 
, so the critical value is z = 1.645.
The sample size and the estimate are given by:
Hence, the bounds of the interval are given by:
The 90% confidence interval is given by: (0.6350, 0.6984).
More can be learned about the z-distribution at brainly.com/question/25890103
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There are 1000 millimeters in a meter and 0.001 meters in a millimeter
