1. Jackie is a toll booth employee. One day, she wrote the expression: 0.75m = 15.75
1 answer:
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Answer:
The width of the box is 6.7 cm
The maximum volume is 148.1 cm³
Step-by-step explanation:
The given parameters of the box Jorge is asked to build are;
The maximum girth of the box = 20 cm
The nature of the sides of the box = 2 square sides and 4 rectangular sides
The side length of square side of the box = w
The length of the rectangular side of the box = l
Therefore, we have;
The girth = 2·w + 2·l = 20 cm
∴ w + l = 20/2 = 10
w + l = 10
l = 10 - w
The volume of the box, V = Area of square side × Length of rectangular side
∴ V = w × w × l = w × w × (10 - w)
V = 10·w² - w³
At the maximum volume, we have;
dV/dw = d(10·w² - w³)/dw = 0
∴ d(10·w² - w³)/dw = 2×10·w - 3·w² = 0
2×10·w - 3·w² = 20·w - 3·w² = 0
20·w - 3·w² = 0 at the maximum volume
w·(20 - 3·w) = 0
∴ w = 0 or w = 20/3 = 6.
Given that 6. > 0, we have;
At the maximum volume, the width of the block, w = 6. cm ≈ 6.7 cm
The maximum volume, , is therefore given when w = 6.
cm = 20/3 cm as follows;
V = 10·w² - w³
= 10·(20/3)² - (20/3)³ = 4000/27 = 148.
The maximum volume, = 148.
cm³ ≈ 148.1 cm³
Using a graphing calculator, also, we have by finding the extremum of the function V = 10·w² - w³, the coordinate of the maximum point is (20/3, 4000/27)
The width of the box is;
6.7 cm
The maximum volume is;
148.1 cm³
Answer:
The correct options are;
B) The mean and median for the security company are both lower than the mean and the median for the collections performed by other companies
B) Since the security company appear to have collected lower revenue than other companies, there is some evidence of stealing by the security company's employees
Step-by-step explanation:
We use the acronym SC for the security company and OC for the other company
SC OC
1.6 1.5
1.8 2.1
1.6 1.9
1.8 2.2
1.7 1.9
1.2 1.7
1.1 2.1
1.2 2.2
1.2 2.2
1.5 1.8
∑x 14.7 19.6
The mean is given by ∑x/n
n = 10
SC OC
∴ Mean 1.47 1.96
The median is the
Hence
SC OC
Median 1.55 2
Therefore, the mean and median for the security company are both lower than the mean and the median for the collections performed by other companies.
b) Since the security company appear to have collected lower revenue than other companies, there is some evidence of stealing by the security company's employees.