Answer:
Hence the width, length is 20 cm and height is 10 cm
Step-by-step explanation:
Since the box has a square base, let length = width = x. Also, let the height = y, therefore:
The volume of box = width * length * height
4000 = x * x * y
4000 = x²y
y=4000/x²
The surface area (SA) = area of the base + sum of the area of each side
SA = x² + xy + xy + xy + xy
SA = x² + 4xy
substitute y = 4000/x²
SA = x² + 4x(4000/x²)
SA = x² + 16000/x
Taking the derivative:
SA' = 2x - 16000/x²
making SA' = 0:
0 = 2x - 16000/x²
2x = 16000/x²
2x³ = 16000
x³ = 8000
x = 20 cm
y = 4000 / x² = 4000 / 20² = 10 cm
Hence the width, length is 20 cm and height is 10 cm
Answer: If the level of confidence is increased without changing the sample size then<em> </em><u><em>The margin of error will decrease because the critical value will decrease. The decreased margin of error will cause the confidence interval to be narrower.</em></u>
where;
<em>Margin of error = Critical value × Standard deviation</em>
<em>Here, it can be duly noted that Margin of error has a positive relation with critical value, i.e </em><u><em>The margin of error will decrease because the critical value will decrease.</em></u>
<u><em>whereas;</em></u>
The confidence interval is <em>the value ± the margin of error.</em>
<em>Therefore, </em><u><em>the decreased margin of error will cause the confidence interval to be narrower.</em></u>
Answer:
25%
Step-by-step explanation:
Given data
Last years shipment= 37220 lamps
These years shipment= 29776 lamps
% Decrease= Initial-Final/Initial*100
% Decrease= 37220-29776/29776*100
% Decrease= 7444/29776*100
% Decrease= 0.25*100
% Decrease= 25%
Hence the decrease is 25%
Answer:
5x + 3y = 2
5x - 3y = -22
Step-by-step explanation:yes
Answer:
8.12
Step-by-step explanation:
We obtain the distance between x and y
d = sqrt[(x2 - x1)² + (y2 - y1)²]
d = sqrt[(1 - 2)² + (2 - 6)²]
d = sqrt[1 + 16)
d = sqrt(17)
d² = 17
From Pythagoras rule;
Hypotenus = sqrt(Adjacent² + opposite²)
Hence,
Hypotenus = sqrt(17 + 7²)
Hypotenus = sqrt(17+ 49)
Hypotenus = sqrt(66)
Hypotenus = 8.124
Hypotenus = 8.12