Answer:
All of these are the same. I would say D as theya re the same.
The largest possible volume of the given box is; 96.28 ft³
<h3>How to maximize volume of a box?</h3>
Let b be the length and the width of the base (length and width are the same since the base is square).
Let h be the height of the box.
The surface area of the box is;
S = b² + 4bh
We are given S = 100 ft². Thus;
b² + 4bh = 100
h = (100 - b²)/4b
Volume of the box in terms of b will be;
V(b) = b²h = b² * (100 - b²)/4b
V(b) = 25b - b³/4
The volume is maximum when dV/db = 0. Thus;
dV/db = 25 - 3b²/4
25 - 3b²/4 = 0
√(100/3) = b
b = 5.77 ft
Thus;
h = (100 - (√(100/3)²)/4(5.77)
h = 2.8885 ft
Thus;
Largest volume = [√(100/3)]² * 2.8885
Largest Volume = 96.28 ft³
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Answer:
The annual interest rate is 4%
The equation that represents the linear function for the set of ordered pairs is: A. y = -3x + 2.
<h3>What is the Equation of a Linear Function?</h3>
Equation of a linear function, where m is the slope and b is the y-intercept, is expressed as y = mx + b.
Find the slope (m):
Slope (m) = change in y/change in x = (-7 -(-4)) / (3 - 2)
Slope (m) = -3/1 = -3
Find b by substituting m = -3 and (1, -1) = (x, y) into y = mx + b:
-1 = -3(1) + b
-1 = -3 + b
-1 + 3 = b
2 = b
b = 2
Substitute m = -3 and b = 2 into y = mx + b
y = -3(x) + 2
y = -3x + 2
Therefore, the equation that represents the linear function for the set of ordered pairs is: A. y = -3x + 2.
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Answer:
Step-by-step explanation:
<u>Total cost of nuts, including the discount and the tax:</u>
- (0.1 + 0.13 + 0.26)*20*[(100- 30)/100]*[(100 + 5.25)/100] = 7.22 (rounded)
<u>Total cost of bolts, including the discount and the tax:</u>
- (0.45 + 0.52 + 0.63+0.93)*35*[(100- 45)/100]*[(100 + 5.25)/100] = 51.26 (rounded)
<u>Total amount Carl paid:</u>
Correct choice is B
