The answer to this question is C.
Based on dimensional analysis and unit conversion theory we conclude that an area of 359 square inches is equivalent to an area of 2.5 square feet.
<h3>How to apply dimensional analysis in unit conversion</h3>
In this question we need to convert a magnitude in a given unit to an <em>equivalent</em> magnitude with another unit. According to dimensional analysis, <em>unit</em> conversions are represented by the following expression:
y = A · x (1)
Where:
- x - Original magnitude, in square inches.
- y - Resulting magnitude, in square feet.
- A - Conversion factor, in square feet per square inch.
Dimensionally speaking, area is equal to the product of length and length:
[Area] = [Length] × [Length]
And a feet is equivalent to 12 inches. Now we proceed to convert the magnitude to square feet:
x = 359 in² × (1 ft/12 in) × (1 ft/12 in)
x = 359 in² × (1 ft²/144 in²)
x = 2.5 ft²
Based on dimensional analysis and unit conversion theory we conclude that an area of 359 square inches is equivalent to an area of 2.5 square feet.
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(16^6-45) 3
(16,777,216-45) 3
(16,777,171) 3
50,331,513
The linear relationship in the form y = y = 3n + 72
What is linear relationship?
In statistics, a straight line of correlation between two variables is referred to as a linear relationship (or linear association). The mathematical equation y = mx + b can be used to represent linear relationships graphically.
<h3>According to the given information :</h3>
Each plant generates 34 oz of beans when she plants 30 stalks, and 33 stalks results in 33 oz of beans per plant, according to the information we have provided.
Equation 1 using data 1:
y = mn + b
Equation 1 using data 1:
30 = 34m + b
Equation 2 using data 2:
33 = 33m + b
Subtract equation 1 from equation 2:
33 - 30 = 34m + b - 33m - b
3 = m
m = 3
Rearrange equation 1 to solve for b:
b = 34(3) - 30
b = 102 - 30
b = 72
Therefore the equation becomes:
y = 3n + 72
The linear relationship in the form y = y = 3n + 72
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Equation A find “m” and “b”:
“B” is the y-intercept when x = 0. They give this in the table as “-2” so b = -2
Find slope (m) = (-8)-(-2)/(-2)-0 = 3
Equation A is y = 3x - 2 (y = mx + b)
Equation B find “m” and “b”:
Find m = (-9)-(-5)/(-3)-(-1) = 2
To find be, plug in m, x, and y from ANY coordinates in table b into y = mx + b:
-9 = 2(-3) + b
-9 = -6 + b
b = -3
Equation b is y = 2x -3
Use substitution and substitute all of equation “b” for “y” in equation a:
2x - 3 = 3x - 2
Algebra: x = -1
Plug back into equation a:
y = 3(-1) -2
y = -5
x = -1
(-1, -5) final answer (B)
