Gallons 11 10 9 8 7 6 5 4 3 2 1 0 0 10 20 litres 30 40 50 The graph shows the relationship between litres and gallons. a) Convert 41 litres to gallons. b) Convert 3.5 gallons to litres.
The Correct Answer and Explanation is:
Converting Volume Measurements
I’ve begun examining the conversion graph provided, focusing initially on the x-axis, which displays litres, and its correlation with gallons. Currently, I’m analyzing the 10-litre intervals marked on the x-axis, aiming to grasp the precise relationship between litres and gallons for an accurate conversion of 41 litres.
Determining the Precise Gallon Value
I’m now zeroing in on pinpointing the exact gallons value for 41 litres. The graph indicates it’s just shy of the 9-gallon mark. To be precise, I’m examining the slope to derive the most accurate gallons for 41 litres, aiming for a definitive answer. I’m focusing on finding the corresponding value on the y-axis.
Precising Gallon Calculation
I’ve determined that the conversion of 41 litres to gallons is approximately 9.1 gallons. To achieve precision, I utilized the line’s slope, derived a conversion factor of approximately 0.222 gallons per litre, and then calculated 41 litres to gallons. The graph reading and calculation align with 9.1 gallons, confirming the result.
Determining Gallons from Litres
Currently, I’m working meticulously through the graph to get an accurate litres-to-gallons conversion. I’m focusing on deriving a precise conversion factor using the provided linear line. My analysis, using the slope and graph reading, has concluded that 41 litres is roughly equivalent to 9.1 gallons.
Calculating Gallons for 41 Litres
I’m now carefully double-checking the graph readings for maximum accuracy. My calculations and graph analysis converge on 9.1 gallons as the precise equivalent of 41 litres, a figure I’m confident in now. I’ve verified the slope, conversion factor, and multiple graph points for a robust conclusion.
Calculating Part B of the Problem
I’m now focusing on part B, aiming to convert 3.5 gallons to liters using the graph. I’m carefully reading the graph at the 3.5-gallon mark on the y-axis, trying to ascertain the corresponding liters value on the x-axis for precision. I am confident in finding the exact litres value based on visual reading.
Finalizing Litre-Gallon Conversions
I’m now concluding the analysis, confident in the conversions. For 41 liters, the reading is approximately 9.1 gallons, aligning with calculations. For 3.5 gallons, the graph indicates approximately 15.75 liters. I’ve cross-referenced points and derived the formula to ensure precision.
Revisiting Graph Conversions
I’m revisiting the graph now, to convert 3.5 gallons to litres. Upon careful examination, 3.5 gallons on the y-axis aligns with approximately 15.75 liters on the x-axis, using the line’s slope, aligning with previous computations and supporting a likely value of 15.8 or even a rough estimate of 16 litres.
I’ve now meticulously reviewed the graph, performing detailed calculations. For 41 liters, the conversion to gallons is approximately 9.1, confirming prior estimations. For the second part, 3.5 gallons converts to around 15.8 liters, aligning with precise calculations and visual readings.
Calculating Accurate Litre Conversions
I’m now focusing on deriving precise values, reviewing the graph and cross-checking calculations. For 41 litres, my analysis confirms 9.1 gallons, and for 3.5 gallons, the figure is approximately 15.8 liters, or a rougher 16, which is aligned.
I’m now focusing on calculating 3.5 gallons to litres, and will then synthesize all findings, confirming the conversions. I’ve re-examined 41 liters, reading around 9.1 gallons, and for 3.5 gallons, I’m finding roughly 15.8 liters via careful calculations.
Finalizing Conversion Analysis
I’m now fully confident in the graph analysis and calculations. For 41 liters, the precise answer is 9.1 gallons. For converting 3.5 gallons, the most accurate value is 15.8 liters, which accounts for precision and the graph reading.
Calculating and Confirming Conversions
I’ve carefully considered the graph’s intricacies, ensuring precise conversion rates. After in-depth analysis and calculation verification, 9.1 gallons equals 41 liters, while 3.5 gallons precisely converts to 15.8 liters, which accounts for precision and graph reading.
Synthesizing Conversions
I’ve re-examined the key calculations and graph readings to solidify the results. With further analysis, the conversion for 41 liters is precisely 9.1 gallons, and for 3.5 gallons, it’s 15.8 liters, which accounts for the most accurate calculation.
Calculating Accurate Conversions
I’m now fully prepared to finalize the conversion problem, armed with detailed calculations and meticulous graph readings. After thorough examination, I can confidently confirm that 41 liters converts precisely to 9.1 gallons, and 3.5 gallons is equivalent to 15.8 liters.
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Here are the correct answers and the explanation for how to solve the problems using the provided graph.
a) 9.1 gallons
b) 15.8 litres
Explanation
The provided graph shows a linear relationship between volume in litres (on the horizontal x-axis) and volume in gallons (on the vertical y-axis). To perform the conversions, we must first understand the scale of the graph.
- Litres (x-axis): The major grid lines are marked in intervals of 10. There are 10 small squares between each mark, so each small horizontal square represents 1 litre.
- Gallons (y-axis): The major grid lines are marked in intervals of 1. There are 5 small squares between each mark, so each small vertical square represents 1 divided by 5, which is 0.2 gallons.
a) Convert 41 litres to gallons
To convert 41 litres to gallons, you start by finding the value 41 on the x-axis. This is one small square to the right of the major grid line for 40. From this point, trace a line vertically up until it intersects with the blue conversion line.
Next, from this point of intersection on the blue line, trace a line horizontally to the left until you reach the y-axis. You can then read the corresponding value in gallons. The horizontal line falls just above the major grid line for 9 gallons. It is about halfway up the first small square above the 9-gallon mark. Since each small square is 0.2 gallons, this position represents approximately 9.1 gallons.
b) Convert 3.5 gallons to litres
To convert 3.5 gallons to litres, you start by finding the value 3.5 on the y-axis. This value is exactly halfway between the major grid lines for 3 and 4 gallons. From this 3.5-gallon mark, trace a line horizontally to the right until it meets the blue conversion line.
From that point of intersection, trace a line vertically down to the x-axis to find the equivalent value in litres. The vertical line lands between the marks for 15 and 16 litres, but it is much closer to 16. A careful reading shows the line at about 15.75 or 15.8 litres. For a more precise calculation, we can see from the graph that 10 gallons equals 45 litres, meaning 1 gallon is 4.5 litres. Therefore, 3.5 gallons is equal to 3.5 times 4.5, which is 15.75 litres. So, 15.8 litres is a very accurate reading from the graph.
