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Sagot :
Sure, let's work through the conversions step by step as per the table structure provided.
### A) Convert grams per liter to ounces per gallon
1. Initial Quantity and Units: 25 grams per liter (g/L)
2. First Ratio:
[tex]\[ \text{Convert grams to ounces: } 1 \text{ gram} = 0.035274 \text{ ounces} \][/tex]
[tex]\[ \text{Intermediate Quantity (ounces per liter)} = 25 \times 0.035274 = 0.88185 \text{ ounces per liter} \][/tex]
3. Second Ratio:
[tex]\[ \text{Convert liters to gallons: } 1 \text{ liter} = 0.264172 \text{ gallons} \][/tex]
[tex]\[ \text{Final Quantity (ounces per gallon)} = \frac{0.88185}{0.264172} \approx 3.338166 \text{ ounces per gallon} \][/tex]
So, our table would look like this for part A:
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline & \text{Initial Quantity} & \text{Initial Units} & \times & \text{First ratio} & \text{Units} & \times & \text{Second Ratio} & \text{Units} & & & & = & \text{Final Quantity} & \text{Final Units} & \text{Videos} \\ \hline (A) & 25 & g/L & \times & 0.035274 & oz/g & \times & \frac{1}{0.264172} & L/gallon & & & & = & 3.338166 & oz/gallon & > \\ \hline \end{array} \][/tex]
### B) Convert square meters per milliliter to square feet per teaspoon
1. Initial Quantity and Units: 5 square meters per milliliter (m²/mL)
2. First Ratio:
[tex]\[ \text{Convert square meters to square feet: } 1 \text{ square meter} = 10.7639 \text{ square feet} \][/tex]
[tex]\[ \text{Intermediate Quantity (square feet per milliliter)} = 5 \times 10.7639 = 53.8195 \text{ square feet per milliliter} \][/tex]
3. Second Ratio:
[tex]\[ \text{Convert milliliters to teaspoons: } 1 \text{ milliliter} = 0.202884 \text{ teaspoons} \][/tex]
[tex]\[ \text{Final Quantity (square feet per teaspoon)} = \frac{53.8195}{0.202884} \approx 265.2723 \text{ square feet per teaspoon} \][/tex]
So, our table would look like this for part B:
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline & \text{Initial Quantity} & \text{Initial Units} & \times & \text{First ratio} & \text{Units} & \times & \text{Second Ratio} & \text{Units} & & & & = & \text{Final Quantity} & \text{Final Units} & \text{Videos} \\ \hline (B) & 5 & m²/mL & \times & 10.7639 & ft²/m² & \times & \frac{1}{0.202884} & mL/teaspoon & & & & = & 265.2723 & ft²/teaspoon & D \\ \hline \end{array} \][/tex]
For the other parts, similar steps will be followed:
1. Identify the initial quantity and the unit conversions.
2. Apply the required unit conversion ratios.
3. Calculate the final quantities after each step.
If you have any other specific part or conversion to be detailed, please let me know!
### A) Convert grams per liter to ounces per gallon
1. Initial Quantity and Units: 25 grams per liter (g/L)
2. First Ratio:
[tex]\[ \text{Convert grams to ounces: } 1 \text{ gram} = 0.035274 \text{ ounces} \][/tex]
[tex]\[ \text{Intermediate Quantity (ounces per liter)} = 25 \times 0.035274 = 0.88185 \text{ ounces per liter} \][/tex]
3. Second Ratio:
[tex]\[ \text{Convert liters to gallons: } 1 \text{ liter} = 0.264172 \text{ gallons} \][/tex]
[tex]\[ \text{Final Quantity (ounces per gallon)} = \frac{0.88185}{0.264172} \approx 3.338166 \text{ ounces per gallon} \][/tex]
So, our table would look like this for part A:
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline & \text{Initial Quantity} & \text{Initial Units} & \times & \text{First ratio} & \text{Units} & \times & \text{Second Ratio} & \text{Units} & & & & = & \text{Final Quantity} & \text{Final Units} & \text{Videos} \\ \hline (A) & 25 & g/L & \times & 0.035274 & oz/g & \times & \frac{1}{0.264172} & L/gallon & & & & = & 3.338166 & oz/gallon & > \\ \hline \end{array} \][/tex]
### B) Convert square meters per milliliter to square feet per teaspoon
1. Initial Quantity and Units: 5 square meters per milliliter (m²/mL)
2. First Ratio:
[tex]\[ \text{Convert square meters to square feet: } 1 \text{ square meter} = 10.7639 \text{ square feet} \][/tex]
[tex]\[ \text{Intermediate Quantity (square feet per milliliter)} = 5 \times 10.7639 = 53.8195 \text{ square feet per milliliter} \][/tex]
3. Second Ratio:
[tex]\[ \text{Convert milliliters to teaspoons: } 1 \text{ milliliter} = 0.202884 \text{ teaspoons} \][/tex]
[tex]\[ \text{Final Quantity (square feet per teaspoon)} = \frac{53.8195}{0.202884} \approx 265.2723 \text{ square feet per teaspoon} \][/tex]
So, our table would look like this for part B:
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline & \text{Initial Quantity} & \text{Initial Units} & \times & \text{First ratio} & \text{Units} & \times & \text{Second Ratio} & \text{Units} & & & & = & \text{Final Quantity} & \text{Final Units} & \text{Videos} \\ \hline (B) & 5 & m²/mL & \times & 10.7639 & ft²/m² & \times & \frac{1}{0.202884} & mL/teaspoon & & & & = & 265.2723 & ft²/teaspoon & D \\ \hline \end{array} \][/tex]
For the other parts, similar steps will be followed:
1. Identify the initial quantity and the unit conversions.
2. Apply the required unit conversion ratios.
3. Calculate the final quantities after each step.
If you have any other specific part or conversion to be detailed, please let me know!
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