Sure, let's determine the mass of flour produced this week step-by-step.
1. Convert the Mixed Fraction to a Decimal:
The factory produced [tex]\(40 \frac{3}{4} \text{ kg}\)[/tex] of flour last week.
[tex]\[
40 \frac{3}{4} = 40 + \frac{3}{4}
\][/tex]
To convert [tex]\(\frac{3}{4}\)[/tex] to a decimal:
[tex]\[
\frac{3}{4} = 0.75
\][/tex]
Therefore,
[tex]\[
40 \frac{3}{4} = 40 + 0.75 = 40.75 \text{ kg}
\][/tex]
2. Determine the Production Percentage Increase:
The production this week is [tex]\(110\%\)[/tex] of last week's production.
To convert the percentage to a decimal form:
[tex]\[
110\% = \frac{110}{100} = 1.1
\][/tex]
3. Calculate the Production of Flour This Week:
Now, multiply last week's production by the percentage increase:
[tex]\[
\text{Flour produced this week} = 40.75 \text{ kg} \times 1.1
\][/tex]
4. Perform the Multiplication:
[tex]\[
40.75 \times 1.1 = 44.825 \text{ kg}
\][/tex]
Thus, the mass of flour produced this week is [tex]\(44.825 \text{ kg}\)[/tex].
\textbf{Answer:} 44.825 kg
