To find the length of the envelope, we can multiply the height of the envelope by the factor that gives the length in relation to the height.
Given:
- Height of the envelope = 3 inches
- Length is given as 4 9/10 times the height
First, we convert 4 9/10 to an improper fraction:
\[ 4 \frac{9}{10} = \frac{40}{10} + \frac{9}{10} = \frac{49}{10} \]
Now we can calculate the length of the envelope:
\[ \text{Length} = \text{Height} \times \text{Factor} \]
We substitute the values:
\[ \text{Length} = 3 \times \frac{49}{10} \]
We convert 3 to a fraction:
\[ 3 = \frac{30}{10} \]
Now we can multiply the fractions:
\[ \text{Length} = \frac{30}{10} \times \frac{49}{10} = \frac{30 \times 49}{10 \times 10} = \frac{1470}{100} \]
Next, we simplify \(\frac{1470}{100}\):
Both the numerator and denominator can be divided by 10:
\[ \frac{1470 \div 10}{100 \div 10} = \frac{147}{10} \]
We can convert this improper fraction into a mixed number:
\[ \frac{147}{10} = 14 \frac{7}{10} \]
So, the length of Connor's envelope is:
\[ \boxed{14 \frac{7}{10}} \text{ inches} \]
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