A new mother changes her baby's diaper 4 times a day, on average. How many diapers will the child use in a year's time? (Enter numeric value only.)

First step is to find to convert the given fractions into approximate decimals as follows:

7/25=0.28

8/15=0.53

4/19=0.21

4/5=0.8

From the above, 0.8 is the largest value. Then, it follows that 4/5 is the largest number

\(\frac{X}{5}=\frac{125}{X}\)

Cross-multiply the above proportion equation

\(X^2=5\ast125 X^2=625 \)

Take square root on both sides\(\sqrt{X^2}=\sqrt{625} X=+25\ or-25 \)

Taking the positive square root, X=25

Carry out the addition as follows

\(7\frac{2}{3}+4+\frac{1}{2}\)

Add whole numbers separately followed by addition of fractions separately

\(7+4+\frac{2}{3}+\frac{1}{2}\)

Least common divisor of 3 and 2 is 6, we add fractions as follows

\(11+\frac{2}{3}+\frac{1}{2}=11+\frac{2\left(2\right)+3}{6}=11+\frac{7}{6} 11+\frac{7}{6}=11+1\frac{1}{6}=12\frac{1}{6} \)

The ratio 5:1000=X:500 can be written in proportion as:

\(\frac{5}{1000}=\frac{X}{500}\)

The value of X is determined by cross-products

\(5\ast500=1000X 2500=1000X \)

Divide both sides by 1000

\(\frac{2500}{1000}=\frac{1000X}{1000} 2.5=X \)

Thus, the value of X is 2.5