(7/30+1/2+4/15):(49/50-14/25-2/5)=

Let’s solve the expression step by step:

First, calculate the left side of the expression: \[ \frac{7}{30} + \frac{1}{2} + \frac{4}{15} \]

To sum these fractions, we need a common denominator. The least common multiple of 30, 2, and 15 is 30.

Convert each fraction:

• \(\frac{1}{2} = \frac{15}{30}\)
• \(\frac{4}{15} = \frac{8}{30}\)

Now add them together: \[ \frac{7}{30} + \frac{15}{30} + \frac{8}{30} = \frac{7 + 15 + 8}{30} = \frac{30}{30} = 1 \]

Now let's calculate the right side of the expression: \[ \frac{49}{50} - \frac{14}{25} - \frac{2}{5} \]

The least common denominator for 50, 25, and 5 is 50.

Convert each fraction:

• \(\frac{14}{25} = \frac{28}{50}\)
• \(\frac{2}{5} = \frac{20}{50}\)

Now, perform the subtraction: \[ \frac{49}{50} - \frac{28}{50} - \frac{20}{50} = \frac{49 - 28 - 20}{50} = \frac{49 - 48}{50} = \frac{1}{50} \]

Now let's combine the results from both sides of the expression: \[ 1 : \frac{1}{50} \]

Dividing by a fraction is the same as multiplying by its reciprocal: \[ 1 \div \frac{1}{50} = 1 \times 50 = 50 \]

Finally, the result of the expression is: \[ \boxed{50} \]