**Sign of product when multiplying negative integers and positive integers**

When multiplying negative integers and positive integers, the sign of the product depends on the number of negative integers involved in the multiplication. Let's analyze the possible scenarios:

1. If all the negative integers cancel out:
- In this case, the product will be positive because there are no negative factors remaining to contribute to the negative sign.
- For example, if we multiply (-1) * (-2) * (-3) * (-4) * (-5) * ... * (-90) * (+1) * (+1) * (+1) * ... * (+9), the result will be positive.

2. If there is an odd number of negative integers:
- In this case, the product will be negative because there will be one negative factor remaining that contributes to the negative sign.
- For example, if we multiply (-1) * (-2) * (-3) * (-4) * (-5) * ... * (-89) * (-90) * (+1) * (+1) * (+1) * ... * (+9), the result will be negative.

3. If there is an even number of negative integers:
- In this case, the product will be positive because pairs of negative integers cancel each other out, leaving no negative factors remaining.
- For example, if we multiply (-1) * (-2) * (-3) * (-4) * (-5) * ... * (-88) * (-89) * (-90) * (+1) * (+1) * (+1) * ... * (+9), the result will be positive.

**Conclusion:**
The sign of the product of multiplying 90 negative integers and 9 positive integers will depend on the number of negative integers involved. If all the negative integers cancel out, the product will be positive. If there is an odd number of negative integers, the product will be negative. If there is an even number of negative integers, the product will be positive.

It's a positive integer