To place a picture in his class newsletter, joaquin must reduce the picture by a scale factor of 0.3. find the dimensions of the reduced picture if the original is 15 centimeters wide and 10 centimeters high.

This is the concept of scale factors. Given that Joaquin has reduce the dimensions of a picture by scale factor of 0.3 and the original dimension was 10 cm length by 10 cm width, the new dimension will be:
New length=(old length)×(scale factor)
New width=(old width)×(scale factor)
Plugging the values in the above formulas we get:

New length=15x0.3=4.5 cm

New width=10×0.3=3 cm