Since not all mammals are dogs, it follows that some cats, being mammals, are not dogs.

Since not all mammals are dogs, it follows that some cats, being mammals, cannot be dogs.

Since some flowers are red, it is possible that some roses, being flowers, are also red.

Since not all flowers are roses, it is possible that some flowers are not roses.

Since some flowers fade quickly and all roses are flowers, it is possible that some roses fade quickly.

The statement indicates that while some flowers fade quickly, it does not apply to all, hence some must not.

Since all squares are rectangles, it is possible that some rectangles are squares.

Since some rectangles are not blue and all squares are rectangles, it is possible that some squares are not blue.

The conclusion is valid because if all students who study hard pass, then not passing implies John did not study hard.

The conclusion is not valid because it depends on whether John studies hard, which is not stated.

The quantum numbers correspond to the 2s orbital, where l=0 indicates an s orbital.

The spin quantum number can be either +1/2 or -1/2, so both values are possible.

For l=1, the electron occupies a p orbital.

For l=1, the orbital is a p orbital.

For l=1, m_l can take values -1, 0, +1.

For l=0, m_l can only be 0.

For l=2, m_l can take values -2, -1, 0, 1, 2. Therefore, all of the options are valid.

For an ellipse, b is the semi-minor axis. Here, b = 6, so b^2 = 6^2 = 36.

3:00 PM + 15 minutes = 3:15 PM.

The recipient will receive the email at 3:15 PM.

If the subject line is 50 characters, 950 characters can be used in the body.

1 million users * 20 emails/user = 20 million emails per day.

1 GB = 1024 MB, so 1024 MB / 10 MB = 102.4, which means 100 emails can be stored.

At a height equal to the radius of the Earth, the gravitational force becomes one-fourth of its value at the surface.

Height = (Initial Speed)²/(2 × g) = (20 m/s)²/(2 × 10 m/s²) = 20 m

Let angle B be x. Then angle A = 3x. Since they are supplementary, x + 3x = 180, leading to 4x = 180, so x = 45. Therefore, angle A = 3 * 45 = 135 degrees.

Supplementary angles sum up to 180 degrees. Therefore, angle B = 180 - 45 = 135 degrees.

Supplementary angles sum to 180 degrees. Therefore, angle B = 180 - 75 = 105 degrees.

By definition, supplementary angles add up to 180 degrees.

The complement of an angle is found by subtracting it from 90 degrees. Thus, angle B = 90 - 30 = 60 degrees.