Ok, MissWalker! Please try your best to understand this, it may get confusing.
I have solved this on a different website, and here is my solving in a picture. I hope I helped!!! :D
Answer:
A) Independent
B) Dependent
Step-by-step explanation:
A) If we take a marble out and put the marble back, it means we have restored the sample to what it was initially and thus it doesn't affect probability of making another selection.
Thus, this is an independent event.
B) A card is taken from a deck of cards without replacement and set aside. Then after that another card is taken from the first sample, this means that the first sample size has now reduced and thus the first card taken affects the probability of the second card to be picked. Thus, this is a dependent event.

To find the gradient of the tangent, we must first differentiate the function.

The gradient at x = 0 is given by evaluating f'(0).

The derivative of the function at this point is negative, which tells us <em>the function is decreasing at that point</em>.
The tangent to the line is a straight line, so we will have a linear equation of the form y = mx + c. We know the gradient, m, is equal to -1, so

Now we need to substitute a point on the tangent into this equation to find c. We know a point when x = 0 lies on here. To find the y-coordinate of this point we need to evaluate f(0).

So the point (0, -1) lies on the tangent. Substituting into the tangent equation: