Answer:
Step-by-step explanation:
given a point
the equation of a line with slope m that passes through the given point is
or equivalently
.
Recall that a line of the form
, the y intercept is b and the x intercept is
.
So, in our case, the y intercept is
and the x intercept is
.
In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph
. Which means that 
The slope of the tangent line is given by the derivative of the function evaluated at
. Using the properties of derivatives, we get
. So evaluated at
we get 
Replacing the values in our previous findings we get that the y intercept is

The x intercept is

The triangle in consideration has height
and base
. So the area is

So regardless of the point we take on the graph, the area of the triangle is always 2.
Answer:
There is a 34.3% probability that he makes all of the shots.
Step-by-step explanation:
For each foul shot that he takes during the game, there are only two possible outcomes. Either he makes it, or he misses. This means that we use the binomial probability distribution to solve this problem.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which
is the number of different combinatios of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.
In this problem we have that:

What is the probability that he makes all of the shots?
This is P(X = 3).


There is a 34.3% probability that he makes all of the shots.
The product of a number and its reciprocal would be equal to one
So just flip the numbers
=32/21
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