Answer:
The probability that the student answers at least seventeen questions correctly is 
.
Step-by-step explanation:
Let the random variable <em>X</em> represent the number of correctly answered questions.
It is provided all the questions have five options with only one correct option.
Then the probability of selecting the correct option is,
There are <em>n</em> = 20 question in the exam.
It is also provided that a student taking the examination answers each of the questions with an independent random guess.
Then the random variable can be modeled by the Binomial distribution with parameters <em>n</em> = 20 and <em>p</em> = 0.20.
The probability mass function of <em>X</em> is:
Compute the probability that the student answers at least seventeen questions correctly as follows:
Thus, the probability that the student answers at least seventeen questions correctly is .
<h2>
Answer:</h2>
There are 2 ways to solve this system: by elimination or by graphing. I will solve it by elimination. First will solve for x.
Now we will solve for y using what we got for x.
Solution:
A: 
The answer is D. Because it is easier to add 9 and 2 and also 8 and 1.
Answer: We have
f'(x) = a x + b,
f'(x) = 0 at x = -b/a
f(x) = a x^2 / 2 + b x + c
Meaning of marked part
❟ ∵ a<0 ❟ f is a quadratic function
∴ f has absolute maximum value at x = -b/a
For all a with a less than zero, f is a quadratic function. Therefore f has a global maximum at x = -b/a
That typesetting seems very sloppy. It probably is supposed to be
∀a < 0, f is a quadratic function.
The second sentence is sloppy in use of "absolute". It can't mean absolute value, so presumably it means "global".
Sometimes a minimum or maximum is only local, but a quadratic function has exactly one extrema, and it is global. And if a < 0, the extrema is a global maximum.
Step-by-step explanation:
An extrema (minimum or maximum) for f(x) occurs only where f'(x) = 0, that is, when the slope of the tangent at x is zero.
But if the function crosses its tangent at that point, the point is an inflection point, not an extrema. A quadratic never crosses it's tangent.
