Which of the following relations represents a function? A. {(1, 1), (1, 2), (1, 3)} B. {(1, 1), (2, 1), (3, 1)} C. {(1, 1), (2,
2 answers:
Answer: option D.
Step-by-step explanation:
A function is defined as a relation in which do no exist two values of y (output values) to a same value of x (input value):
In option A the relation is . You can observe that for the same value x have three distinct values of y, therefore this is not a function.
In option B the relation is . You can observe that the values of x have sames values of y, but there are not two values of y for a same value of x. Then this relation is a function,
In option C the relation is . You can observe that the values of x have distinct values of y, therefore this is a function.
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For a quadratic of the form 
, we have the quadratic formula
,
where a is the coefficient (number before the variable) of the squared term, b is the coefficient of the linear term, and c is the constant term.
So, given
, we can get that 
, and 
. We substitute these numbers into the quadratic formula above.
This is our final answer.
If you've never seen the quadratic formula, you can derive it by completing the square for the general form of a quadratic. Note that the
symbol (read: plus or minus) represents the two possible distinct solutions, except for zero under the radical, which gives only one solution.
where a is the coefficient (number before the variable) of the squared term, b is the coefficient of the linear term, and c is the constant term.
So, given
This is our final answer.
If you've never seen the quadratic formula, you can derive it by completing the square for the general form of a quadratic. Note that the
Answer:
the probability the person's reaction time will be between 0.9 and 1.1 seconds is 0.0378
Step-by-step explanation:
Given the data in the question;
the cumulative distribution function F(x) = ;
probability the person's reaction time will be between 0.9 and 1.1 seconds
P( 0.9 < x < 1.1 ) = P( x ≤ 1.1 ) - P( x ≤ 0.9 )
P( 0.9 < x < 1.1 ) = F(1.1) - F(0.9)
= [ ] - [
]
we substitute
= [ ] - [
]
= [ ] - [
]
= [ ] - [
]
= [ 1 - 0.1079796998 ] - [ 1 - 0.1457938 ]
= 0.8920203 - 0.8542062
= 0.0378
Therefore, the probability the person's reaction time will be between 0.9 and 1.1 seconds is 0.0378