The set of ordered pairs shown represents a function, f,
2 answers:
Answer:
The correct options are A, D and E.
Step-by-step explanation:
The given set of ordered pairs represents a function
We need to find THREE ordered pairs that could be added to the set that would allow f to remain a function.
A relation is a function if there exist unique value of y for each value of x.
The x values for given function are -5, 4, 3 and 0.
If we add (-3,-2) in the given set, then we unique value of y for each value of x. So, option A is correct.
If we add (4,0) in the given set, then we have y=0 and y=9 at x=4. Since the set have more than one value of y for same x-value, therefore option B is incorrect.
If we add (0,-1) in the given set, then we have y=-1 and y=6 at x=0. Since the set have more than one value of y for same x-value, therefore option C is incorrect.
If we add (1,6) in the given set, then we unique value of y for each value of x. So, option D is correct.
If we add (2,3) in the given set, then we unique value of y for each value of x. So, option E is correct.
If we add (-5,9) in the given set, then we have y=9 and y=3 at x=-5. Since the set have more than one value of y for same x-value, therefore option F is incorrect.
Therefore the correct options are A, D and E.
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Answer:
99% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases is [$(-31.82) , $12.02].
Step-by-step explanation:
We are given that a random sample of 16 sales receipts for mail-order sales results in a mean sale amount of $74.50 with a standard deviation of $17.25.
A random sample of 9 sales receipts for internet sales results in a mean sale amount of $84.40 with a standard deviation of $21.25.
The pivotal quantity that will be used for constructing 99% confidence interval for true mean difference is given by;
P.Q. = ~
where, = sample mean for mail-order sales = $74.50
= sample mean for internet sales = $84.40
= sample standard deviation for mail-order purchases = $17.25
= sample standard deviation for internet purchases = $21.25
= sample of sales receipts for mail-order purchases = 16
= sample of sales receipts for internet purchases = 9
Also, =
= 18.74
The true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases is represented by ().
Now, 99% confidence interval for () is given by;
=
Here, the critical value of t at 0.5% level of significance and 23 degrees of freedom is given as 2.807.
=
= [$-31.82 , $12.02]
Hence, 99% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases is [$(-31.82) , $12.02].
PART A
The given equation is
In order to find the maximum height, we write the function in the vertex form.
We factor -16 out of the first two terms to get,
We add and subtract
to get,
We again factor -16 out of the first two terms to get,
This implies that,
The quadratic trinomial above is a perfect square.
This finally simplifies to,
The vertex of this function is
The y-value of the vertex is the maximum value.
Therefore the maximum value is,
PART B
When the ball hits the ground,
This implies that,
We add -29 to both sides to get,
This implies that,
or
Since time cannot be negative, we discard the negative value and pick,
The given equation is
In order to find the maximum height, we write the function in the vertex form.
We factor -16 out of the first two terms to get,
We add and subtract
to get,
We again factor -16 out of the first two terms to get,
This implies that,
The quadratic trinomial above is a perfect square.
This finally simplifies to,
The vertex of this function is
The y-value of the vertex is the maximum value.
Therefore the maximum value is,
PART B
When the ball hits the ground,
This implies that,
We add -29 to both sides to get,
This implies that,
or
Since time cannot be negative, we discard the negative value and pick,