How do you find the value of x in the circle
1 answer:
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Answer:
The Domain is "All Real numbers", and the Range is "All real number less than or equal to 4" which coincides with option C in your problem.
Step-by-step explanation:
Recall that the Domain of a function is the set of all x-values for which there is a y-value obtained by the rule defined by the function.
In this case, whatever real number you enter for "x" in your functional expression, you will find another real value "y". That means that the actual Domain of your function is the full Real number line (all Real numbers).
Recall as well that the Range of a function is the set of y-values that are being "called" (or generated) as you use all the values for x in the Domain. In our case, it is great that they give the graph of the function (see attached image), so you can visualize that the function's graph is that of a "parabola" with branches opening downwards. You can see as well that the parabola presents a maximum value when x = -1, that means that any other value of x you use cannot give you as result a y-value that goes above that maximum.
If you evaluate that maximum value of the vertical coordinate by replacing "x" with "-1" in the actual function, you get:
That means that the maximum y-value one can get from this function is "4". That is, the actual Range of the function can be any number that is smaller or equal to 4.
Bottom line: The Domain is "All Real numbers", and the Range is "All real number less than or equal to 4".
Answer:
Null Hypothesis, : p = 47%
Alternate Hypothesis, : p
47%
Step-by-step explanation:
We are given that in the last mayoral election in a large city, 47% of the adults over the age of 65 voted Republican.
A researcher wishes to determine if the proportion of adults over the age of 65 in the city who plan to vote Republican in the next mayoral election has changed.
<u><em>Let p = proportion of the population of all adults over the age of 65 in the city that plan to vote Republican in the next mayoral election.</em></u>
So, Null Hypothesis, : p = 47%
Alternate Hypothesis, : p
47%
Here, <u>null hypothesis states that</u> the proportion of adults over the age of 65 in the city who plan to vote Republican in the next mayoral election is equal to 47%.
On the other hand, <u>alternate hypothesis states that</u> the proportion of adults over the age of 65 in the city who plan to vote Republican in the next mayoral election is different from 47%.
Also, The test statistics that will be used here is <u>One-sample z proportion</u> <u>statistics;</u>
T.S. = ~ N(0,1)
Hence, the researcher should test the above null and alternative hypotheses.