A researcher is interested in attitudes towards releasing prisoners with Alzheimer's who have a life sentence. 85 randomly selec
ted Americans were asked, "Prisoners with Alzheimer's who have a life sentence should be released: Strongly Agree, Agree, Disagree, Strongly Disagree". Match the vocabulary word with its corresponding example.
1 answer:
Answer and Step-by-step explanation:
The matching of the vocabulary word with its corresponding example is shown below:-
a. Data - The list of answers that the 85 Americans give.
Data refers the information that is to be collected.
b. Variable - The answer "Strongly Agree" or "Agree" or "Disagree" or "Strongly disagree".
Variable refers the changes of the expression according to the context.
c. Parameter - The proportion of all Americans who strongly agree that prisoners with life sentences who has Alzheimer's should be released.
A parameter is a quantity that affects a mathematical object's production or behavior, but is considered constant
d. Statistics - The proportion of 85 Americans surveyed who strongly agree that prisoners with life sentences who has Alzheimer's should be released.
Statistics is a field of mathematics involved in data collection, organisation and analysis.
e. Sample - The 85 Americans who participated in the survey.
A sample is the result of an experiment on randomly.
f. Population - All Americans
Population refers to the number of the public.
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Answer:
When do you hit the water?
1.075 seconds after you jump.
What is your maximum height?
the maximum height is 12.5626 ft
Step-by-step explanation:
The equation:
h(t) = -16*t^2 + 6*t + 12
Is the height as a function of time.
We know that the initial height is the height when t = 0s
h(0s) = 12
and we know that the diving board is 12 foot tall.
Then the zero in h(t)
h(t) = 0
Represents the surface of the water.
When do you hit the water?
Here we just need to find the value of t such that:
h(t) = 0 = -16*t^2 + 6*t + 12
Using the Bhaskara's formula, we get:
Then we have two solutions, and we only care for the positive solution (because the negative time happens before the jump, so that solution can be discarded)
The positive solution is:
t = (-6 - 28.4)/-32 = 1.075
So you hit the water 1.075 seconds after you jump.
What is your maximum height?
The height equation is a quadratic equation with a negative leading coefficient, then the maximum of this parabola is at the vertex.
We know that the vertex of a general quadratic:
a*x^2 + b*x + c
is at
x = -b/2a
Then in the case of our equation:
h(t) = -16*t^2 + 6*t + 12
The vertex is at:
t = -6/(2*-16) = 6/32 = 0.1875
Evaluating the height equation in that time will give us the maximum height, which is:
h(0.1875) = -16*(0.1875 )^2 + 6*(0.1875) + 12 = 12.5626
And the height is in feet, then the maximum height is 12.5626 ft