The points plotted below are on the graph of a polynomial. In what range of x-values must the polynomial have a root?
1 answer:
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Answer:
Assuming a standard significance level of the best conclusion for this case would be:
4. There is not enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034).
Because
If we select a significance level lower than 0.034 then the conclusion would change.
Step-by-step explanation:
Data given
n=300 represent the random sample taken
X=120 represent the people who have a smart phone
estimated proportion of people who have a smart phone
is the value that we want to test
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
System of hypothesis
We need to conduct a hypothesis in order to test the claim that the true proportion of people who have a smart phone is higher than 0.35, the system of hypothesis are.:
Null hypothesis:
Alternative hypothesis:
The statistic is given by:
(1)
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
Statistical decision
Since is a right tailed test the p value would be:
Assuming a standard significance level of the best conclusion for this case would be:
4. There is not enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034).
Because
If we select a significance level lower than 0.034 then the conclusion would change.
Short Answers:
Answer for part A: Definition of perpendicular
Answer for part B: Right Angle Congruence Theorem
Answer for part C: Reflexive Property of Congruence
Answer for part D: Definition of Midpoint
Answer for part E:
Answer for part F: CPCTC
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Explanations:
Part A:
We are given that
which means, in english, "line segment RX is perpendicular to line segment ST"
By the very definition of perpendicular, this means that the two line segments form a right angle. This is visually shown as the red square angle marker for angle RXT. Angle RXS is also a right angle as well.
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Part B:
The Right Angle Congruence Theorem (aka Right Angle Theorem) is the idea that if we have two right angles, then we know that they are both 90 degrees so they must be congruent to one another.
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Part C:
Any line segment is congruent to itself. This is because any line segment will have the same length as itself. It seems silly to even mention something so trivial but it helps establish what we need for the proof.
---------------------
Part D:
We are given "X is the midpoint of segment ST" so by definition, X is in the very exact middle of ST. Midpoints cut segments exactly in half. SX is one half while TX is the other half. The two halves are congruent which is why SX = TX
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Part E:
Writing means "triangle SXR is congruent to triangle TXR". These two triangles are the smaller triangles that form when you draw in segment RX
Side Note: SAS stands for "side angle side". The angle must be between the two sides. The pairing RX and RX forms one of the 'S' letters (see part C), while the pairing SX and TX forms the other 'S' (see part D). The angles between the sides are RXS and RXT (see part B).
---------------------
Part F:
CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent"
It means that if we have two congruent triangles, then the corresponding parts are congruent. Back in part E, we proved the triangles congruent. For this part, we look at the pieces RS and RT (which correspond to one another; they are the hypotenuse of each triangle). They are proven congruent by CPCTC
If CPCTC is an odd concept to think about, then try thinking about something like this: you have two houses which are completely identical in every way. We can say that those two houses are congruent. If the houses are identical, then surely every piece that makes up the house is identical to its corresponding piece to the other house. For example, the front door to each house is both the same size, shape, color, made of the same material, designed in the same pattern, etc. So the two doors are congruent as well.
Answer for part A: Definition of perpendicular
Answer for part B: Right Angle Congruence Theorem
Answer for part C: Reflexive Property of Congruence
Answer for part D: Definition of Midpoint
Answer for part E:
Answer for part F: CPCTC
-------------------------------------------------------------
Explanations:
Part A:
We are given that
By the very definition of perpendicular, this means that the two line segments form a right angle. This is visually shown as the red square angle marker for angle RXT. Angle RXS is also a right angle as well.
---------------------
Part B:
The Right Angle Congruence Theorem (aka Right Angle Theorem) is the idea that if we have two right angles, then we know that they are both 90 degrees so they must be congruent to one another.
---------------------
Part C:
Any line segment is congruent to itself. This is because any line segment will have the same length as itself. It seems silly to even mention something so trivial but it helps establish what we need for the proof.
---------------------
Part D:
We are given "X is the midpoint of segment ST" so by definition, X is in the very exact middle of ST. Midpoints cut segments exactly in half. SX is one half while TX is the other half. The two halves are congruent which is why SX = TX
---------------------
Part E:
Writing
Side Note: SAS stands for "side angle side". The angle must be between the two sides. The pairing RX and RX forms one of the 'S' letters (see part C), while the pairing SX and TX forms the other 'S' (see part D). The angles between the sides are RXS and RXT (see part B).
---------------------
Part F:
CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent"
It means that if we have two congruent triangles, then the corresponding parts are congruent. Back in part E, we proved the triangles congruent. For this part, we look at the pieces RS and RT (which correspond to one another; they are the hypotenuse of each triangle). They are proven congruent by CPCTC
If CPCTC is an odd concept to think about, then try thinking about something like this: you have two houses which are completely identical in every way. We can say that those two houses are congruent. If the houses are identical, then surely every piece that makes up the house is identical to its corresponding piece to the other house. For example, the front door to each house is both the same size, shape, color, made of the same material, designed in the same pattern, etc. So the two doors are congruent as well.