A poll has a percent error of 4%. The poll states 15,000 people will vote for Candidate A in the next election. Which statement
2 answers:
You might be interested in
Answer:
Answer is contained in explanation.
Step-by-step explanation:
Description of visual:
I started with the first picture. This is a picture of triangle ABC.
Now I'm going to draw a line segment from vertex C such that it is a perpendicular bisector of AB.
Proof:
CM is a perpendicular bisectors of AB is a given.
From this we can concluded by definition of perpendicular angles that angle AMC and angle BMC are right angles.
Since angles AMC and BMC are right angles, then they are congruent to each other.
By the definition of bisector and since CM bisects AB, then AM is congruent to MB.
By the reflexive property, we have that CM is congruent to CM.
We can conclude the two triangles, triangle CMA and CMB, are congruent by SAS Postulate.
Since triangles CMA and CMB are congruent, we can conclude that their corresponding parts are congruent.
Since their corresponding parts are congruent, then we now know that side CA and side CB are congruent.
Since two sides of the triangle ABC are congruent to each other, namely side CA and side CB, then the triangle ABC is an isosceles triangle.
//
Setup for coordinate geometry proof:
M is the midpoint of AB since CM is a bisector of AB.
Since M is the midpoint of AB, then M is located at the coordinates .
We found this point such that the length AM is equal to the length MB.
That is, the distance between A and M is the same as the distance between M and B.
Let's check.
We have confirmed that AM=MB.
(Based on the picture, we could have taken a slightly easier route to calculate the distance between M and A, then the distance between B and M. They are both a horizontal distance. So where as
.)
Now we also want to assume that the line segment CM is perpendicular to AB. I have drawn the base of the triangle on the x-axis so a vertical line would be perpendicular to it. Also this would make point . The
-coordinate is
because we don't know how high above the
-axis the point
is.
If we show CA=CB, then we have shown triangle ABC is an isosceles.
Coordinate Geometry Proof:
We want to finally show that the sides CB and CA of triangle ABC are congruent. We will do this using distance formula.
That is we want to show the distance between (b/2,d) and (0,0) is the same as (b/2,d) and (b,0).
Thus, CA=CB. Since CA=CB, then the triangle is an isosceles.
//
D; Both statements are correct
Here, we want to check the correct statement
Basically from the diagram, it is confirmed that what we have is a 30-60-90 triangle
Now, for a 30-60-90 degrees triangle, the side lengths are in a particular ratio
From the diagram, MO faces the right angle and thus, it is the longest side and the hypotenuse
Now, let us take a look at the ratio of the sides in both submissions
For a 30-60-90 degrees triangle, the ratio of the sides is;
Hence, one side must be twice the length of the other
From Kellie's statement we can see MO is twice NO
From Eddie's statement, we can also see that MO is twice NO
Lastly, we can also see in both that dividing MN by NO yields the root of 3 in both statemets which confirms the existence of the theoretical ratio
So the conclusion here is that;
Both students are correct