Answer:
95%
Step-by-step explanation:
For a given sample data, the width of the confidence interval would vary directly with the confidence level i.e. more the confidence level, wider will be the confidence interval.
This is because the critical value associated with the confidence level(e.g z value) becomes larger as the confidence level is increased which results in an increased interval.
The confidence interval for a population proportion is given by the formula:
![p \pm z\sqrt{\frac{pq}{n} }](https://tex.z-dn.net/?f=p%20%5Cpm%20z%5Csqrt%7B%5Cfrac%7Bpq%7D%7Bn%7D%20%7D)
So, for a fixed value of p,q and n, the larger the value of z the wider will be the confidence interval.
Hence 95% confidence interval will be wider than 80% confidence interval.
<h2>Hello!</h2>
The answer is: All of the above.
<h2>Why?</h2>
First, we need to know that both triangles have the same dimensions:
![Base= 5Units\\Height=3Units\\Hypotenuse=\sqrt{5^{2}+3^{2}}=5.83Units](https://tex.z-dn.net/?f=Base%3D%205Units%5C%5CHeight%3D3Units%5C%5CHypotenuse%3D%5Csqrt%7B5%5E%7B2%7D%2B3%5E%7B2%7D%7D%3D5.83Units)
If two triangles have the same side length, the angles will be the same two.
Hence,
If both triangles have the same side length, they are congruent according to the Side-Side-Side(SSS) triangle congruence theorem. It also means that:
Both triangles have the same angles, meaning that its angles are congruent. If there is at least one angle which is congruent, and there are at least two sides that are equal for both triangles, the triangles are congruent according to the Side-Angle-Side (SAS) triangle congruence theorem.
If two angles and at least a side are congruent, the triangles are congruent. According to the Angle-Side-Angle(ASA), if two angles and the included side are congruent, the triangles are congruent.
For this case, each theorem will be satisfied because the triangles have the same side length, meaning that all of the above theorem can prove that the triangles ABC and DEF are congruent.
Have a nice day!
The lines are perpendicular to each other because -8 and 1/8 are opposite reciprocal of each other. <span />
We can solve this one by using the Pythagorean Theorem
Which is a^2+b^2=c^2
C is the hypotenuse, also known as segment AD.
To find the hypotenuse we do a^2, which is either of the two sides plus b^2 which is the other side
a^2 in this case is 4 units
and b^2 in this case is 4 units
4^2+3^2=25
we then take the sqrt if 25 which is 5
So segment AD=5
C is your correct answer
Answer:
x = 8.7
Step-by-step explanation:
The triangles are congruent, which means that the sides are proportional to each other. Line DE and line BE are proportional to each other. This means that:
8 = 12
We can simplify this down to
2 = 3
Now that we have this proportion we can apply it to Lines AE and EC
2(13) = 3x
26 = 3x
8.67 = x
Therefore x is equal to 8.67 (or 8.7 rounded)
Check:
8/12 = 0.6667
8.6667/13 = 0.6667
Since both are the same, the answer is correct.
<em>I hope this helps!!</em>
<em>- Kay :)</em>