Deductive. Since you're making the assumption from something that is mainly true
Figure A maps to figure B with a scale factor of 2/3 -> Every single side of figure B equal to 2/3 of its corresponding side on triangle A.
So, we can find x by taking 10.5 x 2/3 = 7
-> x = 7
9514 1404 393
Answer:
{(0, −5), (2, 9), (−3, −26)}
Step-by-step explanation:
You only need to try the first point in each set to eliminate the wrong answers.
a: 7(-5)-5 = -40 ≠ 0
b: 7(2)-5 = 9 ≠ 7
c: 7(0)-5 = -5 . . . matches given point
d: 7(1)-5 = 2 ≠ 3
The third choice is the correct one: {(0, −5), (2, 9), (−3, −26)}.
The formula of a distance between two points:

We have the points (-3, 3) and (5, 0).
Substitute the coordinates of the points to the formula:

(a) 404 subjects are needed to estimate the mean HDL cholesterol within 2 points with 99% confidence.
(b) When the confidence level decreases to 95%, the number of subjects decreases from 404 to 234.
<u>Explanation:</u>
Given:
σ = 15.6
Let the number of subjects be n
(a)
When the confidence level is 99%, then z = 2.576
E = 2
We know:
![n = [\frac{z X s}{E}]^2](https://tex.z-dn.net/?f=n%20%3D%20%5B%5Cfrac%7Bz%20X%20s%7D%7BE%7D%5D%5E2)
On substituting the value, we get:
![n = [\frac{2.576 X 15.6}{2} ]^2\\\\n = 403.7](https://tex.z-dn.net/?f=n%20%3D%20%5B%5Cfrac%7B2.576%20X%2015.6%7D%7B2%7D%20%5D%5E2%5C%5C%5C%5Cn%20%3D%20403.7)
Thus, 404 subjects are needed to estimate the mean HDL cholesterol within 2 points with 99% confidence.
(b)
When the confidence level is 95%, then z = 1.96
E = 2
We know:
![n = [\frac{z X s}{E}]^2](https://tex.z-dn.net/?f=n%20%3D%20%5B%5Cfrac%7Bz%20X%20s%7D%7BE%7D%5D%5E2)
On substituting the value, we get:
![n = [\frac{1.96 X 15.6}{2} ]^2\\\\n = 233.7](https://tex.z-dn.net/?f=n%20%3D%20%5B%5Cfrac%7B1.96%20X%2015.6%7D%7B2%7D%20%5D%5E2%5C%5C%5C%5Cn%20%3D%20233.7)
n = 234
Thus, when the confidence level decreases to 95%, the number of subjects decreases from 404 to 234.