Answer: ŷ = 0.07X + 5.2
Step-by-step explanation:
Given the following :
Number of citations 5 - 7.5 - 10 - 15 - 20
Outputs Residuals 3 - - 6 - - 10 - 5 - - 6
Using the online regression calculator :
Line of best fit is represented by the equation:
ŷ = 0.06897X + 5.2069
ŷ = 0.07X + 5.2
From the line equation:
y = mx + c
With 0.07 = slope of gradient(m)
Intercept (c) = 5.2 (point where the line of best fit intersect the y_axis
x and y are values of x and y respectively
the number 1010111 in binary is equivalent to 127 in octal.
the number 1011010 in binary is equivalent to 132 in octal.
Answer: E
Taking a poll in the lunchroom would be the most accurate population sample.
Use the cosine law to find the length of side c:
![\begin{gathered} c^2=1^2+9^2-2(1)(9)\cos 60 \\ c^2=1+81-18\cos 60 \\ c^2=82-18\cos 60 \\ c^2=82-9 \\ c^2=73 \\ c=\sqrt[]{73} \\ c\approx8.54 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20c%5E2%3D1%5E2%2B9%5E2-2%281%29%289%29%5Ccos%2060%20%5C%5C%20c%5E2%3D1%2B81-18%5Ccos%2060%20%5C%5C%20c%5E2%3D82-18%5Ccos%2060%20%5C%5C%20c%5E2%3D82-9%20%5C%5C%20c%5E2%3D73%20%5C%5C%20c%3D%5Csqrt%5B%5D%7B73%7D%20%5C%5C%20c%5Capprox8.54%20%5Cend%7Bgathered%7D)
Use the cosine law to find the measure of angles A or B:
![\begin{gathered} \\ \frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c} \\ \\ To\text{ find angle A:} \\ \frac{\sin A}{a}=\frac{\sin C}{c} \\ \\ \frac{\sin A}{1}=\frac{\sin 60}{\sqrt[]{73}} \\ \\ \sin A=\frac{\sin 60}{\sqrt[]{73}} \\ \\ A=\sin ^{-1}(\frac{\sin60}{\sqrt[]{73}}) \\ \\ A\approx5.82º \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%20%5C%5C%20%5Cfrac%7B%5Csin%20A%7D%7Ba%7D%3D%5Cfrac%7B%5Csin%20B%7D%7Bb%7D%3D%5Cfrac%7B%5Csin%20C%7D%7Bc%7D%20%5C%5C%20%20%5C%5C%20To%5Ctext%7B%20find%20angle%20A%3A%7D%20%5C%5C%20%5Cfrac%7B%5Csin%20A%7D%7Ba%7D%3D%5Cfrac%7B%5Csin%20C%7D%7Bc%7D%20%5C%5C%20%20%5C%5C%20%5Cfrac%7B%5Csin%20A%7D%7B1%7D%3D%5Cfrac%7B%5Csin%2060%7D%7B%5Csqrt%5B%5D%7B73%7D%7D%20%5C%5C%20%20%5C%5C%20%5Csin%20A%3D%5Cfrac%7B%5Csin%2060%7D%7B%5Csqrt%5B%5D%7B73%7D%7D%20%5C%5C%20%20%5C%5C%20A%3D%5Csin%20%5E%7B-1%7D%28%5Cfrac%7B%5Csin60%7D%7B%5Csqrt%5B%5D%7B73%7D%7D%29%20%5C%5C%20%20%5C%5C%20A%5Capprox5.82%C2%BA%20%5Cend%7Bgathered%7D)
The angle measure would be 53°.
Complementary angles add up to 90° so, if you're trying to find the other angle measure just subtract the angle measurement that you already know from 90.
90 - 37 = 53
Hope this helps! :)<span />
