Answer:
(4, - 5 )
Step-by-step explanation:
Under a counterclockwise rotation about the origin of 270°
a point (x, y ) → (- y, x ) , thus
(- 5, - 4 ) → (4, - 5 )
2 * plane speed in still air = 289mph + 257mph = 546
plane speed in still air = 273 mph
plane speed in still air + wind speed = 289
273 + wind speed = 289
Therefore, wind speed = 16 mph
Answer:
x^4 - 14x^2 - 40x - 75.
Step-by-step explanation:
As complex roots exist in conjugate pairs the other zero is -1 - 2i.
So in factor form we have the polynomial function:
(x - 5)(x + 3)(x - (-1 + 2i))(x - (-1 - 2i)
= (x - 5)(x + 3)( x + 1 - 2i)(x +1 + 2i)
The first 2 factors = x^2 - 2x - 15 and
( x + 1 - 2i)(x +1 + 2i) = x^2 + x + 2ix + x + 1 + 2i - 2ix - 2i - 4 i^2
= x^2 + 2x + 1 + 4
= x^2 + 2x + 5.
So in standard form we have:
(x^2 - 2x - 15 )(x^2 + 2x + 5)
= x^4 + 2x^3 + 5x^2 - 2x^3 - 4x^2 - 10x - 15x^2 - 30x - 75
= x^4 - 14x^2 - 40x - 75.
Answer:
The condition for r is the following:
And for this case if we analyze the options the only impossible value is given by:
1.0528
Because this value is higher than 1 and not satisfy the general limits for r
Step-by-step explanation:
The correlation coefficient is a measure of dispersion and is a value between -1 and 1, and is defined as:
![r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bn%28%5Csum%20xy%29-%28%5Csum%20x%29%28%5Csum%20y%29%7D%7B%5Csqrt%7B%5Bn%5Csum%20x%5E2%20-%28%5Csum%20x%29%5E2%5D%5Bn%5Csum%20y%5E2%20-%28%5Csum%20y%29%5E2%5D%7D%7D)
The condition for r is the following:
And for this case if we analyze the options the only impossible value is given by:
1.0528
Because this value is higher than 1 and not satisfy the general limits for r
