Answer:
The mode would be 6
Step-by-step explanation:
The mode in mathematics refers to the number that appears the most frequently in the set of data. The number six is the only number that is shown twice, making it the mode.
Answer:
OPTION B: ![$ \frac{-2\sqrt{5}}{5} $](https://tex.z-dn.net/?f=%24%20%5Cfrac%7B-2%5Csqrt%7B5%7D%7D%7B5%7D%20%24)
Step-by-step explanation:
Given ![$ cot \theta = -\frac{\sqrt{5}}{2} $](https://tex.z-dn.net/?f=%24%20cot%20%5Ctheta%20%3D%20-%5Cfrac%7B%5Csqrt%7B5%7D%7D%7B2%7D%20%24)
We know that, ![$ \frac{1}{cot \theta} = tan \theta $](https://tex.z-dn.net/?f=%24%20%5Cfrac%7B1%7D%7Bcot%20%5Ctheta%7D%20%3D%20tan%20%5Ctheta%20%24)
![$ \implies tan \theta = \frac{1}{-\frac{\sqrt{5}}{2}} $](https://tex.z-dn.net/?f=%24%20%5Cimplies%20tan%20%5Ctheta%20%3D%20%5Cfrac%7B1%7D%7B-%5Cfrac%7B%5Csqrt%7B5%7D%7D%7B2%7D%7D%20%24)
![$ = -\frac{2}{\sqrt{5}} $](https://tex.z-dn.net/?f=%24%20%3D%20-%5Cfrac%7B2%7D%7B%5Csqrt%7B5%7D%7D%20%24)
Multiplying and dividing by
, we get:
![$ tan \theta = - \frac{2 \sqrt{5}}{\sqrt{5}\times \sqrt{5}}} $](https://tex.z-dn.net/?f=%24%20tan%20%5Ctheta%20%3D%20-%20%5Cfrac%7B2%20%5Csqrt%7B5%7D%7D%7B%5Csqrt%7B5%7D%5Ctimes%20%5Csqrt%7B5%7D%7D%7D%20%24)
![$ \implies tan \theta = -\frac{2\sqrt{5}}{5} $](https://tex.z-dn.net/?f=%24%20%5Cimplies%20tan%20%5Ctheta%20%3D%20-%5Cfrac%7B2%5Csqrt%7B5%7D%7D%7B5%7D%20%24)
Hence, OPTION B is the answer.
Answer:
The value of ![(-25)^{\frac{1}{2} }=5i](https://tex.z-dn.net/?f=%28-25%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%20%7D%3D5i)
Step-by-step explanation:
We need to find ![(-25)^{\frac{1}{2} }](https://tex.z-dn.net/?f=%28-25%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%20%7D)
We have
![(-25)^{\frac{1}{2} }=\sqrt{-25} \\\\=\sqrt{25} \times\sqrt{-1} \\\\=5 i](https://tex.z-dn.net/?f=%28-25%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%20%7D%3D%5Csqrt%7B-25%7D%20%5C%5C%5C%5C%3D%5Csqrt%7B25%7D%20%5Ctimes%5Csqrt%7B-1%7D%20%5C%5C%5C%5C%3D5%20i)
Answer:
A. the slope of the best fit line would be negative