It is given in the problem that out of 25 students in Hansels class 17 students went to the class trip to the zoo. From the above information it is easy to find the percentage of students that went for the class trip to the zoo.
Total number of students in the class = 25
Number of students that went for the class trip to the zoo = 17
Then
Percentage of students that went to the zoo = (17/25) * 100
= (17 * 4) percent
= 68 percent
So 68% of the students in Hansels class went for the class trip to the zoo.
Answer: 0.22
Step-by-step explanation:
![D)u=\mleft_{}](https://tex.z-dn.net/?f=D%29u%3D%5Cmleft%3C-4%2C-7%5Cmright%3E_%7B%7D)
1) We can find the magnitude of a vector(a.k.a. the norm) of a vector and the direction, by making use of the following formulas:
![\begin{gathered} \mleft\|v\mright\|=\sqrt[]{a^2+b^2} \\ \tan (\theta)=\frac{b}{a} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cmleft%5C%7Cv%5Cmright%5C%7C%3D%5Csqrt%5B%5D%7Ba%5E2%2Bb%5E2%7D%20%5C%5C%20%5Ctan%20%28%5Ctheta%29%3D%5Cfrac%7Bb%7D%7Ba%7D%20%5Cend%7Bgathered%7D)
2) In this question, the magnitude and the direction of that vector have been given to us. So, let's do the other way around to identify which one has this magnitude and direction.
![\begin{gathered} \mleft\|u\mright\|=\sqrt[]{(-4)^2+(-7)^2}=\sqrt[]{16+49}=\sqrt[]{65} \\ \tan (\theta)=\frac{-4}{-7} \\ (\theta)=\tan ^{-1}(\frac{-4}{-7}) \\ D=\tan ^{-1}(\frac{-4}{-7})-180 \\ D=-119.74+360 \\ D=240.2 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cmleft%5C%7Cu%5Cmright%5C%7C%3D%5Csqrt%5B%5D%7B%28-4%29%5E2%2B%28-7%29%5E2%7D%3D%5Csqrt%5B%5D%7B16%2B49%7D%3D%5Csqrt%5B%5D%7B65%7D%20%5C%5C%20%5Ctan%20%28%5Ctheta%29%3D%5Cfrac%7B-4%7D%7B-7%7D%20%5C%5C%20%28%5Ctheta%29%3D%5Ctan%20%5E%7B-1%7D%28%5Cfrac%7B-4%7D%7B-7%7D%29%20%5C%5C%20D%3D%5Ctan%20%5E%7B-1%7D%28%5Cfrac%7B-4%7D%7B-7%7D%29-180%20%5C%5C%20D%3D-119.74%2B360%20%5C%5C%20D%3D240.2%20%5Cend%7Bgathered%7D)
Note that since we want a positive value, we need to add 360 degrees.