You subtract 13 dollars for how much Keith would pay if he payed for the unlimited plan then you get 26 dollars and if each ride was 1 dollar then he went on 26 rides
Answer:
69 child tickets
Step-by-step explanation:
0.15 x 460 = 69
Answer with Step-by-step explanation:
We are given that
A=4i-2j+4k
B=-4i+3k
![\mid A\mid=\sqrt{4^2+(-2)^2+4^2}=6](https://tex.z-dn.net/?f=%5Cmid%20A%5Cmid%3D%5Csqrt%7B4%5E2%2B%28-2%29%5E2%2B4%5E2%7D%3D6)
![mid B\mid=\sqrt{3^2+(-4)^2}=5](https://tex.z-dn.net/?f=mid%20B%5Cmid%3D%5Csqrt%7B3%5E2%2B%28-4%29%5E2%7D%3D5)
![\hat{A}=\frac{A}{\mid A\mid}](https://tex.z-dn.net/?f=%5Chat%7BA%7D%3D%5Cfrac%7BA%7D%7B%5Cmid%20A%5Cmid%7D)
![\hat{A}=\frac{4i-2j+4k}{6}=\frac{2}{3}i-\frac{1}{3}j+\frac{2}{3}k](https://tex.z-dn.net/?f=%5Chat%7BA%7D%3D%5Cfrac%7B4i-2j%2B4k%7D%7B6%7D%3D%5Cfrac%7B2%7D%7B3%7Di-%5Cfrac%7B1%7D%7B3%7Dj%2B%5Cfrac%7B2%7D%7B3%7Dk)
![\hat{B}=\frac{-4i+3k}{5}=\frac{-4}{5}i+\frac{3}{5}k](https://tex.z-dn.net/?f=%5Chat%7BB%7D%3D%5Cfrac%7B-4i%2B3k%7D%7B5%7D%3D%5Cfrac%7B-4%7D%7B5%7Di%2B%5Cfrac%7B3%7D%7B5%7Dk)
Sum of unit vectors=![\hat{A}+\hat{B}](https://tex.z-dn.net/?f=%5Chat%7BA%7D%2B%5Chat%7BB%7D)
Sum of unit vectors=![\frac{2}{3}i-\frac{1}{3}j+\frac{2}{3}k+\frac{-4i+3k}{5}=\frac{-4}{5}i+\frac{3}{5}k](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7Di-%5Cfrac%7B1%7D%7B3%7Dj%2B%5Cfrac%7B2%7D%7B3%7Dk%2B%5Cfrac%7B-4i%2B3k%7D%7B5%7D%3D%5Cfrac%7B-4%7D%7B5%7Di%2B%5Cfrac%7B3%7D%7B5%7Dk)
Sum of unit vectors=![\frac{-2}{15}i-\frac{1}{3}j+\frac{19}{15}k](https://tex.z-dn.net/?f=%5Cfrac%7B-2%7D%7B15%7Di-%5Cfrac%7B1%7D%7B3%7Dj%2B%5Cfrac%7B19%7D%7B15%7Dk)
![\mid \hat{A}+\hat{B}\mid=\sqrt{(\frac{-2}{15})^2+(\frac{1}{3})^2+(\frac{19}{15})^2}](https://tex.z-dn.net/?f=%5Cmid%20%5Chat%7BA%7D%2B%5Chat%7BB%7D%5Cmid%3D%5Csqrt%7B%28%5Cfrac%7B-2%7D%7B15%7D%29%5E2%2B%28%5Cfrac%7B1%7D%7B3%7D%29%5E2%2B%28%5Cfrac%7B19%7D%7B15%7D%29%5E2%7D)
![\mid \hat{A}+\hat{B}\mid=1.32](https://tex.z-dn.net/?f=%5Cmid%20%5Chat%7BA%7D%2B%5Chat%7BB%7D%5Cmid%3D1.32)
![\theta_1=Cos^{-1}(\frac{A\cdot B)}{\mid A\mid \mid B\mid}](https://tex.z-dn.net/?f=%5Ctheta_1%3DCos%5E%7B-1%7D%28%5Cfrac%7BA%5Ccdot%20B%29%7D%7B%5Cmid%20A%5Cmid%20%5Cmid%20B%5Cmid%7D)
![\theta_1=cos^{-1}(\frac{-4}{30})=97.6^{\circ}](https://tex.z-dn.net/?f=%5Ctheta_1%3Dcos%5E%7B-1%7D%28%5Cfrac%7B-4%7D%7B30%7D%29%3D97.6%5E%7B%5Ccirc%7D)
![\theta_2=cos^{-1}(\frac{(Sum\;of\;unt\;vectors\cdot A)}{\mid sum\mid \mid A\mid }](https://tex.z-dn.net/?f=%5Ctheta_2%3Dcos%5E%7B-1%7D%28%5Cfrac%7B%28Sum%5C%3Bof%5C%3Bunt%5C%3Bvectors%5Ccdot%20A%29%7D%7B%5Cmid%20sum%5Cmid%20%5Cmid%20A%5Cmid%20%7D)
![\theta_2=cos^{-1}(\frac{78}{15\cdot 2\cdot 1.32\cdot 6})=49^{\circ}](https://tex.z-dn.net/?f=%5Ctheta_2%3Dcos%5E%7B-1%7D%28%5Cfrac%7B78%7D%7B15%5Ccdot%202%5Ccdot%201.32%5Ccdot%206%7D%29%3D49%5E%7B%5Ccirc%7D)
![\frac{1}{2}\theta_1=\frac{1}{2}(97.6)=48.8\sim 49^{\circ}=\theta_2](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5Ctheta_1%3D%5Cfrac%7B1%7D%7B2%7D%2897.6%29%3D48.8%5Csim%2049%5E%7B%5Ccirc%7D%3D%5Ctheta_2)
Hence, proved.
Refer to the photo for my work and answer. Basically, you are finding the probability of selecting anything but an AAS student. So you add up the other students and divide by 22