Answer:
B
Step-by-step explanation:
Using the exact values
cos150° = - cos30° = - ![\frac{\sqrt{3} }{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D)
sin150° = sin30° = ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
Given
z = 4(cos150° + isin150° ) , substitute values
= 4(-
+
i )
= - 2
+ 2i , that is
(- 2
, 2 ) → B
Answer:
Number of hot dogs sold = 56
Number of hamburgers sold = 52
Step-by-step explanation:
Let
Number of hot dogs sold = x
Number of hamburgers sold = y
We can make equation from given equations:
(Hot dogs were sold for $.50 (fifty cents), and hamburgers were sold for $1 (one dollar). The total money raised by your class was $80. )
(Together you sold 108 hot dogs and hamburgers.)
Now we cam solve these system of equations to find value of x and y
![0.50x+y=80--eq(1)\\x+y=108--eq(2)](https://tex.z-dn.net/?f=0.50x%2By%3D80--eq%281%29%5C%5Cx%2By%3D108--eq%282%29)
Subtract both equations to get value of x:
![0.50x+y=80\\x\:\:\:\:\:\:\:\: + y=108\\-\:\:\:\:\:\:\:\: -\:\:\:\:\:\: -\\---------\\-0.5x=-28\\x=\frac{-28}{-0.5}\\x=56](https://tex.z-dn.net/?f=0.50x%2By%3D80%5C%5Cx%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%20%2B%20y%3D108%5C%5C-%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%20-%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%20-%5C%5C---------%5C%5C-0.5x%3D-28%5C%5Cx%3D%5Cfrac%7B-28%7D%7B-0.5%7D%5C%5Cx%3D56)
We get value of x = 56
Now putting value of x in equation 2 to find value of y
![x+y=108\\56+y=108\\y=108-56\\y=52](https://tex.z-dn.net/?f=x%2By%3D108%5C%5C56%2By%3D108%5C%5Cy%3D108-56%5C%5Cy%3D52)
So, we get y = 52
Therefore,
Number of hot dogs sold = x = 56
Number of hamburgers sold = y = 52
Pretty sure the correct answer is 9/25
That's 4! (faculty), ie., 4x3x2x1 = 24.
one of four can win, then there are 3 left for second place, and so on...