X=Since you have an angle, a hypotenuse, and the opposite side, we can use:
sin(x)=opposite/hypotenuse
sin(60)=x/8 (cross multiply)
sin(60)*8=x
√3/2*8=x
x=8√3/2
x=4√3 so the answer is B
Hope this helps
Answer:
The answer is that adult tickets cost $44.50 and child tickets cost $19.
Step-by-step explanation:
Let c = the cost of child tickets and a = the cost of adult tickets.
The total amount is equal to the number of adult tickets time the cost of adult tickets plus the number of child tickets times the cost of child tickets. Set up two equations:
2a + 4c = 165
4a + 3c = 235
Solve the top equation for a:
2a + 4c = 165
2a = 165 - 4c
a = 165/2 - 4c/2
a = 82.5 - 2c
Substitute into the second equation:
4a + 3c = 235
4(82.5 - 2c) + 3c = 235
330 - 8c + 3c = 235
-5c = -95
c = -95 / -5 = 19, so child ticket cost $19.
Solve for a:
a = 82.50 - 2c
a = 82.50 - 2(19)
a = 82.50 - 38
a = $44.50, so adult tickets cost $44.50.
Proof using the first equation for the Johnson family:
2a + 4c = 165
2(44.50) + 4(19) = 165
89 + 76 = 165
165 = 165
Proof using the second equation for the Robison family:
4a + 3c = 235
4(44.50) + 3(19) = 235
178 + 57 = 235
235 = 235
Answer:
A) 56
B) 21
Step-by-step explanation:
A) The number of delegations possible is given by;
C(n,r) = n!/[(n - r)!(r!)]
In this question, n = 8 and r =3
Thus,
C(8,3) = 8!/[(8 - 3)!(3!)] = 56
B) Since a particular member must be in the delegation, the number of outcomes will now be;
C(n, r) - C(n-1,r)
Thus, we have;
C(8,3) - C(7,3)
= 56 - [7!/[(7 - 3)!(3!)]
= 56 - 35 = 21
