Answer:
84 different lineups are possible
Step-by-step explanation:
The order in which the songs are chosen is not important. So we use the combinations formula to solve this question.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
In this question:
6 musics from a set of 9. So
![C_{9,6} = \frac{9!}{6!(9-6)!} = 84](https://tex.z-dn.net/?f=C_%7B9%2C6%7D%20%3D%20%5Cfrac%7B9%21%7D%7B6%21%289-6%29%21%7D%20%3D%2084)
84 different lineups are possible
Answer:
A. 350 ( A fifth of the cost for the television)
D. The cost of the television 1,750
Step-by-step explanation:
350 x 4 = 1,400
1,400 + 350 = 1,750
Answer:
1675 cm
Step-by-step explanation:
distance = speed · time
total distance = speed1 · time1 + speed2 · time2
= (40 cm/s)(25 s) + (15 cm/s)(45 s) = 1000 cm + 675 cm = 1675 cm
Answer:
∠C=90°
∠A=67°
∠B=23°
Step-by-step explanation:
For angle C:
Thales' Theorem states that an angle inscribed across a circle's diameter is always a right angle.
Therefore, since AB is the diameter(hypotenuse) then angle C is the right angle. (90°)
For Angle A:
The measure of arc BC= 134 degrees. We can just use a formula for an inscribed triangle. ∠A = 1/2 (mBC)
∠A= (1/2)134
∠A= 77°
For angle B:
All triangle angles all add up to 180. We can just subtract angles A and C from 180°:
∠B = 180-(90+67)
∠B = 23°