Answer: see proof below
<u>Step-by-step explanation:</u>
Given: A + B + C = π → C = π - (A + B)
→ sin C = sin(π - (A + B)) cos C = sin(π - (A + B))
→ sin C = sin (A + B) cos C = - cos(A + B)
Use the following Sum to Product Identity:
sin A + sin B = 2 cos[(A + B)/2] · sin [(A - B)/2]
cos A + cos B = 2 cos[(A + B)/2] · cos [(A - B)/2]
Use the following Double Angle Identity:
sin 2A = 2 sin A · cos A
<u>Proof LHS → RHS</u>
LHS: (sin 2A + sin 2B) + sin 2C
![\text{Factor:}\qquad \qquad \qquad 2\sin C\cdot [\cos (A-B)+\cos (A+B)]](https://tex.z-dn.net/?f=%5Ctext%7BFactor%3A%7D%5Cqquad%20%5Cqquad%20%5Cqquad%202%5Csin%20C%5Ccdot%20%5B%5Ccos%20%28A-B%29%2B%5Ccos%20%28A%2BB%29%5D)
LHS = RHS: 4 cos A · cos B · sin C = 4 cos A · cos B · sin C 
Answer:
5
Step-by-step explanation:
1,2,5
Answer:
C = 5Q
Step-by-step explanation:
C = Length of Cloth in Meters (C)
Q = Number of Quilts Made (Q)
C = 5Q
Change C for the numbers under (Length of Cloth in Meters (C))
Nad change Q for the numbers under (Number of Quilts Made (Q))
So the new equations would be:
0 = 5(0) ---------> 0 = 0
5 = 5(1) ---------> 5 = 5
10 = 5(2) ---------> 10 = 10
15 = 5(3) ---------> 15 = 15
20 = 5(4) ---------> 20 = 20
25 = 5(5) ---------> 25 = 25
So the only option that amkes sense is (C = 5Q)
Answer:
g(x) = -|x|
Step-by-step explanation:
Are you familiar with the absolute value function y = |x|?
Its graph is v-shaped and opens up.
If the graph is turned upside down (so that it opens down), then g(x) = -|x|.
Answer:
a.) .95
b.) The expected number of baskets is 10.50.
c.) 1.7748
Step-by-step explanation:
a.) This is a binomial distribution as there are two possibilities: makes a free throw or doesn't. This means that you can use the binomial function on a calculator to figure out the answer. Use the binomial CDF function on a calculator and the number of trials=15, probability of success=.7, lower bound=0, upper bound=7. Once you have evaluated the answer, .0500, it will need to be subtracted from1, as you want everything not included in this section. The answer to part a is thus 1-.0500=.95.
b.) The expected value is calculated by taking the total number of shots and multiplying it by the probability of making the shot: 15×.7=10.5 shots.
c.) The standard deviation of a binomial distribution can be calculated by the formula 
. Plugging in the numbers you get 
=1.7748.
