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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
LHS = RHS: 4 cos A · cos B · sin C = 4 cos A · cos B · sin C
<h3>Answer: B. About 93%</h3>
You have the correct answer.
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Explanation:
Focus solely on the "in anime club" row. We do this because of the phrasing "given the student is in the anime club". We know for a fact that whoever is randomly picked, they are in the anime club. So we don't have to worry about other data values in the other rows.
Divide the value 0.13 which is in the "takes Japanese" column over 0.14, which is in the "total" column.
Basically we're computing where A and B represent the events "takes Japanese" and "in anime club" respectively. The upside down U symbol represents intersection to indicate both events are happening at the same time.
So we end up with 0.13/0.14 = 0.92857142857142 which rounds to 0.93, then that converts to 93% when you move the decimal point over to the right two spots.
Answer:
53.33
Step-by-step explanation:
finding area of ΔPAM
using similar triangles
16 = 12x; x =
ΔPAM = 4/3 * 4 * 1/2 = 16/6 = 8/3
ΔPAL = 4 * 12 * 1/2 = 24
24 + 8/3 = 80/3 (using fraction form for now, will round later)
since there are two ΔPLM (ΔLMU has same area since they are congruent)
we can multiply 80/3 by 2
80/3 * 2 = 160/3 = 53.33