Answer:
see explanation
Step-by-step explanation:
Using the double angle identity for sine
sin2x = 2sinxcosx
Consider left side
cos20°cos40°cos80°
= 
(2sin20°cos20°)cos40°cos80°
= 
(2sin40°cos40°)cos80°
= (sin80°cos80° )
= 
(2sin80°cos80° )
= . sin160°
= . sin(180 - 20)°
= . sin20°
= 
= right side , thus proven
(A)
P(<em>X</em> < 61.25) = P((<em>X</em> - 55.4)/4.1 < (61.25 - 55.4)/4.1)
… ≈ P(<em>Z</em> ≤ 0.1427)
… ≈ 0.5567
(B)
P(<em>X</em> > 46.5) = P((<em>X</em> - 55.4)/4.1 > (46.5 - 55.4)/4.1)
… ≈ P(<em>Z</em> > -2.1707)
… ≈ 1 - P(<em>Z</em> ≤ -2.1707)
… ≈ 0.9850
Answer: 3/2
Step-by-step explanation:
The first one: y=2x+5
X=2y+5.Then solve for y after switching x and y
X-5=2y, X-5/2=y
Since F-1= X-5/ 2, we plug the value of X in
8-5/2, so it should be 3/2
If 50 students prefer vanilla ice cream then 259 students were surveyed.
The wavefunction for a particle in a one-dimension box is a well-known problem, which has as a solution:
Ψ(x) = √(2/l) sin (nπx/l)
When the box has three dimensions, the general solution is simply the multiplication of the solutions for each dimension, therefore:
Ψ(x) = K · sin (n_x·π·x / l) · sin (n_y·π·y / l) · sin <span>(n_z·π·z / l)</span>
