Step-by-step explanation:
½ [cos(a − b) − cos(a + b)]
Using sum and difference formulas:
½ [cos a cos b + sin a sin b − (cos a cos b − sin a sin b)]
Distribute the negative:
½ (cos a cos b + sin a sin b − cos a cos b + sin a sin b)
Combine like terms:
½ (2 sin a sin b)
Simplify:
sin a sin b
Answer:
Ren was 27.5 meters away from her family.
Step-by-step explanation:
Ren Qian was at a height of 10 meters to the ground. Let the distance from her vertical point on the ground to her family (i.e the ground distance) be represented by x.
But the angle of depression is measured with respect to the horizontal plane, so;
the vertical angle = - 20°
=
Applying the appropriate trigonometric function, we have;
Tan θ =
Tan =
⇒ x = 10 x Tan
= 10 x 2.7475
= 27.475
x = 27.5 meters
Ren was 27.5 meters away from her family.
Answer:
2d(d - 4)
Step-by-step explanation:
Given
2d² - 8d ← factor out the common factor of 2d from each term
= 2d(d - 4) ← in factored form
No, it cannot be simplified.
Prime factors of 927:3*3*103
Prime factors of 100:2*2*5*5
No factors are in common, so this is the most simplified state.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data :
Technician __Shutdown
Taylor, T___4
Rousche, R _ 3
Hurley, H__ 3
Huang, Hu___2
Gupta, ___ 5
The Numbe of samples of 2 possible from the 5 technicians :
We use combination :
nCr = n! ÷ (n-r)!r!
5C2 = 5!(3!)2!
5C2 = (5*4)/2 = 10
POSSIBLE COMBINATIONS :
TR, TH, THu, TG, RH, RHu, RG , HHu, HG, HuG
Sample means :
TR = (4+3)/2 = 3.5
TH = (4+3)/2 = 3.5
THu = (4+2) = 6/2 = 3
TG = (4 + 5) = 9/2 = 4.5
RH = (3+3) = 6/2 = 3
RHu = (3+2) /2 = 2.5
RG = (3 + 5) = 8/2 = 4
HHu = (3+2) = 2.5
HG = (3+5) = 8/2 = 4
HuG = (2+5) / 2 = 3.5
Mean of sample mean (3.5+3.5+3+4.5+3+2.5+4+2.5+4+3.5) / 10 = 3.4
Population mean :
(4 + 3 + 3 + 2 + 5) / 5 = 17 /5 = 3.4
Population Mean and mean of sample means are the same.
This distribution should be approximately normal.