Answer:
............
Step-by-step explanation:
..
.
..........
- the number of green blocks which is equal to the number of favourable events
- the number of all blocks, which is equal to the number of all possible outcomes
Answer:
n - (-6) < 9
n < 3
Step-by-step explanation:
When setting up an inequality, using the key words from the problem will help. The word 'difference' would indicate subtraction and 'less than' would be the '<' inequality sign. Since the expression is 'the difference of a number and -6', we write:
n - (-6) < 9
Whenever we subtract a negative number, we change both signs to positive:
n + 6 < 9
Using inverse operations to solve: n + 6 - 6 < 9 - 6
n < 3
Answer:
x ≈ 28.8°
Step-by-step explanation:
Using the sine ratio in the right triangle
sin x = 
= 
= 
, then
x = 
( ) ≈ 28.8° ( to the nearest tenth )
Answer:
a) cos(α+β) ≈ 0.8784
b) sin(β -α) ≈ -0.2724
Step-by-step explanation:
There are a couple of ways to go at these. One is to use the sum and difference formulas for the cosine and sine functions. To do that, you need to find the sine for the angle whose cosine is given, and vice versa.
Another approach is to use the inverse trig functions to find the angles α and β, then combine those angles and find find the desired function of the combination.
For the first problem, we'll do it the first way:
sin(α) = √(1 -cos²(α)) = √(1 -.926²) = √0.142524 ≈ 0.377524
cos(β) = √(1 -sin²(β)) = √(1 -.111²) ≈ 0.993820
__
a) cos(α+β) = cos(α)cos(β) -sin(α)sin(β)
= 0.926×0.993820 -0.377524×0.111
cos(α+β) ≈ 0.8784
__
b) sin(β -α) = sin(arcsin(0.111) -arccos(0.926)) ≈ sin(6.3730° -22.1804°)
= sin(-15.8074°)
sin(β -α) ≈ -0.2724
