Answer:
a. 5,040 ways
b. 210 ways
Step-by-step explanation:
a) We want to pick 4 numbers out of 10 given that orders matter
If orders do matter, it will be a permutation problem
Mathematically;
n P r = n!/(n-r)!
In this case, n is 10 and r is 4
Thus, we have it that;
10 P 4 = 10!/(10-4)! = 5,040
b) if orders do not matter
It will be a combination problem
n C r = n!/(n-r)!r!
n = 10 and r = 4
10 C 4 = 10! /(10-4)!4!
= 210
Answer:
sin X
Step-by-step explanation:
sin X = 
= 
= 
Answer:
θ = 38°
Step-by-step explanation:
The lower right triangle is congruent to the upper left triangle, so we have θ and 20° being the two acute angles in the triangle. The law of sines tells you ...
sin(θ)/9 = sin(20°)/5
sin(θ) = (9/5)sin(20°)
θ = arcsin(9/5·sin(20°)) ≈ 38°
___
Another solution to the triangle is θ = 180° -38° = 142°. The diagram clearly shows θ as an acute angle, so we take this second solution to be extraneous.
(3x + 1) (2x + 7)
Factored by grouping
We know, distributive property: a(b + c) = ab + ac
4(x + 2) = 4x + 8
In short, Your Answer would be Option B
Hope this helps!
