Considering the definition of permutation, in 95,040 different ways he can arrange homes on the lots.
<h3>Definition of Permutation</h3>Permutation is placing elements in different positions. So, permutations of m elements in n positions are called the different ways in which the m elements can be arranged occupying only the n positions.
In other words, permutations are ways of grouping elements of a set in which:
To obtain the total of ways in which m elements can be placed in n positions, the following expression is used:
where "!" indicates the factorial of a positive integer, which is defined as the product of all natural numbers before or equal to it.
<h3>This case</h3>In this case, you know:
To obtain the total of ways in which he can arrange homes on these lots, you use the permutation. This is, 12 elements o models can be arranged occupying only the 5 positions:
Solving:
12P5= 479,001,600 ÷ 5,040
<u><em>12P5=95,040</em></u>
Finally, in 95,040 different ways he can arrange homes on the lots.
Learn more about permutation:
#SPJ4
I have attached a diagram of the triangle described.
We can use any of the trigonometric functions to find angle x. Remember, SOH CAH TOA. And since we're finding the angle, we'll need to use an inverse trigonometric function. For this problem, I'll be using the sine function.
sin(x) = 84 / 85
x = sin^-1(84/85)
x = 81.2026 degrees (feel free to round to however many places you need)
Hope this helps!! :)
Answer:
23.56
Step-by-step explanation:
2() + 2
rh
2(
)+ 2
(1.5)(1)
23.56