Answer:
C
Step-by-step explanation:
The solution to the system of the inequalities lies in the shaded region between the 2 lines.
The ordered pairs (5, - 2), (3, 1), (4, 2) lie within this region ⇒ C
You can make a 6 x 6 square to illustrate the probabilities
1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 *
5 6 7 8 9 * &
6 7 8 9 * & $
* =10, & =11, $ = 12, I wanted maintain spacing
There are 3 4's. So it is 3/36 chance, which is 1/12 chance.
Answer:
88
Step-by-step explanation:
We can divide this into 3 shapes, a square, rectangle, and triangle.
Let's solve the area of each of these shapes and add them all up.
First, let's solve the square.
We know that one side is 4 ft so that means that the other side is also 4ft.
4*4=16
Our area of the square is 16ft^2
Let's solve the rectangle next,
Its length is 12ft and its width is 4ft.
12*4=48
So the rectangle area is 48ft^2
Now for the triangle
Remember that area of a triangle is a=hb/2
Our height is 12 ft and our base is 4ft
12*4=48
48/2=24
Triangle is 24ft^2
That means that we can add them all up
24+48+16=88
88ft^2 or 88
<span>a.{x | x is a real number such that x^2 = 1}
x^2 = 1 => x = +/- 1
=> {-1, 1} <------ answer
b.{x | x is a positive integer less than 12}
1 ≤ x < 12 => {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} <------ answer
c.{x | x is the square of an integer and x < 100}
x = n^2 < 100 => n^2 - 100 < 0
=> (n - 10) (n + 10) < 0
=> a) n - 10 > 0 and n + 10 < 0 => n > 10 and n < - 10 which is not possible
b) n - 10 < 0 and n + 10 > 0 => n < 10 and n > - 10 => - 10 < n < 10
=> n = { - 9, - 8, - 7, - 6, - 5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
=> x = {0, 1, 4, 9, 16, 25, 36, 49, 64, 81} <---- answer
d.{x | x is an integer such that x^2 = 2}
</span>
x = {∅ } because x is √2 which is not an interger but an irrational number
=> Answer: { ∅ }
