Answer:
1/12 chance
Step-by-step explanation:
Encyclopedia
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
The bold letters are the letters in the word Encyclopedia.
Q1. The answers are (–1, 8), (0, 7), (3, 18)
<span>–3x + y ≥ 7
</span>Let's go through all choices:
<span>(–2, –3)
</span>(-3) * (-2) + (-3) ≥ 7
6 - 3 ≥ 7
3 ≥ 7 INCORRECT
(–1, 8)
(-3) * (-1) + 8 ≥ 7
3 + 8 ≥ 7
11 ≥ 7 CORRECT
(0, 7)
(-3) * 0 + 7 ≥ 7
0 + 7 ≥ 7
7 ≥ 7 CORRECT
(1, 9)
(-3) * 1 + 9 ≥ 7
-3 + 9 ≥ 7
6 ≥ 7 INCORRECT
(3, 18)
(-3) * 3 + 18 ≥ 7
-9 + 18 ≥ 7
9 ≥ 7 CORRECT
Q2. The answers are:
5x + 12y ≤ 80
x ≥ 4
<span>y ≥ 0
</span>
<span>x - small boxes
</span><span>y - large boxes
</span>He has x small boxes that weigh 5 lb each and y large boxes that weigh 12 lb each <span>on a shelf that holds up to 80 lb:
5x + 12y </span>≤ 80
Jude needs at least 4 small boxes on the shelf: x ≥ 4
Let's check if y can be 0:
5x + 12y ≤ 80
5x + 12 * 0 ≤ 80
5x + 0 ≤ 80
5x ≤ 80
x ≤ 80 / 5
x ≤ 16
x ≥ 4 can include x ≤ 16
So, y can be 0: y ≥ 0
<span>Remember, the domain of a function is all of the x values in
the (x,y) coordinates. For this, let’s take a few bench mark coordinates. (0,0)
(1,2.5)(2,0) (3, -9). Those definitely aren’t all real numbers, so eliminate A.
X is not only less than or equal to 0, so eliminate C. </span>
<span>It’s B.</span>
The 3 inside angles of a triangle need to add up to 180 degrees.
You have two angles of 104 and 36.
A = 180 - 104 - 36 - 40
The answer is 40
Answer:
If 
is divisible by 3, the n is also divisible by 3.
Step-by-step explanation:
We will prove this with the help of contrapositive that is we prove that if n is not divisible by 3, then, is not divisible by 3.
Let n not be divisible by 3. Then 
can be written in the form of fraction 
, where x and y are co-prime to each other or in other words the fraction is in lowest form.
Now, squaring
Thus,
It can be clearly seen that the fraction 
is in lowest form.
Hence, is not divisible by 3.
Thus, by contrapositivity if is divisible by 3, the n is also divisible by 3.
