we will proceed to resolve each case to determine the solution
we have
we know that
If an ordered pair is the solution of the inequality, then it must satisfy the inequality.
<u>case a)</u> 
Substitute the value of x and y in the inequality
-------> is true
so
The ordered pair is a solution
<u>case b)</u> 
Substitute the value of x and y in the inequality
-------> is False
so
The ordered pair is not a solution
<u>case c)</u> 
Substitute the value of x and y in the inequality
-------> is False
so
The ordered pair is not a solution
<u>case d)</u> 
Substitute the value of x and y in the inequality
-------> is True
so
The ordered pair is a solution
<u>case e)</u> 
Substitute the value of x and y in the inequality
-------> is False
so
The ordered pair is not a solution
Verify
using a graphing tool
see the attached figure
the solution is the shaded area below the line
The points A and D lies on the shaded area, therefore the ordered pairs A and D are solution of the inequality
Answer:
Answer is explained below in the explanation section.
Step-by-step explanation:
Solution:
For this question, we need to have a number line, we can not make the number line here. As it will be very long. Instead, I have attached a number line from -11 to +11 for your understanding and explained it below. Please refer to the attachment below for the number line.
Number Line:
A number line is a line which contains all the numbers from negative infinity to positive infinity divided by a single number zero. It has two sides, left hand side and right hand side. A side left to zero contains all the negative numbers and a side right to 0 contains, all the positive numbers.
So,
We are asked to add 34 in (-212), we will get 178 but with the negative sign, and it will lie on the left hand side of the number line.
SO,
34 + (-212) = 34 - 212 = -178
Hence,
Our sum which is 178 will lie on the left hand side of the number line.
Answer:
22.8 and 37.5
Step-by-step explanation:
Given the
The weights (in pounds) of 18 preschool children are
32, 20, 25, 27, 31, 22, 30, 23, 44, 37, 33, 45, 41, 24, 34, 21, 39, 29
To find its 20th percentile and 75th percentile.
In ascending order we get like this
Position X (Asc. Order)
1 20
2 21
3 22
4 23
5 24
6 25
7 27
8 29
9 30
10 31
11 32
12 33
13 34
14 37
15 39
16 41
17 44
18 45
Percentile position = (no of entries +1)20/100 = 19/5 = 3.8
Since posiiton is not integer we use interpolation method.
The value of 3.8 - 3 = 0.8 corresponds to the proportion of the distance between 22 and 23 where the percentile we are looking for is located at.
Hence 20th percentile = 
So answer is 22.8
----------------------
75th percentile
Percentile posiiton = 19(75)/100 = 14.25
75th percentile= 
Similarities: same atomic number
Differences: they have a different number of neutrons
