Answer:
The solution of |3x-9|≤15 is [-2;8] and the solution |2x-3|≥5 of is (-∞,2] ∪ [8,∞)
Step-by-step explanation:
When solving absolute value inequalities, there are two cases to consider.
Case 1: The expression within the absolute value symbols is positive.
Case 2: The expression within the absolute value symbols is negative.
The solution is the intersection of the solutions of these two cases.
In other words, for any real numbers a and b,
- if |a|> b then a>b or a<-b
- if |a|< b then a<b or a>-b
So, being |3x-9|≤15
Solving: 3x-9 ≤ 15
3x ≤15 + 9
3x ≤24
x ≤24÷3
x≤8
or 3x-9 ≥ -15
3x ≥-15 +9
3x ≥-6
x ≥ (-6)÷3
x ≥ -2
The solution is made up of all the intervals that make the inequality true. Expressing the solution as an interval: [-2;8]
So, being |2x-3|≥5
Solving: 2x-3 ≥ 5
2x ≥ 5 + 3
2x ≥8
x ≥8÷2
x≥8
or 2x-3 ≤ -5
2x ≤-5 +3
2x ≤-2
x ≤ (-2)÷2
x ≤ -2
Expressing the solution as an interval: (-∞,2] ∪ [8,∞)
Answer:
Step-by-step explanation:
How to Find Outliers Using the Interquartile Range(IQR)
Step 1: Find the IQR, Q1(25th percentile) and Q3(75th percentile). ...
Step 2: Multiply the IQR you found in Step 1 by 1.5: ...
Step 3: Add the amount you found in Step 2 to Q3 from Step 1: ...
Step 3: Subtract the amount you found in Step 2 from Q1 from Step 1:
Answer:
Step-by-step explanation:
The first 6 rows of the eruptions data :
eruptions waiting
1 3.600 79
2 1.800 54
3 3.333 74
4 2.283 62
5 4.533 85
6 2.883 55
R code :
1. You can directly access the "Faithful" data in R without importing the data. The dataset faithful is present in the R or you can load the datasets. or use install the datasets.load. package
If you have the data in a text file, make sure all the columns and rows are separated by commas
Step 1: open notepad
Step 2: enter data with no spaces but only commas
Step 3: save the file as ‘faithful.txt’ on your Desktop
# Get R help
?read.table
# Import the data
rain<-read.table("C:/Users/YOUR-NAME/Desktop/faithful.txt", header = TRUE,
sep = ",")
Check the data
data("faithful") #Loading Faithful data
head(faithful, 6) #Reading first 6 rows of the data
That means there would be 28 in California and still 12 in Nevada or if California takes from Nevada it would be California 28 and Nevada 2
