Answer:
The number of ways the arrangements can be made of the letters of the word'WONDERFUL' such that the letter R is always next to E is 10,080 ways
Step-by-step explanation:
We need to find the number of ways the arrangements can be made of the letters of the word'WONDERFUL' such that the letter R is always next to E.
There are 9 letters in the word WONDERFUL
There is a condition that letter R is always next to E.
So, We have two letters fixed WONDFUL (ER)
We will apply Permutations to find ways of arrangements.
The 7 letters (WONDFUL) can be arranged in ways : ⁷P₇ = 7! = 5040 ways
The 2 letters (ER) can be arranged in ways: ²P₂ =2! = 2 ways
The number of ways 'WONDERFUL' can be arranged is: (5040*2) = 10,080 ways
So, the number of ways the arrangements can be made of the letters of the word'WONDERFUL' such that the letter R is always next to E is 10,080 ways
Answer:
The distance is 
or 
.
Step-by-step explanation:
Slope of parallel: 2
Slope of perpendicular: -1/2
Pick a point for y =2x + 7. For example (0,7)
Use the perpendicular slope to get to the other line to find the other point of y=2x-3. Look at the screenshot...I got (4,5).
Distance formula 
Insert (0,7) and (4,5)
= 
Answer:
Step-by-step explanation:
Divide the number of miles in the trip by the number of miles your vehicle gets per gallon. For example, if you are traveling 1,500 miles to Orlando and your vehicle gets 30 miles per gallon, you will use 50 gallons of fuel.
Using proportions, it is found that the original sample weighed 
grams.
- This question is solved by <em>proportions</em>, using a rule of three.
- The weight of 1 batch, in grams, is of
. How much do the sample of 12 batches weigh?
The rule of three is:
1 batch - grams.
12 batches - x grams
Applying cross multiplication:
Applying scientific notation:
The original sample weighed grams.
You can learn more about proportions at brainly.com/question/24372153
Answer:
x=4
Step-by-step explanation:
1. isolate the variable by subtracting 7 on both sides: 4x=23-7
2. simplify: 4x=16
3. divide both sides by 4: x=16/4
4. simplify: x=4
