How many different arrangements can be made using all of the letters in the word iowa?

1. Check the tree diagram in the attached picture.

2. The first Letter can be one of the letters I, O , W or A. Assume your first letter is I, then you have 3 choices for the second letter, that is O, W or A.

3. Assume you pick O, then you have 2 options for the third letter; W or A. 

4. If you pick A, then the last letter can only be W. 

5. the path described is the "red line path" in the picture; that is the arrangement IOAW.

6. Another path is the "dashed line path" IAOW.

7. We count 6 "paths", where I is the first letter, each "path" standing for one arrangement. 

8. 4*6=24 is the total number of paths, that is arrangements of the letters IOWA.

9. Remark: The first choice is 4, combined (multiplied) by 3 choices for the second letter, combined (multiplied) by 2 choices for the third and finally multiplied by 1.

10. Thus there are 4*3*2*1 arrangements of 4 (different) letters.

The answer is 15×7=105therefore, 105×5=525 miles

first anwser choice.

step-by-step explanation:

the greater/less or equal to symbol (> or < with the line at the bottom) is a closed/filled in circle.

when multiplying or dividing by a negative on both sides you have to flip the inequality sign. this rule only applies to multiplying or dividing by a negative number in inequality equations. this rule is really important.

-5c + 2 _< _27

subtract from both sides by 2

-5c _< _ 27

divide both sides by -5

c _< _ 5.4

flip the inequality sign

c _> _5.4

the only possible answer that would match the simplified inequality is the first answer choice