My answer isn't in your choices so it's probably wrong, but hopefully my approach can give you hints.

The vowels are AEAI
The vowels can be arranged in 4*3*2=24 ways.

The non vowels are MTHMTCS
If the vowels must be together, there have to be in one of the spaces between the non vowels.
If we look at it like this:
-M-T-H-M-T-C-S-
The 4 vowels must go in one of the places marked with a dash.
There are thus 8 places to choose from.

But we must also consider that the non vowels can be arranged in any way. There are 7 of them, so they can be arranged in 7*6*5*4*3*2=5040 ways.

Multiply everything together to get 8*5040*24=967680

3 0

3 years ago

In proper paragraph form,explain the difference between the union and intersection of two sets.

Sophie [7]

The <em><u>correct answer</u></em> is:

The union of two sets is a combination of all elements from both sets. The intersection of two sets, on the other hand, is a set of the elements common to both sets.

For instance, if we have the sets {1, 3, 5, 7, 9} and {3, 6, 9, 12, 15}, the union would be the combination of both:

{1, 3, 5, 6, 7, 9, 12, 15}

The intersection of the sets would be the common elements. The only elements that are in both sets are 3 and 9. This makes the intersection

{3, 9}

6 0

3 years ago

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The numbers on two consecutively numbered gym lockers have a sum of 141. What are the locker numbers?

lesantik [10]

Answer:

70 and 71

Step-by-step explanation:

Consecutive means in a row

x is the first number

x+1 is the next number

x+ x+1 = 141

Combine like terms

2x+1 =141

Subtract 1 from each side

2x+1-1=141-1

2x= 140

Divide each side by 2

2x/2 =140/2

x = 70

The two lockers are 70,71

5 0

3 years ago

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