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kvasek [131]
2 years ago
8

You want to randomly arrange 4 discs in a CD rack. What is the probability that the rack ends up in alphabetical order

Mathematics
1 answer:
VLD [36.1K]2 years ago
6 0

Answer:

The probability is 1/24

Step-by-step explanation:

The total number of possible arrangements is;

4! = 4 * 3 * 2 * 1 = 24

Now, out of all these, there is only one possible correct alphabetical arrangement

so, to get this probability, we have to divide 1 by the total number of possible arrangements

we have this simply as 1/24

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Rewrite 1/5 as a percent​
il63 [147K]

Answer:

20%

Step-by-step explanation:

1/5 as a percent is 20%

The 1 in 1/5 is equal to 10.

The 5 in 1/5 is equal to 50.

Therefore you would multiply 50 x 2 to get 100.

Then, you would multiply 10 x 2 to get 20/100 or 20%

7 0
3 years ago
Read 2 more answers
A rectangle is twice as long as it is wide and has the same perimeter as a square whose area is 36 square feet larger than that
Korvikt [17]

Answer:

  • rectangle: 12 ft × 24 ft
  • square: 18 ft square

Step-by-step explanation:

You want the dimensions of a rectangle and square such that they have the same perimeter, but the square has an area of 36 more square feet. The rectangle is twice as long as wide.

<h3>Setup</h3>

Let x represent the side length of the square. Then its area is x², and the area of the rectangle is (x² -36).

This area is the product of length and width. The expression factors as ...

  rectangle area = x² -36 = (x +6)(x -6)

<h3>Solution</h3>

If we assume these factors are the dimensions of the rectangle, then the longer dimension is twice the shorter one:

  (x +6) = 2(x -6)

  18 = x . . . . . . . . . add 12-x to both sides

This is the side length of the square. The rectangle dimensions are ...

  x+6 = 18+6 = 24 . . . . feet long

  x -6 = 18 -6 = 12 . . . . feet wide

The rectangle is 12 feet wide and 24 feet long. The square is 18 feet on a side.

__

<em>Additional comment</em>

The perimeter in each case is 4x = 2((x+6) +(x -6)) = 72 ft.

The area of the rectangle is (12 ft)(24 ft) = 288 ft². The area of the square is (18 ft)² = 324 ft², a value that is 36 ft² more than the rectangle area.

<em>Alternate solution</em>

Using x for the width of the rectangle, the length is 2x and its area is x(2x) = 2x². The perimeter is 2(x +2x) = 6x, so the side length of the square is (6x)/4 = 3/2x and its area is (3/2x)² = 9/4x².

The difference is 36 square feet, so we have ...

  9/4x² -2x² = 36 = x²/4   ⇒   x = √(36·4) = 6·2 = 12 . . . . width of rectangle

8 0
1 year ago
Easy geometric shapes question!
Evgen [1.6K]

Answer:

Cylinder

Step-by-step explanation:

The given geometric shape is of a cylinder.

8 0
2 years ago
Read 2 more answers
Find the number of integral solutions of x+y +z = 12, where −3 ≤ x ≤ 4, 2 ≤ y ≤ 11, and<br> z ≥ 3.
SashulF [63]

There are 59 integer solutions

Such questions are best solved by writing cases and calculating the total number of cases. So beginning with

1)  x = -3. The possible combinations are as follows:-

-3 2 13

-3 3 12

-3 4 11

-3 5 10

-3 6 9

-3 7 8

-3 8 7

-3 9 6

-3 10 5

-3 11 4

10 combinations

2) x = -2

-2 2 12

through

-2 11 3

10 combinations

3) x = -1

-1 2 11

through

-1 10 3

9 combinations

4) x = 0

0 2 10

through

0 9 3

8 combinations

as we can see from the pattern at x =1  we get 7 combinations, at x =2  we get 6 combinations, at x=3 we get 5 combinations and at x =4  we get 5 combinations.

Thus total number of combinations 4+5+6+7+8+9+10+10 = 59 integer solution.

Learn more about combinations here :

brainly.com/question/13387529

#SPJ1

5 0
1 year ago
it's sixth grade math I'm sorry for the words that are cut off you'll be able to figure out what they are i dont have a better p
alekssr [168]

8x6=48 min

Hope I helped!

7 0
2 years ago
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