Giving extra points and brainliest

0/1 For positive integer n, n? = n! · (n − 1)! · … · 1! And n# = n? · (n − 1)? · … · 1?. What is the value of 4# · 3# · 2# · 1#?

MakcuM [25]

Answer:

331776

Step-by-step explanation:

Since n? = n! · (n − 1)! · … · 1! And n# = n? · (n − 1)? · … · 1?

Then 4# = 4? · (4 − 1)? · (4 − 2)?· 1?

= 4? · 3? · 2?· 1?

Now, n? = n! · (n − 1)! · … · 1!

So, 4? = 4! · (4 − 1)! · (4 − 2)! · 1! = 4! · 3! · 2! · 1! = 288

Thus, 3? = 3! · (3 − 1)! · 1! = 3! · 2! · 1! = 12

Also, 2? = 2! · (2 − 1)! · 1! = 2! · 1! · 1! = 2

and 1? = 1! · (1 − 1)! · 1! = 1! · 0! · 1! = 1

So, 4# = 4? · 3? · 2?· 1? = 288 × 12 × 2 × 1 = 6912

We now find 3#

3# = 3? · (3 − 1)? · 1? = 3? · 2?· 1?

Now, n? = n! · (n − 1)! · … · 1!

So, 3? = 3! · (3 − 1)! · 1! = 3! · 2! · 1! = 12

Thus, 2? = 2! · (2 − 1)! · 1! = 2! · 1! · 1! = 2

and, 1? = 1! · (1 − 1)! · 1! = 1! · 0! · 1! = 1

So, 3# = 3? · 2?· 1? = 12 × 2 × 1 = 24

We now find 2#

2# = 2? · (2 − 1)? · 1? = 2? · 1?· 1?

Now, n? = n! · (n − 1)! · … · 1!

So, 2? = 2! · (2 − 1)! · 1! = 2! · 1! · 1! = 2

1? = 1! · (1 − 1)! · 1! = 1! · 0! · 1! = 1

So, 2# = 2?· 1? = 2 × 1 = 2

We now find 1#

1# = 1? · 1? = 1? · 1?

Now, n? = n! · (n − 1)! · … · 1!

So, 1? = 1! · (1 − 1)! · 1! = 1! · 0! · 1! = 1

And, 1# = 1? · 1? = 1 × 1 = 1

So, 4# · 3# · 2# · 1#? = 6912 · 24 · 2 · 1? = 331776

7 0

3 years ago

In a game of chance, two pyramid-shaped, four-sided dice (with sides 1, 2, 3, 4). one colored red and the other colored green, a

Soloha48 [4]

Answer:

0.25 or 25%

Step-by-step explanation:

There are 4 possible outcomes for each die, which gives us 16 possible combinations (4 x 4). In order for the sum to exceed 5, the possible outcomes are:

Red = 3, and Green = 3

Red = 3, and Green = 4

Red = 4, and Green = 3

Red = 4, and Green = 4

Therefore, the probability of winning on a single play is:

$P=\frac{4}{16}\\P=0.25$

The probability is 0.25 or 25%.

5 0

3 years ago

Help I guess? sorry I'm asking a lot of questions today

valina [46]

Answer:

63 houses have been sold this year.

Step-by-step explanation:

There are 81 houses in the community. If 7/9 are sold this year, then all you have to do is multiplication.

In this case, you would multiply 81 by 7/9 to get your answer.

81/1 x 7/9:

Cancel out the 9 and the 81. Then the denominator will be 1 x 1 and the numerator would be 7 x 9. It would be 63 (7x9=63) over 1 (1x1=1) which is just 63. Make sure to include units.

4 0

3 years ago

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Marla bought 12 books at a garage sale. Some of them were hardback and the rest were paperback. She paid $0.50 for each paperbac

olga nikolaevna [1]

Answer: The number of books bought were 9 paperbacks and 3 hardbacks

Step-by-step explanation: We shall start by assigning letters to the unknown variables, hence let the hardback be called h, while the paperback shall be called p.

If Marla bought 12 books at the garage sale, that means she bought

h + p = 12 ------(1)

Then she paid 0.5 dollars for paperback and 0.75 dollars for hardback and the total spent was 6.75 dollars for all of them, then we can express these as follows;

0.5p + 0.75h = 6.75 ------(2)

We now have a pair of simultaneous equations which are

h + p = 12 ------(1)

0.5p + 0.75h = 6.75 ------(2)

From equation (1), make h the subject of the equation,

h = 12- p

Substitute for h into equation (2)

0.5p + 0.75(12 - p) = 6.75

0.5p + 9 - 0.75p = 6.75

0.5p - 0.75p = 6.75 - 9

-0.25p = -2.25

Divide both sides of the equation by -0.25

p = 9

Now, substitute for p into equation (1)

h + p = 12

h + 9 = 12

Subtract 9 from both sides of the equation

h = 3

Therefore Marla bought 9 paperbacks and 3 hardbacks

6 0

3 years ago

Read 2 more answers

which statements are true? check all that apply. the line x = 0 is perpendicular to the line y = –3. all lines that are parallel

CaHeK987 [17]

1) True that line x = 0 is perpedicular to y = -3. Because x = 0 is parallel to the y-axis and y = -3 is parallel to the x-axis.

2) True that all the lines that are parallel to the y-axis are vertucal lines (the y-axis is vertical)

3) False that all lines perpendicular to the x-axis have a slope o 0. Their slope trends to infinity.

4) False that the equation of the line parallel to the x-axis that passes through the point (2, –6) is x = 2. The right equation is y = - 6

5) True thath the equation of the line perpendicular to the y-axis that passes through the point (–5, 1) is y = 1

4 0

3 years ago

Read 2 more answers