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Helen [10]
3 years ago
5

How many distinguishable permutations of the letters in DECEMBER are possible?

Mathematics
2 answers:
Lyrx [107]3 years ago
7 0
5 percent off the floor in the morning and
Genrish500 [490]3 years ago
7 0

#1

avatar+17746

+10

This can be calculated by using a fraction:

Count the number of letters in the word (in this case, 9) and create the numerator by the factorial of that number.

Since there are 9 letters in the word COMMITTEE, the numerator is  9!

Count the number of times each different letter is used and create the numerator by multiplying together the factorials of those numbers.  OK, that description may be clear as mud, so here's an example:

For COMMITTEE, the C is used once:  1!, the O is used once: 1!, the M is used twice: 2!, the I is used once: 1!, the T is used twice: 2!, and the E is used twice: 2!.

Putting these together, the denominator is  1!·1!·2!·1!·2!·2!  

So the answer is:  9! / [ 1!·1!·2!·1!·2!·2!  ]  =  45360

(A couple things about the denominator:  you really don't need to write down all the 1!, because their values are 1, but if you do, the sum of the numbers used in the denominator is equal to the number of letters in the word.)

Another example:  MISSISSIPPI  =  11! / [ 1!·4!·4!·2! ]


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In early spring, you buy 6 potted tomato plants for your container garden. The plants contained in 8 inch pots sell for $5 and t
prohojiy [21]
X - the number of plants in 8 in pots
y - the number of plants in 10 in pots

x+y=6\\
5x+8y=36\\\\
x=6-y\\
5x+8y=36\\
5(6-y)+8y=36\\
30-5y+8y=36\\
3y=6\\
y=2\\\\
x+2=6\\
x=4

4 plants in 8 in pots and 2 in 10 in pots.

3 0
2 years ago
What type of number has a decimal that does not repeat or end?
galina1969 [7]
A number that has a decimal that does not repeat or end in an irrational number.  The decimal goes on forever, without a pattern.  Think of it as it is irrational to keep going on and on and on.   Irrational numbers also cannot be put into fractions.
-5 is an integer, it is a whole (positive or negative without a decimal/fraction) number.  An integer can be any whole number as long as it is a whole number and does not have a decimal.<span />
4 0
3 years ago
Determine which equation is belongs to the graph of the limacon curve below.
JulsSmile [24]

Answer: Option C.

Step-by-step explanation:

We have functions of r(θ)

In our graph, we can see that the minimum value of r is when θ = 0°, and the maximum value is when θ = 180°.

We also know that the graph is in the square (-5, 5)x(-5, 5) and you can see that the maximum radius is almost less than 5.

Then let's analyze the options:

A) r = 3 - 2*cos(θ)

the maximum is at the right angle, but the maximum is:

r = 3 -2*(-1) = 5, so this maximum value is bigger than the one in the graph.

B) r = 3 - sin(θ)

For the sin functions, the maximum and minimum do not correspond with the values i write earlier, so we can discard this option.

C) r = 3 - cos(θ)

The maximum is: r = 3 - (-1) = 4, so this may be the correct answer.

the minimum is r = 3 - 1 = 2,

this is a possible equation for our circle.

D) r = 2 - 2*cos(θ)

Here, when θ = 0, we have: r = 2 - 2*1 = 0, but in the graph we can see that the radius is not 0 when θ = 0, so we can discard this option.

So the only option that makes sense is option C.

8 0
3 years ago
5(6-i)+(6-i)(3-i). show work.
Bumek [7]

47 -14i

You can work this out in the straight-forward way, or you can recognize that (6-i) is a common factor. In the latter case, you have ...

... = (6-i)(5 + 3-i)

... = (6 -i)(8 -i)

This product of binomials is found in the usual way. Each term of one factor is multiplied by each term of the other factor and the results summed. Of course, i = √-1, so i² = -1.

... = 6·8 -6i -8i +i²

... = 48 -14i -1

... =

_____

A suitable graphing calculator will work these complex number problems easily.

4 0
3 years ago
Margo wants to convince her father to change her curfew from 9 P.M. to 10 P.M. She gathers data on curfew times from a random sa
Irina-Kira [14]

Answer: No; Most students have a curfew of 9 pm or earlier

3 0
3 years ago
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