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Goshia [24]
3 years ago
13

Which inequality is true x=20

Mathematics
1 answer:
Licemer1 [7]3 years ago
5 0
There isn’t enough Information to answer
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Suppose we want to choose 4 colors, without replacement, from 18 distinct colors.
amm1812

Answers:

  • (a) 73440
  • (b)  3060

=====================================================

Explanation for part (a)

Consider four slots labeled A,B,C,D.

We have

  • 18 choices for slot A
  • 17 choices for slot B
  • 16 choices for slot C
  • 15 choices for slot D

We started at 18 and counted down until we filled the four slots. The countdown is because we cannot repeat a color. Multiply out those values to get the answer: 18*17*16*15 = 73440

You can use the nPr permutation formula as an alternative method

_nP_r = \frac{n!}{(n-r)!}

in this case n = 18 and r = 4. The exclamation marks indicate factorial.

-----------------------------------

Explanation for part (b)

Let's say we had color labels A,B,C,... all the way up to R which is the 18th letter in the English alphabet. From those 18 letters, we can only pick four. Let's say we pick D,E,F,G.

Focusing solely on the set {D,E,F,G}, we only have one set and the order doesn't matter. So {D,E,F,G} is the same as {D,E,G,F}.

There are 4*3*2*1 = 24 ways to arrange those four items meaning that we'll need to divide the result of part (a) by 24 to get the result of part (b)

73440/24 = 3060

You could use the nCr combination formula to get the same result

_nC_r = \frac{n!}{r!(n-r)!}

where n = 18 and r = 4 are the same from last time.

The connection between nPr and nCr is this

_nC_r = \frac{_nP_r}{r!}

which can be rearranged into

_nP_r = r!*\left( _nC_r \right)

these formulas are handy to help us go back and forth between nCr or nPr.

8 0
3 years ago
|×|=×<br>is the absolute value of x always, sometimes, or never x​
il63 [147K]

Answer:

Sometimes

Step-by-step explanation:

I’ll give you an example so you can understand:

Let’s say x is 4. So plug 4 into the problem:

|4|=4  →  This is a very true statement, where the absolute value of 4 is equal to 4.

Now, let’s say x is -7. So plug -7 into the problem:

|-7|=-7  →  This is a false statement because it’s saying that the absolute value of -7 is -7 which is very untrue.

So |x|=x only works for positive numbers, but not negative numbers. Therefore, |x|=x is the absolute value of x <u>sometimes.</u>

<u />

Hope this helps and answers your question! :)

6 0
3 years ago
Can anybody help????
pychu [463]

Answer:

x = 110° (vertically opposite angel)

6 0
3 years ago
At 1 p.m., the number of cars in a parking lot is 78. Given the formula found in the first part of the question, An=78⋅1.09n, es
Harrizon [31]

Answer:

At 6 p.m., the number of cars in a parking lot is 120

Step-by-step explanation:

At 1 p.m., the number of cars in a parking lot is 78.

Given,

A_n=78\cdot 1.09^n

Note that

A_0=78\cdot 1.09^0=78\cdot 1=78

So, 1 p.m. goes for n = 0, then

6 p.m. goes for n = 5

Thus,

A_5=78\cdot 1.09^5\approx 120

4 0
3 years ago
A candle is 6 inches tall and burns at a rate of 1/2 inch per hour. How much would be left of the candle after 3 hours?
aleksandr82 [10.1K]
The candle would be 4.5 inches tall after three hours.
8 0
3 years ago
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