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Harlamova29_29 [7]
2 years ago
14

The numbers 1, 2, 3, 4,5, 6, 7, 8, 9 are arranged in a list so that each number is either greater than all the numbers that come

before it or is less than all the numbers that come before it. For example, 4, 5, 6, 3, 2, 7, 1, 8, 9 is one such list: Notice that (for instance) the 6 is greater than all the numbers that come before it, and the 2 is less than all the numbers that come before it. How many such lists of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 are possible?
Mathematics
1 answer:
Nina [5.8K]2 years ago
4 0

The lists of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 that are possible is; 256

<h3>How to Solve Probability Combinations?</h3>

We are told that the last digit has to be either a one (1) or nine (9), then are two (2) options (>,<) for the remaining eight digits, so there are 2⁸ = 256 arraignments where each digit is either greater than or less than the preceding digits. This can be confirmed as below;

Numbers beginning with 1 = 8C0 = 1

Numbers beginning with 2 = 8C1 = 8

Numbers beginning with 3 = 8C2 = 28

Numbers beginning with 4 = 8C3 = 56

Numbers beginning with 5 = 8C4 = 70

Numbers beginning with 6 = 8C5 = 56

Numbers beginning with 7 = 8C6 = 28

Numbers beginning with 8 = 8C7 = 8

Numbers beginning with 9 = 8C8 = 1

Total lists of numbers possible = 1 + 8 + 28 + 56 + 70 + 56 + 28 + 8 + 1 = 256

Read more about Probability Combinations at; brainly.com/question/25688842

#SPJ1

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anzhelika [568]

Answer:

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Step-by-step explanation:

The proportion is equal to \frac{x}{10}=\frac{42}{35}

We can simplify the right side by dividing by 7/7 to get the right side equal to 6/5. Now we can cross-multiply to get

60=5x

Dividing both sides by 5, we have the answer as

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6 0
3 years ago
34(4a + 12) = 21 a = <br> please find my answer
noname [10]

Answer: a = 2,84

Step-by-step explanation:

34(4a + 12) = 21 a =

136a + 408 = 21

136a = -408 + 21

136a = - 387

a =   <u>- 387 </u>

         136

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8 0
3 years ago
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2 years ago
Solve the inequality and express your answer in interval notation. x^2+6x+7&lt;0
d1i1m1o1n [39]
<h2>Hello!</h2>

The answer is:

The interval notation will be:  (-∞,-1.59) and (-4.41,∞+)

<h2>Why?</h2>

To solve the expression, we need to perform the following steps:

- Find the roots or zeroes of the expression:

Using the quadratic equation, we have:

\frac{-b+-\sqrt{b^{2}-4*a*c } }{2*a}

We are given the quadratic expression:

x^{2} +6x+7

Where,

a=1\\b=6\\c=7

Then, substituting and calculating we have:

\frac{-6+-\sqrt{6^{2}-4*1*7 } }{2*1}=\frac{-6+-\sqrt{36-28 } }{2}\\\\\frac{-6+-\sqrt{36-28}}{2}=\frac{-6+-\sqrt{8}}{2}\\\\x_{1}=\frac{-6+\sqrt{8}}{2}=\frac{-6+2.82}{2}=-1.59\\\\x_{2}=\frac{-6-\sqrt{8}}{2}=\frac{-6-2.82}{2}=-4.41

- Inequality interpretation:

Now that we already know the roots of the quadratic expression, and we can see that the parabola open upwards (positive quadratic coefficient), we can conclude that the function is less than 0 between the numbers -4.41. and -1.59

The interval notation will be:and  (-∞,-1.59) and (-4.41,∞+)

Have a nice day!

Note: I have attached a picture for better understanding.

3 0
3 years ago
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