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Sergeu [11.5K]
3 years ago
9

What's the next number? 0 , 1/3 , 1/2 , 3/5 , 2/3​

Mathematics
1 answer:
madam [21]3 years ago
6 0

Answer:

The next number of the series 0, 1/3, 1/2, 3/5, and 2/3 is 5/7

Step-by-step explanation:

The given numbers are;

0, 1/3, 1/2, 3/5, and 2/3

The number sequence is formed adding \dfrac{1}{\left (\dfrac{n^2 + n}{2} \right ) } to each (n - 1)th term to get the nth term number in the sequence, with the first term equal to 0, as follows;

For the 2nd term, the (n - 1)th term is 0, and n = 2, gives;

The

0 +\dfrac{1}{\left (\dfrac{2^2 + 2}{2} \right ) } = 0 + \dfrac{1}{3} = \dfrac{1}{3}

For the 3rd term, the (n - 1)th term is 1/3, and n = 3, gives;

\dfrac{1}{3} +\dfrac{1}{\left (\dfrac{3^2 + 3}{2} \right ) } = \dfrac{1}{3} + \dfrac{1}{6} = \dfrac{1}{2}

For the 4th term, the (n - 1)th term is 1/2, and n = 4, gives;

\dfrac{1}{2} +\dfrac{1}{\left (\dfrac{4^2 + 4}{2} \right ) } = \dfrac{1}{2} + \dfrac{1}{10} = \dfrac{3}{5}

For the 5th term, the (n - 1)th term is 3/5, and n = 5, gives;

\dfrac{3}{5} +\dfrac{1}{\left (\dfrac{5^2 + 5}{2} \right ) } = \dfrac{3}{5} + \dfrac{1}{15} = \dfrac{2}{3}

For the next or 6th term, the (n - 1)th term is 2/3, and n = 6, gives;

\dfrac{2}{3} +\dfrac{1}{\left (\dfrac{6^2 + 6}{2} \right ) } = \dfrac{2}{3} + \dfrac{1}{21} =  \dfrac{15}{21} = \dfrac{5}{7}

The next number of the series 0, 1/3, 1/2, 3/5, and 2/3 = 5/7.

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Naddik [55]
Because the nonagon is regular, the angles are equal. Nona means nine. The total of the measures of the interior angles of any polygon is (n-2)180. Use this formula to find the measure of one interior angle.
(9-2)180
7*180=1260. Divide by 9 to get the measure of one angle.
1260/9=140

The answer is 140 :)
5 0
3 years ago
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What is the probability that the first marble is blue and the second marble is yellow?
Cloud [144]

Answer:

\frac{1}{14}

Step-by-step explanation:

<u><em>First time drawing:</em></u>

Total outcome is 8

Favorable outcome is 2

The probability that the first marble drawing in random is blue is

\frac{2}{8} = \frac{1}{4}

<u><em>Second time drawing (with no replacement): </em></u>

Total outcome is 7  (8 - 1 = 7)  

Favorable outcome is 2

The probability that the second marble drawing in random is yellow is

\frac{2}{7}

<em>The probability that the first marble is blue and the second marble is yellow is</em> \frac{1}{4} × \frac{2}{7} = \frac{2}{28} = \frac{1}{14}

5 0
3 years ago
Correct answers only please!
MrRissso [65]

Answer:

23.6°

Step-by-step explanation:

In this question we have to use some trigonometry to work out angle XVW. Since we are working out angles all of the trigonometric functions will have to be to the ⁻¹. The first thing we need to identify is will formula will we use out of the following:

Sin⁻¹ = Opposite ÷ Hypotenuse

Tan⁻¹ = Opposite ÷ Adjacent

Cos⁻¹ = Adjacent ÷ Hypotenuse

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

10 = Hypotenuse

4 = Opposite

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We know which formula to use because the length won't be in the triangle for example we will be using the Sin triangle because we don't have an adjacent. If we don't have an adjacent then the other formula's won't work.

Now we substitute in the values to find the value of angle XVW

Sin⁻¹ = Opposite ÷ Hypotenuse

Sin⁻¹ = 4 ÷ 10

The value of angle XVW is 23.57817848

6 0
3 years ago
PLEASE HELP ASAP 35 POINTS
podryga [215]

Your answer is A

It cannot be C because the line y > -2  uses the (>) greater than symbol.

When equations have a greater than symbol, they are graphed using a <u>dotted line. </u>

It cannot be D because the line is  y ≤ - l x-1 l

with the less than or equal to sign (≤) , you use a <u>solid line</u> to graph


With the<u> greater than</u> symbol for y > -2 , the shaded region must be <em>above </em>this line.

With the <em>less than </em>or equal to sign in y ≤ - l x-1 l , the shaded region must be <em>below </em>the line.


Hope I helped - message me if you have any questions :)

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jek_recluse [69]

Answer:

I hope this is correct but 8.5 or 8 1/2 Units

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