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dusya [7]
2 years ago
9

Help me out please and thank youuuu!!

Mathematics
1 answer:
nataly862011 [7]2 years ago
7 0

Answer:

a) 9/10 or 90%

b)2/3 or 67%

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Describe the rule for the sequence 2, 1, 2/3, 1/2, 2/5, 1/3, 1/7,...
Triss [41]

Multiply 2 by 1/2 to get 1.

Multiply 1 by 2/3 to get 2/3.

Multiply 2/3 by 3/4 to get 6/12 = 1/2.

Multiply 1/2 by 4/5 to get 4/10 = 2/5.

Multiply 2/5 by 5/6 to get 10/30 = 1/3.

Multiply 1/3 by 6/7 to get 6/21 = 2/7. (I suspect there's a typo in the question.)

And so on, so that the <em>n</em>th term in the sequence is multiplied by <em>n</em>/(<em>n</em> + 1) to get the (<em>n</em> + 1)th term.

Recursively, the sequence is given by

\begin{cases}a_1=2\\a_n=\dfrac{n-1}na_{n-1}&\text{for }n>1\end{cases}

We can solve this exactly by iterating:

a_n=\dfrac{n-1}na_{n-1}=\dfrac{n-1}n\dfrac{n-2}na_{n-1}=\dfrac{n-1}n\dfrac{n-2}{n-1}\dfrac{n-3}{n-2}a_{n-3}=\cdots

and so on down to

a_n=\dfrac{(n-1)\cdot(n-2)\cdot(n-3)\cdot\cdots\cdot3\cdot2\cdot1}{n\cdot(n-1)\cdot(n-2)\cdot\cdots\cdot4\cdot3\cdot2}a_1

or

a_n=\dfrac{(n-1)!}{n!}a_1

and with lots of cancellation, we end up with

a_n=\dfrac{a_1}n=\boxed{\dfrac2n}

6 0
3 years ago
Asp helppp will mark brainliest if correct answer.
GalinKa [24]

Answer:

two dice are thrown, so S = {(1,1); (1,2); (1,3); ...;(6,5); (6,6)} ---> 36

the sum is 2, 4, 6

sum = 2 --> (1,1) ---> 1

       = 4 --> (1,3); (2;2); (3,1) ---> 3

       = 6 --> (1,5); (2,4); (3,3); (4;2); (5,1) ---> 5

⇒ \frac{1 + 3+ 5}{36} = 9/36 = 1/4

6 0
3 years ago
Read 2 more answers
What is the domain of the function y=tan (x/8)<br> Please Help<br> 15 Points
7nadin3 [17]

1. You have the function y=tan(\frac{x}{8} )

2. You know that y=\frac{sinx}{cosx} with cosx\neq 0, because the division by zero is not defined. So , cosx=0 for \frac{(2n+1)\pi}{2} where n is a integer number.

3. Then, to find the domain of the function given in the problem, you must make \frac{x}{8} \neq \frac{k\pi}{2}  \\ x\neq 4k\pi

Where k is odd number.

4. Therefore:

x\neq 4\pi (2n+1)

5. Finally, the domain is: 4\pi (2n+1)

The answer is: 4\pi (2n+1)

5 0
3 years ago
Read 2 more answers
A lumberjack can cut a log into 5 pieces in 20 minutes. How long does it take to cut a log of the same size and shape into 7 pie
Nitella [24]

Answer:

28minutes

Step-by-step explanation:

Use this simple trick, it can be used almost everywhere

Time taken pieces

20mins 5

? 7

An x shape is always multiply and straight line is divide

So (7 x 20) ÷5

If u still don't understand, just comment again

8 0
3 years ago
Help please pls pls pls
Marysya12 [62]

Answer:

The right answer is  neither

Step-by-step explanation:

I said because Exponential describes a very rapid increase. ... Exponential is also a mathematical term, meaning "involving an exponent." When you raise a number to the tenth power, for example, that's an exponential increase in that number. the part involves exponent is the y part same number multiple to it self to get the next answer  while the x part one specific number to get the next number which is linear but since theyre asking about the relationship it’s neither because both were supposed to have the same relationship linea for x and y or exponential for x and y but they both are different.

3 0
3 years ago
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