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Viktor [21]
2 years ago
11

Divide. 8.43) 12.645 The quotient is

Mathematics
1 answer:
12345 [234]2 years ago
8 0

Answer:

1.5 or 3/2

Step-by-step explanation:

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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
What is StartFraction 8 Over 9 EndFraction divided by two-thirds? A fraction bar labeled 1. Under the 1 are 9 boxes containing o
marshall27 [118]

Answer:

C 1 1/3 I got it right in the quiz

4 0
3 years ago
Read 2 more answers
Help please!!!!!!!!!!!!!!
zhenek [66]

Answer:

y=-1/3x+9

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Abby and Alex were practicing free throws. Abby attempted 40 shots and made 36 of them. Alex attempted 60 shots and made 54 of t
ZanzabumX [31]

Answer:

Abby is the answer

Step-by-step explanation:

When you calculate Abby’s free throws you should realize

40 - 36 = 4

However with Alex’s free throws you calculate

60 - 54 = 6

When you compare the two Abby has a higher percentage of attempts because she was more successfu!

3 0
3 years ago
Read 2 more answers
Last week, a skate shop originally sold a skateboard for $120. Today, there is a sale and the same skateboard costs $96. What is
Tamiku [17]
120 - 96 = 24

Now we have to find what percent of 120 24 is.

x × 120 = 24
x = 0.2

0.2 means 20%.

The discount is 20% off.
8 0
3 years ago
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