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Schach [20]
2 years ago
12

Sarah has 25 candies. Sarah gave 2/5 of the candies to her sister. Of the amount left she gave 2/3 to her friend. How many candi

es does Sarah have left
Mathematics
1 answer:
satela [25.4K]2 years ago
3 0

Answer:

5 candies

Step-by-step explanation:

Total of candy Sarah has = 25candies

If Sarah gave 2/5 of the candies to her sister, the total amount she gave her sister will be 2/5 of 25

2/5 of 25 = 10

The remaining candy left will be 25-10 which is 15.

If she gave 2/3 of amount left to her friend, the amount she gave her friend will be 2/3×15 = 10candies.

The amount of candy Sarah have left will be 15- 10 which is 5candies.

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Determine formula of the nth term 2, 6, 12 20 30,42​
nalin [4]

Check the forward differences of the sequence.

If \{a_n\} = \{2,6,12,20,30,42,\ldots\}, then let \{b_n\} be the sequence of first-order differences of \{a_n\}. That is, for n ≥ 1,

b_n = a_{n+1} - a_n

so that \{b_n\} = \{4, 6, 8, 10, 12, \ldots\}.

Let \{c_n\} be the sequence of differences of \{b_n\},

c_n = b_{n+1} - b_n

and we see that this is a constant sequence, \{c_n\} = \{2, 2, 2, 2, \ldots\}. In other words, \{b_n\} is an arithmetic sequence with common difference between terms of 2. That is,

2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2

and we can solve for b_n in terms of b_1=4:

b_{n+1} = b_n + 2

b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2

b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2

and so on down to

b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)

We solve for a_n in the same way.

2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)

Then

a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)

a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))

a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))

and so on down to

a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2

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6 0
2 years ago
What percent of 1.60 is 6
JulsSmile [24]
N% x 1.60 = 6   (I turned it from English to math)
Can't move n% back two places to make it a decimal so I will move the number I am multiplying by n% back two places instead.
Here is a sample to show you why it works.    .34 x 57 = 34 x .57

So
.016n = 6   (.016 is 1.60 decimal moved back two places)

Now divide both sides by .016
<u>.016</u>n   = <u>6
</u><u />.016     .016      n = 375%     

Why is the percent over 100% you might ask?

What % of 1.60 is 1.60  (Answer - all of it or 100%)
So What % of 1.60 is 6  - the number 6 being much bigger than 1.60, it is not surprising that the percent is more than 100.

What % of 1.60 is 1.60  - 100%
What %  of 1.60 is 3.20 - 200%   (notice that 3.20 is twice 1.60)
What % of 1.6 is 4.80   - 300%   (notice that 4.80 is three times 1.60)
What % of 1.6 is  6.40   - 400%  (notice that  6.40 is four times 1.60)
6 (the number in the problem) is just a bit less than 6.40  so 375% makes a lot a sense.
Hope you found this helpful. 

6 0
3 years ago
What is the solution to the equation represented by the model below?
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Answer: C: X=2

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PLZ MARK BRAINLIEST

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33 pages because you subtract 13 from 103 which is 90 then divide that by 3 and that gives you 30 pages then you add the other 3 pages that costed $13.

4 0
3 years ago
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