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3 years ago

70% of what number is 280

Mathematics

2 answers:

Nataly_w [17]3 years ago

8 0

Multiply 280 by 0.7/ the percent divided by 100
you should get 196 as your answer

Ira Lisetskai [31]3 years ago

6 0

$1\% = \frac{1}{100}\\ \\70\% = \not70^7*\frac{1}{\not100 ^{10}}=\frac{7}{10}\\ \\\frac{7}{\not10^1}* \not280^{28}=7*28 = 196$

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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

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

$\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}$

6 0

2 years ago

Help!!!!! I'm timed!!!!!

djverab [1.8K]

Answer:

Option C, $28$

Step-by-step explanation:

$2\sqrt{98} * 2$

$2\sqrt{7^2*2} *\sqrt{2}$

$14\sqrt{2} * \sqrt{2}$

$14*2$

$28$

Answer: Option C, $28$

5 0

3 years ago

Write the integer represented by H. List its opposite and absolute value.

musickatia [10]

Answer:

The integer represented by H is -2

Its opposite is 2 and the absolute value is also 2

4 0

3 years ago

PLEASE help (desperate) :(

mars1129 [50]

Answer:

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6 0

3 years ago

if i supposedly got 2 cats and trained them to bring me quarters and they did and supposedly everyday i got 10 quarters how much

ivanzaharov [21]

Answer:

After a year you would have $1,825

Step-by-step explanation:

Amount for one cat a day in cents

10x25=250

Amount for one cat for a year in cents

250x365=91,250

Amount for both cats for a year in cents

91,250x2=182,500

Amount for both cats for a year dollars

182,500/100=1,825

8 0

2 years ago