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3 years ago

Kamil and Sean share some money in the ratio 3:5. Sean gets $56 more than Kamil. How much do they get each?

1 answer:

3 0

Let Kamil get x. Therefore Sean would get (x + 56).

Kamil and Sean are in the ratio: 3:5

That means: x : (x + 56) = 3 : 5

x / (x + 56) = 3/5

5*x = 3*(x + 56)

5x = 3*x + 3*56

5x = 3x + 168

5x - 3x = 168

2x = 168

x = 168 / 2

x = 84

Therefore Kamil had, x = 84, and Sean had (x + 56) = 84 + 56 = 140

Kamil had $84 and Sean had $140

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Businesses deposit large sums of money into bank accountsImagine an account with $10 million dollars in it.

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$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$10000000\\ r=rate\to 2.12\%\to \frac{2.12}{100}\dotfill &0.0212\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{daily, thus 365} \end{array}\dotfill &365\\ t=years\dotfill &1 \end{cases}$

$A=10000000\left(1+\frac{0.0212}{365}\right)^{365\cdot 1}\implies A\approx 10214256.88 \\\\\\ \underset{\textit{earned interest amount}}{10214256.88~~ - ~~10000000 ~~ \approx ~~ \boxed{214256.88}}$

what's their difference? well

$\stackrel{\textit{compounded daily}}{\approx 214256.88}~~ - ~~\stackrel{\textit{simple interest}}{212000}\implies \boxed{2256.88}$

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2 years ago

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Tpy6a [65]

The answer is 90 degrees. SO it would be B

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3 years ago

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Consider the relation y = −8|x + 3| − 9. what are the coordinates of the vertex? (−3, 9) (−3, −9) (3, −9) (3, 9)

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(b) If a series follows geometric progression, show that the ratio of the sum of term to the sum from (n+1) term to (2n) term is

Nadusha1986 [10]

Proof with explanation:

We know that the sum of first 'n' terms of a Geometric progression is given by

$S_{n}=\frac{a(1-r^{n})}{1-r}$

where

a = first term of G.P

r is the common ratio

'n' is the number of terms

Thus the sum of 'n' terms is

$S_{n}=\frac{a(1-r^{n})}{1-r}$

Now the sum of first '2n' terms is

$S_{2n}=\frac{a(1-r^{2n})}{1-r}$

Now the sum of terms from $(n+1)^{th}$ to $(2n)^{th}$ term is $S_{2n}-S_{n}$

Thus the ratio becomes

$\frac{S_{n}}{S_{2n}-S_{n}}\\\\=\frac{\frac{a(1-r^{n})}{1-r}}{\frac{a(1-r^{2n})}{1-r}-\frac{a(1-r^{n})}{1-r}}\\\\=\frac{1-r^{n}}{r^{n}-r^{2n}}\\\\=\frac{1-r^{n}}{r^{n}(1-r^{n})}\\\\=\frac{1}{r^{n}}$

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3 years ago