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Katarina [22]
3 years ago
14

Trent invests $8700 in two different accounts. The first account paid 4 %, the second account paid 8 % in interest. At the end o

f the first year he had earned $540 in interest. How much was in each account
please i need it
Mathematics
1 answer:
Mnenie [13.5K]3 years ago
4 0

a = amount invested at 4%

b = amount invested at 8%

we know the total amount invested is 8700, so if he invested "a" already, the second amount must be b = 8700 - a.

\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{4\% of a}}{\left( \cfrac{4}{100}\right)a\implies 0.04a}~\hfill \stackrel{\textit{8\% of b}}{\left( \cfrac{8}{100} \right)b\implies 0.08b} \\\\[-0.35em] ~\dotfill

\bf \stackrel{\textit{sum of the percentages}}{0.04a+0.08b}~~=~~\stackrel{\textit{yield for 1 year}}{540}\implies 0.04a+0.08\left(\boxed{8700-a} \right) = 540 \\\\\\ 0.04a-0.08a+696=540\implies -0.04a+696=540\implies -0.04a=-156 \\\\\\ a= \cfrac{-156}{-0.04}\implies \blacktriangleright a = 3900 \blacktriangleleft~\hfill b = 8700-3900\implies \blacktriangleright b = 4800 \blacktriangleleft

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Here, the equation is solved by subtracting 17/3, then subtracting 1/2x, then multiplying by the inverse of the coefficient of x. After each of these steps is a simplification.

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Answer:

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Step-by-step explanation:

Let the random variable <em>X</em> represent the number of chocolate chips in a bag of chocolate chip cookies.

The random variable <em>X</em> is normally distributed with mean, <em>μ </em>= 1263 and a standard deviation, <em>σ </em>= 117.

(a)

Compute the 29th percentile for the number of chocolate chips in a bag as follows:

P (X < x) = 0.29

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The value of <em>z</em> for the above probability is, <em>z</em> = -0.55.

Compute the value of <em>x</em> as follows:

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P (1263 - 117 < X < 1263 + 117) = 0.95

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IQR = 1.349 <em>σ</em>

Compute the inter-quartile range of the number of chocolate chips in a bag of chocolate chip​ cookies as follows:

IQR = 1.349 <em>σ</em>

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Thus, the inter-quartile range of the number of chocolate chips in a bag of chocolate chip​ cookies is 157.83.

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