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maksim [4K]
2 years ago
10

A man 6 feet tall casts a shadow that is 11 feet long. A building casts a shadow of 139 feet long. The building is tall. Round y

our answer to the nearest 10th
Mathematics
1 answer:
dmitriy555 [2]2 years ago
8 0

Given:

Height of man = 6 ft

Height of man's shadow = 11 feet

Height of building's shadow = 139 feet

To find:

The height of the building.

Solution:

We know that the heights of the objects and there shadows are always proportional.

\dfrac{\text{Height of man}}{\text{Height of man's shadow}}=\dfrac{\text{Height of the building}}{\text{Height of building's shadow}}

Let x be the height of the building.

\dfrac{6}{11}=\dfrac{x}{139}

Multiply both sides by 139.

\dfrac{6}{11}\times 139=x

\dfrac{834}{11}=x

75.8181...=x

x\approx 75.8

Therefore, the building is 75.8 feet long.

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Answer:

80 parrots were purchased.

Step-by-step explanation:

Let the total number of parrots be k.

If 20% (or 20/100 = 1/5) flew away and 5% (5/100 = 1/20) died, the remaining parrots will be k – (¹/₅k + ¹/₂₀k) = k – ¼k = ¾k.

Of the remaining, 45% (or 45/100 = 9/20) were sold, which means the total number of sold parrots will be ¾k × ⁹/₂₀ = ²⁷/₈₀k.

The remaining parrots = ¾k – ²⁷/₈₀k = ³³/₈₀k = 33

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Step-by-step explanation:

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If you deposit $12,500 in an account that pays 4.5% interest quarterly, what is the balance after 8 years? How much did the acco
Masja [62]

In order to determine the balance of the account, use the following formula for the amount of money obtained after t years, basen on a compound interest:

A=P(1+\frac{r}{n})^{nt}

where,

P: principal = $12,500

A: amount earnt after t years = ?

r: interest rate in decimal form = 0.045 (4.5%)

n: times at year for the compund interes = 4 (quaterly)

Replace the previous values of the parameters into the formula for A and simplify:

\begin{gathered} A=12,500(1+\frac{0.045}{4})^{4\cdot8} \\ A=12,500(1+0.01125)^{32} \\ A=12,500(1.01125)^{32} \\ A=12,500(1.430451402) \\ A\approx17,880.64 \end{gathered}

Hence, the balance after 8 years is approximately $17,880.64 in the account.

The interest earnt by the account is given by the difference between the previous result and the principal invesment:

I = $17,880.64 - $12,500 = $5,380.64

Hence, the interest earnt is $5,380.64

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