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victus00 [196]
3 years ago
10

A snail moves 1/50 a mile in 5/6 of an hour. If the snail continues at this pace, how far, in miles, does it move in one hour?

Mathematics
1 answer:
MatroZZZ [7]3 years ago
5 0
\dfrac{5}{6} \text { of an hour = }   \dfrac{1}{50}  \text { mile}

--------------------------------------------------------------
Find 1/6 hour :
--------------------------------------------------------------
\dfrac{1}{6} \text { of an hour = }   \dfrac{1}{50} \div 5  \text { mile}

\dfrac{1}{6} \text { of an hour = }   \dfrac{1}{50} \times  \dfrac{1}{5}   \text { mile}

\dfrac{1}{6} \text { of an hour = }   \dfrac{1}{250} \text { mile}

--------------------------------------------------------------
Find 6/6 hour ( 1 hour) :
--------------------------------------------------------------
\dfrac{6}{6} \text { of an hour = }   \dfrac{1}{250} \times 6 \text { mile}

\dfrac{6}{6} \text { of an hour = }   \dfrac{6}{250} \text { mile}

\dfrac{6}{6} \text { of an hour = }   \dfrac{3}{125} \text { mile}

--------------------------------------------------------------
Answer: It moves 3/125 mile in an hour.
--------------------------------------------------------------
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Step-by-step explanation:

Recall that increasing an amount C in x% is equivalent to multiply it by (1+x/100)

As we have 4% APR, the monthly interest would be (4/12)% = 0.04/12

<u>Month 0</u> (first payment)

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Month 1

250 + 250 \frac{0.04}{12}= 250(\frac{12.04}{12})

<u>Month 2</u>

250(1+\frac{12.04}{12}+(\frac{12.04}{12})^2)

<u>Month 3</u>

250(1+\frac{12.04}{12}+(\frac{12.04}{12})^2+(\frac{12.04}{12})^3)

<u>Month 24 (2 years)</u>

250(1+\frac{12.04}{12}+(\frac{12.04}{12})^2+(\frac{12.04}{12})^3+...+(\frac{12.04}{12})^{24})

The sum  

1+\frac{12.04}{12}+(\frac{12.04}{12})^2+(\frac{12.04}{12})^3+...+(\frac{12.04}{12})^{24}

is the sum of the first 24 terms of a geometric sequence with common ratio \frac{12.04}{12} which is

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2 years ago
A factory buys 10% of its components from suppliers B and the rest from supplier C. It is known that 6% of the components it buy
Aleks [24]

Answer:

The percentage of the components bought from supplier C that are faulty = 88%

Complete Question:

A factory buys 10% of its components from supplier A, 30% from supplier B,and the rest from supplier C. it is known that 6% of the components it buys are faulty. of the components bought from supplier A, 9% are faulty and of the components bought from supplier B, 3% are faulty.

find the percentage of the components bought from supplier C that are faulty ?

Step-by-step explanation:

Let x be the total components bought by the factory

Components supplied by A = 10% of x

Components supplied by B = 30% of x

The rest supplied by C:

Percentage supplied by C = 100-(30+10) = 100-40 = 60%

Components supplied by C = 60% of x

% of all faulty components = 6%

Amount of faulty component = 6% of x

faulty components from A= 9%

Amount of faulty component from A= 9% × (6% of x) = 0.0054x

faulty components from B= 3%

Amount of faulty component from A= 3% × (6% of x) = 0.0018x

Amount of faulty component from C = (6% of x) - (0.0054x+0.0018x)

= 0.06x - 0.0072x

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Let the percentage of the components bought from supplier C that are faulty = y%

y% × 6% of x = 0.0528x

y% × 0.06x = 0.0528x

y% = 0.0528x/0.06x

y% = 0.88 = 88%

The percentage of the components bought from supplier C that are faulty = 88%

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3 years ago
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